Ian Jauslin
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authorIan Jauslin <ian.jauslin@roma1.infn.it>2015-06-14 00:52:45 +0000
committerIan Jauslin <ian.jauslin@roma1.infn.it>2015-06-14 00:52:45 +0000
commitaa0f3ae2988d372b190b9bde2e75a6d17e744e93 (patch)
tree14482245c2fca27fcdad3078e97d0871352d52a7 /src
Initial commitv1.2
Diffstat (limited to 'src')
-rw-r--r--src/array.c628
-rw-r--r--src/array.h134
-rw-r--r--src/cli_parser.c123
-rw-r--r--src/cli_parser.h35
-rw-r--r--src/coefficient.c739
-rw-r--r--src/coefficient.h78
-rw-r--r--src/definitions.cpp60
-rw-r--r--src/expansions.c28
-rw-r--r--src/expansions.h34
-rw-r--r--src/fields.c489
-rw-r--r--src/fields.h98
-rw-r--r--src/flow.c167
-rw-r--r--src/flow.h35
-rw-r--r--src/grouped_polynomial.c765
-rw-r--r--src/grouped_polynomial.h74
-rw-r--r--src/idtable.c122
-rw-r--r--src/idtable.h44
-rw-r--r--src/istring.c99
-rw-r--r--src/istring.h40
-rw-r--r--src/kondo.c1449
-rw-r--r--src/kondo.h76
-rw-r--r--src/kondo_preprocess.c126
-rw-r--r--src/mean.c793
-rw-r--r--src/mean.h70
-rw-r--r--src/meankondo.c301
-rw-r--r--src/meantools.c116
-rw-r--r--src/meantools_deriv.c195
-rw-r--r--src/meantools_deriv.h30
-rw-r--r--src/meantools_eval.c129
-rw-r--r--src/meantools_eval.h29
-rw-r--r--src/meantools_exp.c130
-rw-r--r--src/meantools_exp.h27
-rw-r--r--src/number.c551
-rw-r--r--src/number.h120
-rw-r--r--src/numkondo.c226
-rw-r--r--src/parse_file.c796
-rw-r--r--src/parse_file.h56
-rw-r--r--src/polynomial.c1263
-rw-r--r--src/polynomial.h131
-rw-r--r--src/rational.h23
-rw-r--r--src/rational_float.c196
-rw-r--r--src/rational_float.h64
-rw-r--r--src/rational_int.c190
-rw-r--r--src/rational_int.h59
-rw-r--r--src/rcc.c95
-rw-r--r--src/rcc.h39
-rw-r--r--src/tools.c142
-rw-r--r--src/tools.h49
-rw-r--r--src/types.h219
49 files changed, 11482 insertions, 0 deletions
diff --git a/src/array.c b/src/array.c
new file mode 100644
index 0000000..11d14f7
--- /dev/null
+++ b/src/array.c
@@ -0,0 +1,628 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "array.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdarg.h>
+#include "istring.h"
+#include "definitions.cpp"
+
+// init
+int init_Int_Array(Int_Array* array, int memory){
+ (*array).values=calloc(memory,sizeof(int));
+ (*array).memory=memory;
+ (*array).length=0;
+ return(0);
+}
+int free_Int_Array(Int_Array array){
+ free(array.values);
+ return(0);
+}
+
+// copy
+int int_array_cpy(Int_Array input, Int_Array* output){
+ init_Int_Array(output,input.length);
+ int_array_cpy_noinit(input,output);
+ return(0);
+}
+int int_array_cpy_noinit(Int_Array input, Int_Array* output){
+ int i;
+ if((*output).memory<input.length){
+ fprintf(stderr,"error: trying to copy an array of length %d to another with memory %d\n",input.length, (*output).memory);
+ exit(-1);
+ }
+ for(i=0;i<input.length;i++){
+ (*output).values[i]=input.values[i];
+ }
+ (*output).length=input.length;
+ return(0);
+}
+
+// resize memory
+int int_array_resize(Int_Array* array, int newsize){
+ Int_Array new_array;
+ init_Int_Array(&new_array, newsize);
+ int_array_cpy_noinit(*array,&new_array);
+ free_Int_Array(*array);
+ *array=new_array;
+ return(0);
+}
+
+// add a value
+int int_array_append(int val, Int_Array* output){
+ if((*output).length>=(*output).memory){
+ int_array_resize(output,2*(*output).memory+1);
+ }
+ (*output).values[(*output).length]=val;
+ (*output).length++;
+ return(0);
+}
+
+// concatenate
+int int_array_concat(Int_Array input, Int_Array* output){
+ int i;
+ int offset=(*output).length;
+ if((*output).length+input.length>(*output).memory){
+ // make it longer than needed by (*output).length (for speed)
+ int_array_resize(output,2*(*output).length+input.length);
+ }
+ for(i=0;i<input.length;i++){
+ (*output).values[offset+i]=input.values[i];
+ }
+ (*output).length=offset+input.length;
+ return(0);
+}
+
+// find (does not assume the array is sorted)
+int int_array_find(int val, Int_Array array){
+ int i;
+ for(i=0;i<array.length;i++){
+ if(array.values[i]==val){
+ return(i);
+ }
+ }
+ return(-1);
+}
+int int_array_find_err(int val, Int_Array array){
+ int i;
+ for(i=0;i<array.length;i++){
+ if(array.values[i]==val){
+ return(i);
+ }
+ }
+ fprintf(stderr,"error: value %d not found in array\n",val);
+ exit(-1);
+}
+
+// sort
+int int_array_sort(Int_Array array, int begin, int end){
+ int i;
+ int tmp;
+ int index;
+ // the pivot: middle of the array
+ int pivot=(begin+end)/2;
+ // if the array is non trivial
+ if(begin<end){
+ // send pivot to the end
+ tmp=array.values[pivot];
+ array.values[pivot]=array.values[end];
+ array.values[end]=tmp;
+
+ // loop over the others
+ for(i=begin, index=begin;i<end;i++){
+ // compare with pivot
+ if(array.values[i]<array.values[end]){
+ // if smaller, exchange with reference index
+ tmp=array.values[index];
+ array.values[index]=array.values[i];
+ array.values[i]=tmp;
+ // move reference index
+ index++;
+ }
+ }
+ // put pivot (which we had sent to the end) in the right place
+ tmp=array.values[end];
+ array.values[end]=array.values[index];
+ array.values[index]=tmp;
+
+ // recurse
+ int_array_sort(array, begin, index-1);
+ int_array_sort(array, index+1, end);
+ }
+ return(0);
+}
+
+// compare Int_Array's
+int int_array_cmp(Int_Array array1, Int_Array array2){
+ int i;
+
+ // compare lengths
+ if(array1.length<array2.length){
+ return(-1);
+ }
+ if(array1.length>array2.length){
+ return(1);
+ }
+
+ // compare terms
+ for(i=0;i<array1.length;i++){
+ if(array1.values[i]<array2.values[i]){
+ return(-1);
+ }
+ if(array1.values[i]>array2.values[i]){
+ return(1);
+ }
+ }
+
+ // if equal
+ return(0);
+}
+
+// check whether an array is a sub-array of another
+// allows for the elements to be separated by others, but the order must be respected
+int int_array_is_subarray_ordered(Int_Array input, Int_Array test_array){
+ int i;
+ int matches=0;
+
+ for(i=0;i<test_array.length && matches<input.length;i++){
+ if(input.values[matches]==test_array.values[i]){
+ matches++;
+ }
+ }
+ if(matches==input.length){
+ return(1);
+ }
+ else{
+ return(0);
+ }
+}
+
+
+// print array
+int int_array_print(Int_Array array){
+ int i;
+ printf("(");
+ for(i=0;i<array.length-1;i++){
+ printf("%d,",array.values[i]);
+ }
+ printf("%d)",array.values[array.length-1]);
+ return(0);
+}
+
+// read array
+int int_array_read(Char_Array str, Int_Array* array){
+ char* buffer=calloc(str.length+1,sizeof(char));
+ char* buffer_ptr=buffer;
+ int i,j;
+ int comment_mode=0;
+
+ // alloc
+ init_Int_Array(array,str.length);
+
+ *buffer_ptr='\0';
+ // loop over the input
+ for(j=0;j<str.length;j++){
+ if(comment_mode==1){
+ if(str.str[j]=='\n'){
+ comment_mode=0;
+ }
+ }
+ else{
+ switch(str.str[j]){
+ // new term
+ case ',':
+ // write
+ sscanf(buffer,"%d",&i);
+ int_array_append(i,array);
+ // reset buffer
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ break;
+
+ // ignore
+ case '(':break;
+ case ')':break;
+ // comments
+ case '#':
+ comment_mode=1;
+ break;
+
+ default:
+ // write to buffer
+ buffer_ptr=str_addchar(buffer_ptr,str.str[j]);
+ break;
+ }
+ }
+ }
+
+ // write
+ sscanf(buffer,"%d",&i);
+ int_array_append(i,array);
+
+ free(buffer);
+ return(0);
+}
+
+
+// ------------------- CharArray ------------------------
+
+// init
+int init_Char_Array(Char_Array* array, int memory){
+ (*array).str=calloc(memory,sizeof(char));
+ (*array).memory=memory;
+ (*array).length=0;
+ return(0);
+}
+int free_Char_Array(Char_Array array){
+ free(array.str);
+ return(0);
+}
+
+// copy
+int char_array_cpy(Char_Array input, Char_Array* output){
+ init_Char_Array(output,input.length+1);
+ char_array_cpy_noinit(input,output);
+ return(0);
+}
+int char_array_cpy_noinit(Char_Array input, Char_Array* output){
+ int i;
+ if((*output).memory<input.length){
+ fprintf(stderr,"error: trying to copy an array of length %d to another with memory %d\n",input.length, (*output).memory);
+ exit(-1);
+ }
+ for(i=0;i<input.length;i++){
+ (*output).str[i]=input.str[i];
+ }
+ (*output).length=input.length;
+ return(0);
+}
+
+// resize memory
+int char_array_resize(Char_Array* array, int newsize){
+ Char_Array new_array;
+ init_Char_Array(&new_array, newsize);
+ char_array_cpy_noinit(*array,&new_array);
+ free_Char_Array(*array);
+ *array=new_array;
+ return(0);
+}
+
+// add a value
+int char_array_append(char val, Char_Array* output){
+ if((*output).length>=(*output).memory){
+ char_array_resize(output,2*(*output).memory+1);
+ }
+ (*output).str[(*output).length]=val;
+ (*output).length++;
+ return(0);
+}
+// append a string
+int char_array_append_str(char* str, Char_Array* output){
+ char* ptr;
+ for (ptr=str;*ptr!='\0';ptr++){
+ char_array_append(*ptr, output);
+ }
+ return(0);
+}
+
+// concatenate
+int char_array_concat(Char_Array input, Char_Array* output){
+ int i;
+ int offset=(*output).length;
+ if((*output).length+input.length>(*output).memory){
+ // make it longer than needed by (*output).length (for speed)
+ char_array_resize(output,2*(*output).length+input.length);
+ }
+ for(i=0;i<input.length;i++){
+ (*output).str[offset+i]=input.str[i];
+ }
+ (*output).length=offset+input.length;
+ return(0);
+}
+
+
+
+// convert to char*
+int char_array_to_str(Char_Array input, char** output){
+ int i;
+ (*output)=calloc(input.length+1,sizeof(char));
+ for(i=0;i<input.length;i++){
+ (*output)[i]=input.str[i];
+ }
+ if((*output)[input.length-1]!='\0'){
+ (*output)[input.length]='\0';
+ }
+ return(0);
+}
+// noinit (changes the size of input if needed)
+char* char_array_to_str_noinit(Char_Array* input){
+ if((*input).str[(*input).length-1]!='\0'){
+ if((*input).length==(*input).memory){
+ char_array_resize(input,(*input).length+1);
+ }
+ // add final '\0'
+ (*input).str[(*input).length]='\0';
+ }
+ return((*input).str);
+}
+
+
+// convert from char*
+int str_to_char_array(char* str, Char_Array* output){
+ char* ptr;
+ init_Char_Array(output, str_len(str));
+ for(ptr=str;*ptr!='\0';ptr++){
+ char_array_append(*ptr,output);
+ }
+ return(0);
+}
+
+
+// format strings
+int char_array_snprintf(Char_Array* output, char* fmt, ...){
+ size_t size=STR_SIZE;
+ unsigned int extra_size;
+ char* out_str=calloc(size,sizeof(char));
+ char* ptr;
+ va_list vaptr;
+
+ // initialize argument list starting after fmt
+ va_start(vaptr, fmt);
+ // print format
+ extra_size=vsnprintf(out_str, size, fmt, vaptr);
+ va_end(vaptr);
+
+ // if too large
+ if(extra_size>size){
+ // resize
+ free(out_str);
+ // +1 for '\0'
+ size=extra_size+1;
+ out_str=calloc(size,sizeof(char));
+ // read format again
+ va_start(vaptr, fmt);
+ vsnprintf(out_str,size,fmt,vaptr);
+ va_end(vaptr);
+ }
+
+ // write to char array
+ for(ptr=out_str;*ptr!='\0';ptr++){
+ char_array_append(*ptr, output);
+ }
+
+ free(out_str);
+
+ return(0);
+}
+
+
+// replace '%' with given character
+int replace_star(char c, Char_Array str, Char_Array* out){
+ int i;
+ init_Char_Array(out, str.length);
+ for(i=0;i<str.length;i++){
+ if(str.str[i]!='%'){
+ char_array_append(str.str[i],out);
+ }
+ else{
+ char_array_append(c,out);
+ }
+ }
+ return(0);
+}
+
+
+// ------------------- Str_Array ------------------------
+
+// init
+int init_Str_Array(Str_Array* array, int memory){
+ (*array).strs=calloc(memory,sizeof(Char_Array));
+ (*array).memory=memory;
+ (*array).length=0;
+ return(0);
+}
+int free_Str_Array(Str_Array array){
+ int i;
+ for(i=0;i<array.length;i++){
+ free_Char_Array(array.strs[i]);
+ }
+ free(array.strs);
+ return(0);
+}
+
+// copy
+int str_array_cpy(Str_Array input, Str_Array* output){
+ init_Str_Array(output,input.length);
+ str_array_cpy_noinit(input,output);
+ return(0);
+}
+int str_array_cpy_noinit(Str_Array input, Str_Array* output){
+ int i;
+ if((*output).memory<input.length){
+ fprintf(stderr,"error: trying to copy an array of length %d to another with memory %d\n",input.length, (*output).memory);
+ exit(-1);
+ }
+ for(i=0;i<input.length;i++){
+ char_array_cpy(input.strs[i],(*output).strs+i);
+ }
+ (*output).length=input.length;
+ return(0);
+}
+
+// resize memory
+int str_array_resize(Str_Array* array, int newsize){
+ Str_Array new_array;
+ init_Str_Array(&new_array, newsize);
+ str_array_cpy_noinit(*array,&new_array);
+ free_Str_Array(*array);
+ *array=new_array;
+ return(0);
+}
+
+// add a value
+int str_array_append(Char_Array val, Str_Array* output){
+ if((*output).length>=(*output).memory){
+ str_array_resize(output,2*(*output).memory+1);
+ }
+ char_array_cpy(val, (*output).strs+(*output).length);
+ (*output).length++;
+ return(0);
+}
+int str_array_append_noinit(Char_Array val, Str_Array* output){
+ if((*output).length>=(*output).memory){
+ str_array_resize(output,2*(*output).memory+1);
+ }
+ (*output).strs[(*output).length]=val;
+ (*output).length++;
+ return(0);
+}
+
+// concatenate
+int str_array_concat(Str_Array input, Str_Array* output){
+ int i;
+ int offset=(*output).length;
+ if((*output).length+input.length>(*output).memory){
+ // make it longer than needed by (*output).length (for speed)
+ str_array_resize(output,2*(*output).length+input.length);
+ }
+ for(i=0;i<input.length;i++){
+ char_array_cpy(input.strs[i],(*output).strs+offset+i);
+ }
+ (*output).length=offset+input.length;
+ return(0);
+}
+int str_array_concat_noinit(Str_Array input, Str_Array* output){
+ int i;
+ int offset=(*output).length;
+ if((*output).length+input.length>(*output).memory){
+ // make it longer than needed by (*output).length (for speed)
+ str_array_resize(output,2*(*output).length+input.length);
+ }
+ for(i=0;i<input.length;i++){
+ (*output).strs[offset+i]=input.strs[i];
+ }
+ (*output).length=offset+input.length;
+
+ // free input arrays
+ free(input.strs);
+ return(0);
+}
+
+
+// ------------------- Labels ------------------------
+
+// allocate memory
+int init_Labels(Labels* labels,int size){
+ (*labels).labels=calloc(size,sizeof(Char_Array));
+ (*labels).indices=calloc(size,sizeof(int));
+ (*labels).length=0;
+ (*labels).memory=size;
+ return(0);
+}
+
+// free memory
+int free_Labels(Labels labels){
+ int i;
+ for(i=0;i<labels.length;i++){
+ free_Char_Array(labels.labels[i]);
+ }
+ free(labels.labels);
+ free(labels.indices);
+
+ return(0);
+}
+
+// resize the memory allocated to a labels table
+int resize_labels(Labels* labels,int new_size){
+ Labels new_labels;
+ int i;
+
+ init_Labels(&new_labels,new_size);
+ for(i=0;i<(*labels).length;i++){
+ new_labels.labels[i]=(*labels).labels[i];
+ new_labels.indices[i]=(*labels).indices[i];
+ }
+ new_labels.length=(*labels).length;
+
+ free((*labels).labels);
+ free((*labels).indices);
+
+ *labels=new_labels;
+ return(0);
+}
+
+// copy a labels table
+int labels_cpy(Labels input, Labels* output){
+ init_Labels(output,input.length);
+ labels_cpy_noinit(input,output);
+ return(0);
+}
+int labels_cpy_noinit(Labels input, Labels* output){
+ int i;
+ if((*output).memory<input.length){
+ fprintf(stderr,"error: trying to copy a labels collection of length %d to another with memory %d\n",input.length,(*output).memory);
+ exit(-1);
+ }
+ for(i=0;i<input.length;i++){
+ char_array_cpy(input.labels[i],(*output).labels+i);
+ (*output).indices[i]=input.indices[i];
+ }
+ (*output).length=input.length;
+
+ return(0);
+}
+
+// append an element to a labels
+int labels_append(Char_Array label, int index, Labels* output){
+ int offset=(*output).length;
+
+ if((*output).length>=(*output).memory){
+ resize_labels(output,2*(*output).memory);
+ }
+
+ // copy and allocate
+ char_array_cpy(label,(*output).labels+offset);
+ (*output).indices[offset]=index;
+ // increment length
+ (*output).length++;
+ return(0);
+}
+// append an element to a labels without allocating memory
+int labels_append_noinit(Char_Array label, int index, Labels* output){
+ int offset=(*output).length;
+
+ if((*output).length>=(*output).memory){
+ resize_labels(output,2*(*output).memory);
+ }
+
+ // copy without allocating
+ (*output).labels[offset]=label;
+ (*output).indices[offset]=index;
+ // increment length
+ (*output).length++;
+ return(0);
+}
+
+// concatenate two labels tables
+int labels_concat(Labels input, Labels* output){
+ int i;
+ for(i=0;i<input.length;i++){
+ labels_append(input.labels[i],input.indices[i],output);
+ }
+ return(0);
+}
+
diff --git a/src/array.h b/src/array.h
new file mode 100644
index 0000000..fb74e67
--- /dev/null
+++ b/src/array.h
@@ -0,0 +1,134 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/* Array structures */
+
+#ifndef ARRAY_H
+#define ARRAY_H
+
+#include "types.h"
+
+// init
+int init_Int_Array(Int_Array* array, int memory);
+int free_Int_Array(Int_Array array);
+
+// copy
+int int_array_cpy(Int_Array input, Int_Array* output);
+int int_array_cpy_noinit(Int_Array input, Int_Array* output);
+
+// resize memory
+int int_array_resize(Int_Array* array, int newsize);
+
+// add a value
+int int_array_append(int val, Int_Array* output);
+// concatenate
+int int_array_concat(Int_Array input, Int_Array* output);
+
+// find (does not assume the array is sorted)
+int int_array_find(int val, Int_Array array);
+int int_array_find_err(int val, Int_Array array);
+
+// sort
+int int_array_sort(Int_Array array, int begin, int end);
+
+// compare Int_Array's
+int int_array_cmp(Int_Array array1, Int_Array array2);
+
+// check whether an array is a sub-array of another
+int int_array_is_subarray_ordered(Int_Array input, Int_Array test_array);
+
+// print array
+int int_array_print(Int_Array array);
+// read array
+int int_array_read(Char_Array str, Int_Array* array);
+
+
+// Char_Array
+
+// init
+int init_Char_Array(Char_Array* array, int memory);
+int free_Char_Array(Char_Array array);
+
+// copy
+int char_array_cpy(Char_Array input, Char_Array* output);
+int char_array_cpy_noinit(Char_Array input, Char_Array* output);
+
+// resize memory
+int char_array_resize(Char_Array* array, int newsize);
+
+// add a value
+int char_array_append(char val, Char_Array* output);
+int char_array_append_str(char* str, Char_Array* output);
+// concatenate
+int char_array_concat(Char_Array input, Char_Array* output);
+
+// convert to char*
+int char_array_to_str(Char_Array input, char** output);
+// noinit (changes the size of input if needed)
+char* char_array_to_str_noinit(Char_Array* input);
+// convert from char*
+int str_to_char_array(char* str, Char_Array* output);
+
+// format strings
+int char_array_snprintf(Char_Array* output, char* fmt, ...);
+
+// replace '*' with given character
+int replace_star(char c, Char_Array str, Char_Array* out);
+
+
+// Str_Array
+
+// init
+int init_Str_Array(Str_Array* array, int memory);
+int free_Str_Array(Str_Array array);
+
+// copy
+int str_array_cpy(Str_Array input, Str_Array* output);
+int str_array_cpy_noinit(Str_Array input, Str_Array* output);
+
+// resize memory
+int str_array_resize(Str_Array* array, int newsize);
+
+// add a value
+int str_array_append(Char_Array val, Str_Array* output);
+int str_array_append_noinit(Char_Array val, Str_Array* output);
+// concatenate
+int str_array_concat(Str_Array input, Str_Array* output);
+int str_array_concat_noinit(Str_Array input, Str_Array* output);
+
+
+// Labels
+
+// allocate memory
+int init_Labels(Labels* labels,int size);
+// free memory
+int free_Labels(Labels labels);
+
+// resize the memory allocated to a labels table
+int resize_labels(Labels* labels,int new_size);
+
+// copy a labels table
+int labels_cpy(Labels input, Labels* output);
+int labels_cpy_noinit(Labels input, Labels* output);
+
+// append an element to a labels table
+int labels_append(Char_Array label, int index, Labels* output);
+int labels_append_noinit(Char_Array label, int index, Labels* output);
+
+// concatenate two labels tables
+int labels_concat(Labels input, Labels* output);
+
+#endif
diff --git a/src/cli_parser.c b/src/cli_parser.c
new file mode 100644
index 0000000..bdca700
--- /dev/null
+++ b/src/cli_parser.c
@@ -0,0 +1,123 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "cli_parser.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include "definitions.cpp"
+#include "array.h"
+
+// read a config file and write the output to str_args
+int read_config_file(Str_Array* str_args, const char* file, int read_from_stdin){
+ FILE* infile;
+ char c;
+ Char_Array buffer;
+
+ // allocate memory
+ init_Str_Array(str_args, ARG_COUNT);
+ init_Char_Array(&buffer, STR_SIZE);
+
+ // read from file
+ if(read_from_stdin==0){
+ infile=fopen(file,"r");
+ if(infile==NULL){
+ fprintf(stderr,"error: can't open file %s\n",file);
+ exit(-1);
+ }
+ }
+ else{
+ infile=stdin;
+ }
+
+ while(1){
+ c=fgetc(infile);
+ // add to str_args
+ if(c=='&'){
+ str_array_append_noinit(buffer,str_args);
+ init_Char_Array(&buffer, STR_SIZE);
+ }
+ else if(c==EOF){
+ str_array_append_noinit(buffer,str_args);
+ break;
+ }
+ else{
+ char_array_append(c,&buffer);
+ }
+ }
+ fclose(infile);
+
+ return(0);
+}
+
+
+// get the title from a string argument
+int get_str_arg_title(Char_Array str_arg, Char_Array* out){
+ int j,k;
+
+ init_Char_Array(out,STR_SIZE);
+
+ // find "#!" at beginning of line
+ for(j=0;j<str_arg.length-2;j++){
+ if(str_arg.str[j]=='#' && str_arg.str[j+1]=='!' && (j==0 || str_arg.str[j-1]=='\n')){
+ break;
+ }
+ }
+ // if no title then error
+ if(j>=str_arg.length-2){
+ fprintf(stderr, "error: an entry in the configuration file does not have a title (which should be preceeded by '#!' at the beginning of a line)\n");
+ exit(-1);
+ }
+
+ // get title until end of line
+ for(k=j+2;k<str_arg.length && str_arg.str[k]!='\n'; k++){
+ char_array_append(str_arg.str[k],out);
+ }
+
+ return(0);
+}
+
+// find a string argument with the specified title
+int find_str_arg(char* title, Str_Array str_args){
+ int i,k;
+ char* ptr;
+ Char_Array buffer;
+
+ for(i=0;i<str_args.length;i++){
+ get_str_arg_title(str_args.strs[i], &buffer);
+ // match title
+ for(k=0, ptr=title; k<buffer.length; k++, ptr++){
+ if(buffer.str[k]!=*ptr){
+ break;
+ }
+ }
+ // if match
+ if(k==buffer.length){
+ free_Char_Array(buffer);
+ break;
+ }
+
+ free_Char_Array(buffer);
+ }
+ // if found
+ if(i<str_args.length){
+ return(i);
+ }
+ else{
+ return(-1);
+ }
+}
+
diff --git a/src/cli_parser.h b/src/cli_parser.h
new file mode 100644
index 0000000..b050e37
--- /dev/null
+++ b/src/cli_parser.h
@@ -0,0 +1,35 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+Parse command-line arguments
+*/
+
+#ifndef CLI_PARSER_H
+#define CLI_PARSER_H
+
+#include "types.h"
+
+// read a config file and write the output to str_args
+int read_config_file(Str_Array* str_args, const char* file, int read_from_stdin);
+
+// get the title from a string argument
+int get_str_arg_title(Char_Array str_arg, Char_Array* out);
+// find a string argument with the specified title
+int find_str_arg(char* title, Str_Array str_args);
+
+
+#endif
diff --git a/src/coefficient.c b/src/coefficient.c
new file mode 100644
index 0000000..c26b668
--- /dev/null
+++ b/src/coefficient.c
@@ -0,0 +1,739 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "coefficient.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include "definitions.cpp"
+#include "rational.h"
+#include "istring.h"
+#include "array.h"
+#include "number.h"
+#include "tools.h"
+
+
+// allocate memory
+int init_Coefficient(Coefficient* coef,int size){
+ (*coef).factors=calloc(size,sizeof(Int_Array));
+ (*coef).nums=calloc(size,sizeof(Number));
+ (*coef).denoms=calloc(size,sizeof(coef_denom));
+ (*coef).length=0;
+ (*coef).memory=size;
+
+ return(0);
+}
+
+// free memory
+int free_Coefficient(Coefficient coef){
+ int i;
+ for(i=0;i<coef.length;i++){
+ free_Int_Array(coef.factors[i]);
+ free_Number(coef.nums[i]);
+ }
+ free(coef.factors);
+ free(coef.nums);
+ free(coef.denoms);
+
+ return(0);
+}
+
+// copy a coefficient
+int coefficient_cpy(Coefficient input, Coefficient* output){
+ init_Coefficient(output,input.length);
+ coefficient_cpy_noinit(input,output);
+ return(0);
+}
+int coefficient_cpy_noinit(Coefficient input, Coefficient* output){
+ int i;
+
+ // if output does not have enough memory allocated to it
+ if(input.length>(*output).memory){
+ resize_Coefficient(output,input.length);
+ }
+
+ for(i=0;i<input.length;i++){
+ int_array_cpy(input.factors[i],(*output).factors+i);
+ number_cpy(input.nums[i],(*output).nums+i);
+ (*output).denoms[i]=input.denoms[i];
+ }
+ (*output).length=input.length;
+ return(0);
+}
+
+
+// resize the memory allocated to a coefficient
+int resize_Coefficient(Coefficient* coefficient,int new_size){
+ Coefficient new_coef;
+ int i;
+
+ init_Coefficient(&new_coef,new_size);
+ for(i=0;i<(*coefficient).length;i++){
+ new_coef.factors[i]=(*coefficient).factors[i];
+ new_coef.nums[i]=(*coefficient).nums[i];
+ new_coef.denoms[i]=(*coefficient).denoms[i];
+ }
+ new_coef.length=(*coefficient).length;
+
+ free((*coefficient).factors);
+ free((*coefficient).nums);
+ free((*coefficient).denoms);
+
+ *coefficient=new_coef;
+ return(0);
+}
+
+
+// append an element to a coefficient
+int coefficient_append(Int_Array factor,Number num, coef_denom denom, Coefficient* output){
+ int offset=(*output).length;
+
+ if((*output).length>=(*output).memory){
+ resize_Coefficient(output,2*(*output).memory+1);
+ }
+ // copy and allocate
+ int_array_cpy(factor,(*output).factors+offset);
+ number_cpy(num,(*output).nums+offset);
+ (*output).denoms[offset]=denom;
+ // increment length
+ (*output).length++;
+ return(0);
+}
+// append an element to a coefficient without allocating memory
+int coefficient_append_noinit(Int_Array factor, Number num, coef_denom denom, Coefficient* output){
+ int offset=(*output).length;
+
+ if((*output).length>=(*output).memory){
+ resize_Coefficient(output,2*(*output).memory+1);
+ }
+ // copy without allocating
+ (*output).factors[offset]=factor;
+ (*output).nums[offset]=num;
+ (*output).denoms[offset]=denom;
+ // increment length
+ (*output).length++;
+ return(0);
+}
+
+// concatenate coefficients and simplify result
+int coefficient_concat(Coefficient input, Coefficient* output){
+ int i;
+ for(i=0;i<input.length;i++){
+ coefficient_append(input.factors[i],input.nums[i],input.denoms[i],output);
+ }
+
+ coefficient_simplify(output);
+ return(0);
+}
+int coefficient_concat_noinit(Coefficient input, Coefficient* output){
+ int i;
+ for(i=0;i<input.length;i++){
+ coefficient_append_noinit(input.factors[i],input.nums[i],input.denoms[i],output);
+ }
+
+ coefficient_simplify(output);
+
+ // free input arrays
+ free(input.factors);
+ free(input.nums);
+ free(input.denoms);
+ return(0);
+}
+
+
+// simplify a Coefficient
+int coefficient_simplify(Coefficient* coefficient){
+ int i;
+ Coefficient output;
+ init_Coefficient(&output,(*coefficient).length);
+ // the combination of numerical factors
+ Number new_num;
+ init_Number(&new_num,NUMBER_SIZE);
+
+ // sort the factors in the coefficient
+ for(i=0;i<(*coefficient).length;i++){
+ int_array_sort((*coefficient).factors[i],0,(*coefficient).factors[i].length-1);
+ }
+ // in order to perform a simplification, the list of terms must be
+ // sorted (so that terms that are proportional are next to each other)
+ sort_coefficient(coefficient,0,(*coefficient).length-1);
+
+ for(i=0;i<(*coefficient).length;i++){
+ // if the term actually exists
+ if(number_is_zero((*coefficient).nums[i])!=1){
+ // combine numerical factors
+ number_add_chain((*coefficient).nums[i],&new_num);
+ }
+ // if the number is 0, the previous terms that may have the same factors should still be added, hence the 'if' ends here
+
+ // if the factor is different from the next then add term
+ if(i==(*coefficient).length-1 || (int_array_cmp((*coefficient).factors[i],(*coefficient).factors[i+1])!=0) || coef_denom_cmp((*coefficient).denoms[i],(*coefficient).denoms[i+1])!=0){
+ // check that the coefficient is not trivial
+ if(number_is_zero(new_num)!=1){
+ coefficient_append((*coefficient).factors[i],new_num,(*coefficient).denoms[i],&output);
+ }
+
+ // reset new numerical factor
+ free_Number(new_num);
+ init_Number(&new_num,NUMBER_SIZE);
+ }
+ }
+
+ free_Number(new_num);
+ free_Coefficient(*coefficient);
+ *coefficient=output;
+ return(0);
+}
+
+// sort the terms in an equation (quicksort algorithm)
+int sort_coefficient(Coefficient* coefficient, int begin, int end){
+ int i;
+ int index;
+ // the pivot: middle of the array
+ int pivot=(begin+end)/2;
+ // if the array is non trivial
+ if(begin<end){
+ // send pivot to the end
+ exchange_coefficient_terms(pivot,end,coefficient);
+ // loop over the others
+ for(i=begin, index=begin;i<end;i++){
+ // compare with pivot
+ if(coef_denom_cmp((*coefficient).denoms[i],(*coefficient).denoms[end])<0 || ( coef_denom_cmp((*coefficient).denoms[i],(*coefficient).denoms[end])==0 && (int_array_cmp((*coefficient).factors[i],(*coefficient).factors[end])<0)) ){
+ // if smaller, exchange with reference index
+ exchange_coefficient_terms(i,index,coefficient);
+ // move reference index
+ index++;
+ }
+ }
+ // put pivot (which we had sent to the end) in the right place
+ exchange_coefficient_terms(index,end,coefficient);
+ // recurse
+ sort_coefficient(coefficient, begin, index-1);
+ sort_coefficient(coefficient, index+1, end);
+ }
+ return(0);
+}
+
+// exchange two terms (for the sorting algorithm)
+int exchange_coefficient_terms(int i, int j, Coefficient* coefficient){
+ Int_Array ptmp;
+ Number tmpq;
+ coef_denom tmpc;
+
+ ptmp=(*coefficient).factors[j];
+ (*coefficient).factors[j]=(*coefficient).factors[i];
+ (*coefficient).factors[i]=ptmp;
+
+ tmpq=(*coefficient).nums[j];
+ (*coefficient).nums[j]=(*coefficient).nums[i];
+ (*coefficient).nums[i]=tmpq;
+
+ tmpc=(*coefficient).denoms[j];
+ (*coefficient).denoms[j]=(*coefficient).denoms[i];
+ (*coefficient).denoms[i]=tmpc;
+ return(0);
+}
+
+// derive a coefficient with respect to an index
+int coefficient_deriv_noinit(Coefficient input, int index, Coefficient* output){
+ int i,j;
+ // temp list of indices
+ Int_Array factor;
+ // number of times index was found
+ int match_count;
+ // whether the output contains at least one factor
+ int at_least_one=0;
+ coef_denom denom;
+
+ // loop over monomials
+ for(i=0;i<input.length;i++){
+ init_Int_Array(&factor,input.factors[i].length);
+ // init match count
+ match_count=0;
+ // loop over indices
+ for(j=0;j<input.factors[i].length;j++){
+ // if found
+ if(input.factors[i].values[j]==index){
+ // if it's the first match, don't add it
+ if(match_count!=0){
+ int_array_append(index,&factor);
+ }
+ match_count++;
+ }
+ // add the index
+ else{
+ int_array_append(input.factors[i].values[j],&factor);
+ }
+ }
+
+ denom=input.denoms[i];
+ // if the index is that of 1/C
+ if(index==input.denoms[i].index){
+ // if no C in the numerator (which is normal behavior)
+ if(match_count==0){
+ denom.power++;
+ }
+ match_count-=input.denoms[i].power;
+ }
+
+
+ // if the derivative doesn't vanish, add it to the coefficient
+ if(match_count!=0){
+ at_least_one=1;
+ coefficient_append_noinit(factor,number_Qprod_ret(quot(match_count,1),input.nums[i]), denom, output);
+ }
+ else{
+ free_Int_Array(factor);
+ }
+ }
+
+ if(at_least_one==1){
+ coefficient_simplify(output);
+ }
+ else{
+ // add a trivial element to the coefficient
+ init_Int_Array(&factor,0);
+ denom.index=-1;
+ denom.power=0;
+ coefficient_append_noinit(factor,number_zero(),denom,output);
+ }
+
+ return(0);
+}
+
+int coefficient_deriv(Coefficient input, int index, Coefficient* output){
+ init_Coefficient(output, COEF_SIZE);
+ coefficient_deriv_noinit(input, index, output);
+ return(0);
+}
+
+/*
+// derive a coefficient with respect to an index (as a polynomial) (does not derive the 1/(1+C)^p )
+int coefficient_deriv_noinit(Coefficient input, int index, Coefficient* output){
+ int i;
+ // temp list of indices
+ Int_Array factor;
+ // number of times index was found
+ int match_count;
+ // whether the output contains at least one factor
+ int at_least_one=0;
+ coef_denom denom;
+
+ // loop over monomials
+ for(i=0;i<input.length;i++){
+ // derivative of monomial
+ monomial_deriv(input.factors[i], index, &factor, &match_count);
+
+ // if the derivative doesn't vanish, add it to the coefficient
+ if(match_count>0){
+ at_least_one=1;
+ coefficient_append_noinit(factor,number_Qprod_ret(quot(match_count,1),input.nums[i]), input.denoms[i],output);
+ }
+ else{
+ free_Int_Array(factor);
+ }
+ }
+
+ if(at_least_one>0){
+ coefficient_simplify(output);
+ }
+ else{
+ // add a trivial element to the coefficient
+ init_Int_Array(&factor,0);
+ denom.index=-1;
+ denom.power=0;
+ coefficient_append_noinit(factor,number_zero(),denom,output);
+ }
+
+ return(0);
+}
+
+// derive a monomial with respect to an index
+int monomial_deriv(Int_Array factor, int index, Int_Array* out_factor, int* match_count){
+ int j;
+
+ init_Int_Array(out_factor,factor.length);
+ // init match count
+ *match_count=0;
+
+ // loop over indices
+ for(j=0;j<factor.length;j++){
+ // if found
+ if(factor.values[j]==index){
+ // if it's the first match, don't add it
+ if(*match_count!=0){
+ int_array_append(index,out_factor);
+ }
+ (*match_count)++;
+ }
+ // add the index
+ else{
+ int_array_append(factor.values[j],out_factor);
+ }
+ }
+
+ return(0);
+}
+*/
+
+
+
+// product of two coefficients
+int coefficient_prod(Coefficient coef1, Coefficient coef2, Coefficient* output){
+ int i,j;
+ // tmp factor
+ Int_Array factor;
+ coef_denom denom;
+
+ // init
+ init_Coefficient(output,COEF_SIZE);
+
+ // loop over coef1
+ for(i=0;i<coef1.length;i++){
+ // loop over coef2
+ for(j=0;j<coef2.length;j++){
+ init_Int_Array(&factor,coef1.factors[i].length+coef2.factors[j].length);
+ int_array_concat(coef1.factors[i],&factor);
+ int_array_concat(coef2.factors[j],&factor);
+
+ // don't throw an error if the power is 0
+ if(coef2.denoms[i].power==0){
+ coef2.denoms[i].index=coef1.denoms[i].index;
+ }
+ else if(coef1.denoms[i].power==0){
+ coef1.denoms[i].index=coef2.denoms[i].index;
+ }
+ if(coef1.denoms[i].index!=coef2.denoms[j].index){
+ fprintf(stderr,"error: cannot multiply flow equations with different constants\n");
+ exit(-1);
+ }
+ denom=coef1.denoms[i];
+ denom.power+=coef2.denoms[j].power;
+ coefficient_append_noinit(factor,number_prod_ret(coef1.nums[i],coef2.nums[j]), denom, output);
+ }
+ }
+
+ // simplify output
+ coefficient_simplify(output);
+ return(0);
+}
+
+// product of coefficients, output replaces the second coefficient
+int coefficient_prod_chain(Coefficient in, Coefficient* inout){
+ Coefficient tmp_coef;
+ coefficient_prod(in,*inout,&tmp_coef);
+ free_Coefficient(*inout);
+ *inout=tmp_coef;
+ return(0);
+}
+
+
+// print coefficient
+// offset specifies the amount of blank space to the left of the terms after the first
+// prepend indices by ind_pre
+int coefficient_sprint(Coefficient coef, Char_Array* output, int offset, char index_pre){
+ Char_Array buffer;
+ int i,j,k;
+ int dcount;
+
+ if(coef.length==0){
+ char_array_snprintf(output, " (0)\n");
+ }
+
+ for(i=0;i<coef.length;i++){
+ if(i==0){
+ char_array_snprintf(output, " ");
+ }
+ else{
+ for(j=0;j<=offset;j++){
+ char_array_append(' ',output);
+ }
+ char_array_append('+',output);
+ }
+
+ // print numerical coefficient
+ char_array_append('(',output);
+ init_Char_Array(&buffer, STR_SIZE);
+ number_sprint(coef.nums[i], &buffer);
+ char_array_concat(buffer, output);
+ free_Char_Array(buffer);
+ char_array_append(')',output);
+
+ // print factors
+ for(j=0;j<coef.factors[i].length;j++){
+ // constant indices
+ if(coef.factors[i].values[j]<0){
+ // count derivatives
+ dcount=-coef.factors[i].values[j]/DOFFSET;
+ char_array_append('[',output);
+ for(k=0;k<dcount;k++){
+ char_array_append('d',output);
+ }
+ char_array_snprintf(output,"C%d]",-coef.factors[i].values[j]-dcount*DOFFSET);
+ }
+ else{
+ // count derivatives
+ dcount=coef.factors[i].values[j]/DOFFSET;
+ char_array_append('[',output);
+ for(k=0;k<dcount;k++){
+ char_array_append('d',output);
+ }
+ char_array_snprintf(output,"%c%d]",index_pre,coef.factors[i].values[j]-dcount*DOFFSET);
+ }
+ }
+
+ // print constant denominators
+ if(coef.denoms[i].power!=0){
+ char_array_snprintf(output,"[/C%d^%d]",-coef.denoms[i].index,coef.denoms[i].power);
+ }
+
+ char_array_append('\n',output);
+ }
+
+ return(0);
+}
+
+
+// read from a string
+#define PP_NULL_MODE 0
+#define PP_BRACKET_MODE 1
+#define PP_INDICES_MODE 2
+#define PP_POWER_MODE 3
+#define PP_COMMENT_MODE 4
+#define PP_NUMBER_MODE 5
+#define PP_CONSTANT_MODE 6
+#define PP_CONSTANT_DENOM_MODE 7
+int char_array_to_Coefficient(Char_Array str_coef, Coefficient* output){
+ // buffer
+ char* buffer=calloc(str_coef.length+1,sizeof(char));
+ char* buffer_ptr=buffer;
+ Int_Array indices;
+ coef_denom denom;
+ Number num, tmp1_num;
+ int mode;
+ int i,j;
+ int parenthesis_count=0;
+ int dcount=0;
+
+ // allocate memory
+ init_Coefficient(output,COEF_SIZE);
+
+ // init
+ init_Int_Array(&indices, MONOMIAL_SIZE);
+ num=number_one();
+ denom.index=-1;
+ denom.power=0;
+
+ *buffer_ptr='\0';
+ // loop over the input polynomial
+ // start in null mode
+ mode=PP_NULL_MODE;
+ for(j=0;j<str_coef.length;j++){
+ if(mode==PP_COMMENT_MODE){
+ if(str_coef.str[j]=='\n'){
+ mode=PP_NULL_MODE;
+ }
+ }
+ else{
+ switch(str_coef.str[j]){
+ // new indices
+ case '+':
+ if(mode==PP_NULL_MODE){
+ coefficient_append_noinit(indices, num, denom, output);
+ // reset indices, num
+ init_Int_Array(&indices, MONOMIAL_SIZE);
+ num=number_one();
+ denom.index=-1;
+ denom.power=0;
+ }
+ break;
+
+ // enter indices or power mode
+ case '[':
+ if(mode==PP_NULL_MODE){
+ mode=PP_BRACKET_MODE;
+ // reset derivatives count
+ dcount=0;
+ }
+ break;
+ // indices mode
+ case '%':
+ if(mode==PP_BRACKET_MODE){
+ mode=PP_INDICES_MODE;
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ break;
+ case 'C':
+ if(mode==PP_BRACKET_MODE){
+ mode=PP_CONSTANT_MODE;
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ break;
+ case '/':
+ if(mode==PP_BRACKET_MODE){
+ mode=PP_CONSTANT_DENOM_MODE;
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ else if(mode!=PP_NULL_MODE){
+ // write to buffer
+ buffer_ptr=str_addchar(buffer_ptr,str_coef.str[j]);
+ }
+ break;
+ // derivatives
+ case 'd':
+ if(mode==PP_BRACKET_MODE || mode==PP_INDICES_MODE || mode==PP_CONSTANT_MODE){
+ dcount++;
+ }
+ break;
+ // power mode
+ case '^':
+ if(mode==PP_CONSTANT_DENOM_MODE){
+ sscanf(buffer,"%d",&i);
+ denom.index=-i;
+ mode=PP_POWER_MODE;
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ else{
+ buffer_ptr=str_addchar(buffer_ptr,str_coef.str[j]);
+ }
+ break;
+ // read indices or power
+ case ']':
+ sscanf(buffer,"%d",&i);
+ if(mode==PP_INDICES_MODE){
+ int_array_append(i+dcount*DOFFSET,&indices);
+ }
+ else if(mode==PP_CONSTANT_MODE){
+ int_array_append(-i-dcount*DOFFSET,&indices);
+ }
+ else if(mode==PP_POWER_MODE){
+ denom.power=i;
+ }
+ // switch back to null mode
+ mode=PP_NULL_MODE;
+ break;
+
+ // numerical pre-factor
+ case '(':
+ if(mode==PP_NULL_MODE){
+ mode=PP_NUMBER_MODE;
+ parenthesis_count=0;
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ else if(mode==PP_NUMBER_MODE){
+ // match parentheses
+ parenthesis_count++;
+ buffer_ptr=str_addchar(buffer_ptr,str_coef.str[j]);
+ }
+ break;
+ case ')':
+ if(mode==PP_NUMBER_MODE){
+ if(parenthesis_count==0){
+ // write num
+ str_to_Number(buffer,&tmp1_num);
+ number_prod_chain(tmp1_num,&num);
+ free_Number(tmp1_num);
+ // back to null mode
+ mode=PP_NULL_MODE;
+ }
+ else{
+ parenthesis_count--;
+ buffer_ptr=str_addchar(buffer_ptr,str_coef.str[j]);
+ }
+ }
+ break;
+
+ // characters to ignore
+ case ' ':break;
+ case '&':break;
+ case '\n':break;
+
+ // comments
+ case '#':
+ mode=PP_COMMENT_MODE;
+ break;
+
+ default:
+ if(mode!=PP_NULL_MODE){
+ // write to buffer
+ buffer_ptr=str_addchar(buffer_ptr,str_coef.str[j]);
+ }
+ break;
+ }
+ }
+ }
+
+ // last term
+ coefficient_append_noinit(indices, num, denom, output);
+
+ free(buffer);
+ return(0);
+}
+
+int str_to_Coefficient(char* str, Coefficient* output){
+ Char_Array array;
+ array.length=str_len(str);
+ array.str=str;
+ char_array_to_Coefficient(array, output);
+ return(0);
+}
+
+// compare coefficient denominators
+int coef_denom_cmp(coef_denom denom1, coef_denom denom2){
+ if(denom1.index<denom2.index){
+ return(1);
+ }
+ else if(denom1.index>denom2.index){
+ return(-1);
+ }
+
+ if(denom1.power<denom2.power){
+ return(-1);
+ }
+ else if(denom1.power>denom2.power){
+ return(1);
+ }
+
+ return(0);
+}
+
+
+// evaluate a coefficient on a vector
+int evalcoef(RCC rccs, Coefficient coef, long double* out){
+ int i,j;
+ long double num_factor;
+
+ *out=0;
+
+ // for each monomial
+ for(i=0;i<coef.length;i++){
+ // product of factors
+ for(j=0, num_factor=1.;j<coef.factors[i].length;j++){
+ num_factor*=rccs.values[intlist_find_err(rccs.indices,rccs.length,coef.factors[i].values[j])];
+ }
+ // denominator
+ if(coef.denoms[i].power>0){
+ num_factor/=dpower(rccs.values[intlist_find_err(rccs.indices,rccs.length,coef.denoms[i].index)],coef.denoms[i].power);
+ }
+ *out+=num_factor*number_double_val(coef.nums[i]);
+ }
+ return(0);
+}
diff --git a/src/coefficient.h b/src/coefficient.h
new file mode 100644
index 0000000..a7a151c
--- /dev/null
+++ b/src/coefficient.h
@@ -0,0 +1,78 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+Coefficients represent the collection of terms which appear
+ on the right hand side of a single flow equation.
+
+They are used as an elementary building block of grouped polynomials.
+*/
+
+#ifndef COEFFICIENT_H
+#define COEFFICIENT_H
+
+#include "types.h"
+
+// allocate memory
+int init_Coefficient(Coefficient* coef,int size);
+// free memory
+int free_Coefficient(Coefficient coef);
+
+// copy a coefficient
+int coefficient_cpy(Coefficient input, Coefficient* output);
+int coefficient_cpy_noinit(Coefficient input, Coefficient* output);
+
+// resize the memory allocated to a coefficient
+int resize_Coefficient(Coefficient* coefficient,int new_size);
+
+// append an element to a coefficient
+int coefficient_append(Int_Array factor,Number num, coef_denom denom, Coefficient* output);
+int coefficient_append_noinit(Int_Array factor, Number num, coef_denom denom, Coefficient* output);
+
+// concatenate coefficients and simplify result
+int coefficient_concat(Coefficient input, Coefficient* output);
+int coefficient_concat_noinit(Coefficient input, Coefficient* output);
+
+// simplify a Coefficient
+int coefficient_simplify(Coefficient* coefficient);
+// sort the terms in an equation (quicksort algorithm)
+int sort_coefficient(Coefficient* coefficient, int begin, int end);
+// exchange two terms (for the sorting algorithm)
+int exchange_coefficient_terms(int i, int j, Coefficient* coefficient);
+
+// derive a coefficient with respect to an index (as a polynomial) (does not derive the 1/(1+C)^p )
+int coefficient_deriv_noinit(Coefficient input, int index, Coefficient* output);
+int coefficient_deriv(Coefficient input, int index, Coefficient* output);
+
+// product of two coefficients
+int coefficient_prod(Coefficient coef1, Coefficient coef2, Coefficient* output);
+// product of coefficients, output replaces the second coefficient
+int coefficient_prod_chain(Coefficient in, Coefficient* inout);
+
+// print coefficient
+int coefficient_sprint(Coefficient coef, Char_Array* output, int offset, char index_pre);
+
+// read from a string
+int char_array_to_Coefficient(Char_Array str_coef, Coefficient* output);
+int str_to_Coefficient(char* str, Coefficient* output);
+
+// compare coefficient denominators
+int coef_denom_cmp(coef_denom denom1, coef_denom denom2);
+
+// evaluate a coefficient on a vector
+int evalcoef(RCC rccs, Coefficient coef, long double* out);
+
+#endif
diff --git a/src/definitions.cpp b/src/definitions.cpp
new file mode 100644
index 0000000..d32537d
--- /dev/null
+++ b/src/definitions.cpp
@@ -0,0 +1,60 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#ifndef DEFINITIONS_GCC
+#define DEFINITIONS_GCC
+
+#define VERSION "1.2"
+
+// number of entries in a configuration file
+#define ARG_COUNT 10
+// size of string representing a monomial
+#define MONOMIAL_SIZE 20
+// size of various strings
+#define STR_SIZE 100
+// number of terms in coefficients
+#define COEF_SIZE 100
+// number of terms in polynomials
+#define POLY_SIZE 100
+// number of equations
+#define EQUATION_SIZE 20
+// number of fields
+#define FIELDS_SIZE 50
+// number of elements in numbers
+#define NUMBER_SIZE 5
+// number of elements in a group
+#define GROUP_SIZE 5
+
+
+// display options
+#define DISPLAY_EQUATION 1
+#define DISPLAY_NUMERICAL 2
+#define DISPLAY_EXPLOG 3
+#define DISPLAY_FINAL 4
+
+// available preprocessors
+#define PREPROCESSOR_KONDO 1
+
+// offset derivative indices
+#define DOFFSET 1000000
+
+// types of fields (the order matters)
+#define FIELD_PARAMETER 1
+#define FIELD_EXTERNAL 2
+#define FIELD_INTERNAL 3
+#define FIELD_SYMBOL 4
+
+#endif
diff --git a/src/expansions.c b/src/expansions.c
new file mode 100644
index 0000000..c889829
--- /dev/null
+++ b/src/expansions.c
@@ -0,0 +1,28 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "expansions.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include "definitions.cpp"
+#include "tools.h"
+#include "array.h"
+#include "polynomial.h"
+#include "number.h"
+#include "rational.h"
+
+
diff --git a/src/expansions.h b/src/expansions.h
new file mode 100644
index 0000000..85d6c2b
--- /dev/null
+++ b/src/expansions.h
@@ -0,0 +1,34 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+Compute exp(V) and log(1+W)
+*/
+
+#ifndef EXPANSIONS_H
+#define EXPANSIONS_H
+
+#include "polynomial.h"
+#include "fields.h"
+
+// exp(V)
+int expand_exponential(Polynomial input_polynomial,Polynomial* output, Fields_Table fields);
+
+// log(1+W)
+int expand_logarithm(Polynomial input_polynomial, Polynomial* output, Fields_Table fields);
+
+
+#endif
diff --git a/src/fields.c b/src/fields.c
new file mode 100644
index 0000000..1b221f2
--- /dev/null
+++ b/src/fields.c
@@ -0,0 +1,489 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "fields.h"
+#include "definitions.cpp"
+#include <stdio.h>
+#include <stdlib.h>
+#include "number.h"
+#include "tools.h"
+#include "polynomial.h"
+#include "array.h"
+#include "rational.h"
+
+// init and free for Fields_Table
+int init_Fields_Table(Fields_Table* fields){
+ init_Int_Array(&((*fields).parameter),FIELDS_SIZE);
+ init_Int_Array(&((*fields).external),FIELDS_SIZE);
+ init_Int_Array(&((*fields).internal),FIELDS_SIZE);
+ init_Identities(&((*fields).ids), FIELDS_SIZE);
+ init_Symbols(&((*fields).symbols), FIELDS_SIZE);
+ init_Int_Array(&((*fields).fermions),FIELDS_SIZE);
+ return(0);
+}
+int free_Fields_Table(Fields_Table fields){
+ free_Int_Array(fields.parameter);
+ free_Int_Array(fields.external);
+ free_Int_Array(fields.internal);
+ free_Identities(fields.ids);
+ free_Symbols(fields.symbols);
+ free_Int_Array(fields.fermions);
+ return(0);
+}
+
+// determine field type
+int field_type(int index, Fields_Table fields){
+ if(int_array_find(abs(index), fields.parameter)>=0){
+ return(FIELD_PARAMETER);
+ }
+ else if(int_array_find(abs(index), fields.external)>=0){
+ return(FIELD_EXTERNAL);
+ }
+ else if(int_array_find(abs(index), fields.internal)>=0){
+ return(FIELD_INTERNAL);
+ }
+ else if(intlist_find(fields.symbols.indices, fields.symbols.length, index)>=0){
+ return(FIELD_SYMBOL);
+ }
+
+ fprintf(stderr,"error: index %d is neither a parameter nor an external or an internal field, nor a symbol\n",index);
+ exit(-1);
+}
+
+// check whether a field anticommutes
+int is_fermion(int index, Fields_Table fields){
+ if(int_array_find(abs(index), fields.fermions)>=0){
+ return(1);
+ }
+ else{
+ return(0);
+ }
+}
+
+
+// ------------------ Identities --------------------
+
+// allocate memory
+int init_Identities(Identities* identities,int size){
+ (*identities).lhs=calloc(size,sizeof(Int_Array));
+ (*identities).rhs=calloc(size,sizeof(Polynomial));
+ (*identities).length=0;
+ (*identities).memory=size;
+ return(0);
+}
+
+// free memory
+int free_Identities(Identities identities){
+ int i;
+ for(i=0;i<identities.length;i++){
+ free_Int_Array(identities.lhs[i]);
+ free_Polynomial(identities.rhs[i]);
+ }
+ free(identities.lhs);
+ free(identities.rhs);
+ return(0);
+}
+
+// resize
+int resize_identities(Identities* identities,int new_size){
+ Identities new_identities;
+ int i;
+
+ init_Identities(&new_identities,new_size);
+ for(i=0;i<(*identities).length;i++){
+ new_identities.lhs[i]=(*identities).lhs[i];
+ new_identities.rhs[i]=(*identities).rhs[i];
+ }
+ new_identities.length=(*identities).length;
+
+ free((*identities).lhs);
+ free((*identities).rhs);
+
+ *identities=new_identities;
+ return(0);
+}
+
+// copy
+int identities_cpy(Identities input, Identities* output){
+ init_Identities(output,input.length);
+ identities_cpy_noinit(input,output);
+ return(0);
+}
+int identities_cpy_noinit(Identities input, Identities* output){
+ int i;
+ if((*output).memory<input.length){
+ fprintf(stderr,"error: trying to copy an identities collection of length %d to another with memory %d\n",input.length,(*output).memory);
+ exit(-1);
+ }
+ for(i=0;i<input.length;i++){
+ int_array_cpy(input.lhs[i],(*output).lhs+i);
+ polynomial_cpy(input.rhs[i],(*output).rhs+i);
+ }
+ (*output).length=input.length;
+
+ return(0);
+}
+
+// append an element to a identities
+int identities_append(Int_Array lhs, Polynomial rhs, Identities* output){
+ int offset=(*output).length;
+
+ if((*output).length>=(*output).memory){
+ resize_identities(output,2*(*output).memory+1);
+ }
+
+ // copy and allocate
+ int_array_cpy(lhs,(*output).lhs+offset);
+ polynomial_cpy(rhs,(*output).rhs+offset);
+ // increment length
+ (*output).length++;
+ return(0);
+}
+// append an element to a identities without allocating memory
+int identities_append_noinit(Int_Array lhs, Polynomial rhs, Identities* output){
+ int offset=(*output).length;
+
+ if((*output).length>=(*output).memory){
+ resize_identities(output,2*(*output).memory+1);
+ }
+
+ // copy without allocating
+ (*output).lhs[offset]=lhs;
+ (*output).rhs[offset]=rhs;
+ // increment length
+ (*output).length++;
+ return(0);
+}
+
+// concatenate two identitiess
+int identities_concat(Identities input, Identities* output){
+ int i;
+ for(i=0;i<input.length;i++){
+ identities_append(input.lhs[i],input.rhs[i],output);
+ }
+ return(0);
+}
+
+
+// resolve the identities
+// requires both the monomials in polynomial and the ids in fields to be sorted
+int resolve_ids(Polynomial* polynomial, Fields_Table fields){
+ int i,j,k,l;
+ int sign;
+ int fermion_count;
+ int at_least_one;
+ int security;
+ Int_Array monomial;
+ Number num;
+ Number tmp_num;
+
+ // loop over monomials
+ for(i=0;i<(*polynomial).length;i++){
+ at_least_one=1;
+ security=0;
+ // repeat the simplification until the monomial is fully simplified
+ while(at_least_one>0){
+ at_least_one=0;
+
+ // prevent infinite loops
+ security++;
+ if(security>1000000){
+ fprintf(stderr,"error: 1000000 iterations reached when trying to simplify a monomial\n");
+ exit(-1);
+ }
+
+ // loop over ids
+ for(j=0;j<fields.ids.length;j++){
+ // check whether the monomial matches the id
+ if(int_array_is_subarray_ordered(fields.ids.lhs[j],(*polynomial).monomials[i])==1){
+ init_Int_Array(&monomial, (*polynomial).monomials[i].length);
+
+ // remove lhs from monomial
+ // sign from moving the fields out of the monomial
+ sign=1;
+ // number of Fermions to remove from the monomial
+ fermion_count=0;
+ for(k=0,l=0;k<(*polynomial).monomials[i].length;k++){
+ // check whether the field is identical to the "current" one in the id
+ // if l is too large, then keep the field
+ if(l>=fields.ids.lhs[j].length || (*polynomial).monomials[i].values[k]!=fields.ids.lhs[j].values[l]){
+ int_array_append((*polynomial).monomials[i].values[k],&monomial);
+ // sign correction
+ if(fermion_count % 2 ==1 && is_fermion((*polynomial).monomials[i].values[k], fields)){
+ sign*=-1;
+ }
+ }
+ else{
+ // increment fermion_count
+ if(is_fermion(fields.ids.lhs[j].values[l],fields)){
+ fermion_count++;
+ }
+ // increment "current" field in the id
+ l++;
+ }
+ }
+
+ num=number_Qprod_ret(quot(sign,1),(*polynomial).nums[i]);
+ // add extra monomials (if there are more than 1)
+ for(k=1;k<fields.ids.rhs[j].length;k++){
+ number_prod(num, fields.ids.rhs[j].nums[k], &tmp_num);
+ polynomial_append(monomial, (*polynomial).factors[i], tmp_num, polynomial);
+ free_Number(tmp_num);
+ int_array_concat(fields.ids.rhs[j].monomials[k],(*polynomial).monomials+(*polynomial).length-1);
+ // re-sort monomial
+ sign=1;
+ monomial_sort((*polynomial).monomials[(*polynomial).length-1],0,(*polynomial).monomials[(*polynomial).length-1].length-1,fields,&sign);
+ number_Qprod_chain(quot(sign,1),(*polynomial).nums+(*polynomial).length-1);
+ }
+ // correct i-th monomial
+ free_Number((*polynomial).nums[i]);
+ (*polynomial).nums[i]=number_prod_ret(num,fields.ids.rhs[j].nums[0]);
+ free_Int_Array((*polynomial).monomials[i]);
+ (*polynomial).monomials[i]=monomial;
+ int_array_concat(fields.ids.rhs[j].monomials[0],(*polynomial).monomials+i);
+ // re-sort monomial
+ sign=1;
+ monomial_sort((*polynomial).monomials[i],0,(*polynomial).monomials[i].length-1,fields,&sign);
+ number_Qprod_chain(quot(sign,1),(*polynomial).nums+i);
+
+ // free num
+ free_Number(num);
+
+ // repeat the step (in order to perform all of the replacements if several are necessary)
+ j--;
+ if(at_least_one==0){
+ at_least_one=1;
+ }
+ }
+ }
+ }
+ }
+
+ return(0);
+}
+
+
+// ------------------ Symbols --------------------
+
+// allocate memory
+int init_Symbols(Symbols* symbols,int size){
+ (*symbols).indices=calloc(size,sizeof(int));
+ (*symbols).expr=calloc(size,sizeof(Polynomial));
+ (*symbols).length=0;
+ (*symbols).memory=size;
+ return(0);
+}
+
+// free memory
+int free_Symbols(Symbols symbols){
+ int i;
+ for(i=0;i<symbols.length;i++){
+ free_Polynomial(symbols.expr[i]);
+ }
+ free(symbols.indices);
+ free(symbols.expr);
+ return(0);
+}
+
+// resize
+int resize_symbols(Symbols* symbols,int new_size){
+ Symbols new_symbols;
+ int i;
+
+ init_Symbols(&new_symbols,new_size);
+ for(i=0;i<(*symbols).length;i++){
+ new_symbols.indices[i]=(*symbols).indices[i];
+ new_symbols.expr[i]=(*symbols).expr[i];
+ }
+ new_symbols.length=(*symbols).length;
+
+ free((*symbols).indices);
+ free((*symbols).expr);
+
+ *symbols=new_symbols;
+ return(0);
+}
+
+// copy
+int symbols_cpy(Symbols input, Symbols* output){
+ init_Symbols(output,input.length);
+ symbols_cpy_noinit(input,output);
+ return(0);
+}
+int symbols_cpy_noinit(Symbols input, Symbols* output){
+ int i;
+ if((*output).memory<input.length){
+ fprintf(stderr,"error: trying to copy a symbols collection of length %d to another with memory %d\n",input.length,(*output).memory);
+ exit(-1);
+ }
+ for(i=0;i<input.length;i++){
+ (*output).indices[i]=input.indices[i];
+ polynomial_cpy(input.expr[i],(*output).expr+i);
+ }
+ (*output).length=input.length;
+
+ return(0);
+}
+
+// append an element to a symbols
+int symbols_append(int index, Polynomial expr, Symbols* output){
+ int offset=(*output).length;
+
+ if((*output).length>=(*output).memory){
+ resize_symbols(output,2*(*output).memory+1);
+ }
+
+ // copy and allocate
+ (*output).indices[offset]=index;
+ polynomial_cpy(expr,(*output).expr+offset);
+ // increment length
+ (*output).length++;
+ return(0);
+}
+// append an element to a symbols without allocating memory
+int symbols_append_noinit(int index, Polynomial expr, Symbols* output){
+ int offset=(*output).length;
+
+ if((*output).length>=(*output).memory){
+ resize_symbols(output,2*(*output).memory+1);
+ }
+
+ // copy without allocating
+ (*output).indices[offset]=index;
+ (*output).expr[offset]=expr;
+ // increment length
+ (*output).length++;
+ return(0);
+}
+
+// concatenate two symbolss
+int symbols_concat(Symbols input, Symbols* output){
+ int i;
+ for(i=0;i<input.length;i++){
+ symbols_append(input.indices[i],input.expr[i],output);
+ }
+ return(0);
+}
+
+
+
+// ------------------ Groups --------------------
+
+// allocate memory
+int init_Groups(Groups* groups,int size){
+ (*groups).indices=calloc(size,sizeof(Int_Array));
+ (*groups).length=0;
+ (*groups).memory=size;
+ return(0);
+}
+
+// free memory
+int free_Groups(Groups groups){
+ int i;
+ for(i=0;i<groups.length;i++){
+ free_Int_Array(groups.indices[i]);
+ }
+ free(groups.indices);
+ return(0);
+}
+
+// resize
+int resize_groups(Groups* groups,int new_size){
+ Groups new_groups;
+ int i;
+
+ init_Groups(&new_groups,new_size);
+ for(i=0;i<(*groups).length;i++){
+ new_groups.indices[i]=(*groups).indices[i];
+ }
+ new_groups.length=(*groups).length;
+
+ free((*groups).indices);
+
+ *groups=new_groups;
+ return(0);
+}
+
+// copy
+int groups_cpy(Groups input, Groups* output){
+ init_Groups(output,input.length);
+ groups_cpy_noinit(input,output);
+ return(0);
+}
+int groups_cpy_noinit(Groups input, Groups* output){
+ int i;
+ if((*output).memory<input.length){
+ fprintf(stderr,"error: trying to copy a groups collection of length %d to another with memory %d\n",input.length,(*output).memory);
+ exit(-1);
+ }
+ for(i=0;i<input.length;i++){
+ int_array_cpy(input.indices[i],(*output).indices+i);
+ }
+ (*output).length=input.length;
+
+ return(0);
+}
+
+// append an element to a groups
+int groups_append(Int_Array indices, Groups* output){
+ int offset=(*output).length;
+
+ if((*output).length>=(*output).memory){
+ resize_groups(output,2*(*output).memory+1);
+ }
+
+ // copy and allocate
+ int_array_cpy(indices,(*output).indices+offset);
+ // increment length
+ (*output).length++;
+ return(0);
+}
+// append an element to a groups without allocating memory
+int groups_append_noinit(Int_Array indices, Groups* output){
+ int offset=(*output).length;
+
+ if((*output).length>=(*output).memory){
+ resize_groups(output,2*(*output).memory+1);
+ }
+
+ // copy without allocating
+ (*output).indices[offset]=indices;
+ // increment length
+ (*output).length++;
+ return(0);
+}
+
+// concatenate two groupss
+int groups_concat(Groups input, Groups* output){
+ int i;
+ for(i=0;i<input.length;i++){
+ groups_append(input.indices[i],output);
+ }
+ return(0);
+}
+
+// find which group an index belongs to
+int find_group(int index, Groups groups){
+ int i,j;
+ for(i=0;i<groups.length;i++){
+ for(j=0;j<groups.indices[i].length;j++){
+ if(groups.indices[i].values[j]==index){
+ return(i);
+ }
+ }
+ }
+ return(-1);
+}
diff --git a/src/fields.h b/src/fields.h
new file mode 100644
index 0000000..3795d92
--- /dev/null
+++ b/src/fields.h
@@ -0,0 +1,98 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/* declaring fields */
+
+#ifndef FIELDS_H
+#define FIELDS_H
+
+#include "types.h"
+
+// init
+int init_Fields_Table(Fields_Table* fields);
+int free_Fields_Table(Fields_Table fields);
+
+// determine field type
+int field_type(int index, Fields_Table fields);
+// check whether a field anticommutes
+int is_fermion(int index, Fields_Table fields);
+
+
+// init
+int init_Identities(Identities* identities,int size);
+int free_Identities(Identities identities);
+
+// resize
+int resize_identities(Identities* identities,int new_size);
+
+// copy
+int identities_cpy(Identities input, Identities* output);
+int identities_cpy_noinit(Identities input, Identities* output);
+
+// append an element to a identities
+int identities_append(Int_Array lhs, Polynomial rhs, Identities* output);
+int identities_append_noinit(Int_Array lhs, Polynomial rhs, Identities* output);
+
+// concatenate two identitiess
+int identities_concat(Identities input, Identities* output);
+
+// resolve the identities
+int resolve_ids(Polynomial* polynomial, Fields_Table fields);
+
+
+// init
+int init_Symbols(Symbols* symbols,int size);
+int free_Symbols(Symbols symbols);
+
+// resize
+int resize_symbols(Symbols* symbols,int new_size);
+
+// copy
+int symbols_cpy(Symbols input, Symbols* output);
+int symbols_cpy_noinit(Symbols input, Symbols* output);
+
+// append an element to a symbols
+int symbols_append(int index, Polynomial expr, Symbols* output);
+int symbols_append_noinit(int index, Polynomial expr, Symbols* output);
+
+// concatenate two symbolss
+int symbols_concat(Symbols input, Symbols* output);
+
+
+// init
+int init_Groups(Groups* groups,int size);
+int free_Groups(Groups groups);
+
+// resize
+int resize_groups(Groups* groups,int new_size);
+
+// copy
+int groups_cpy(Groups input, Groups* output);
+int groups_cpy_noinit(Groups input, Groups* output);
+
+// append an element to a groups
+int groups_append(Int_Array indices, Groups* output);
+int groups_append_noinit(Int_Array indices, Groups* output);
+
+// concatenate two groupss
+int groups_concat(Groups input, Groups* output);
+
+// find which group an index belongs to
+int find_group(int index, Groups groups);
+
+
+#define FIELDS_H_DONE
+#endif
diff --git a/src/flow.c b/src/flow.c
new file mode 100644
index 0000000..d271e44
--- /dev/null
+++ b/src/flow.c
@@ -0,0 +1,167 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "flow.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include "tools.h"
+#include "math.h"
+#include "definitions.cpp"
+#include "number.h"
+#include "array.h"
+#include "coefficient.h"
+
+
+
+// compute flow numerically, no exponentials
+// inputs: flow_equation
+// init, niter, tol (the allowed error at each step), ls (whether to display the results in terms of ls), display_mode (what to print)
+int numerical_flow(Grouped_Polynomial flow_equation, RCC init, Labels labels, int niter, long double tol, int display_mode){
+ // running coupling contants
+ RCC rccs=init;
+ int i,j;
+
+ if(display_mode==DISPLAY_NUMERICAL){
+ // print labels
+ printf("%5s ","n");
+ for(j=0;j<rccs.length;j++){
+ print_label(rccs.indices[j], labels);
+ }
+ printf("\n\n");
+
+ // print initial values
+ printf("%5d ",0);
+ for(j=0;j<rccs.length;j++){
+ printf("% 14.7Le ",rccs.values[j]);
+ }
+ printf("\n");
+ }
+
+ for(i=0;i<niter;i++){
+ // compute a single step
+ step_flow(&rccs, flow_equation, tol);
+ // convert ls to alphas
+ if(display_mode==DISPLAY_NUMERICAL){
+ // print the result
+ printf("%5d ",i+1);
+ for(j=0;j<rccs.length;j++){
+ printf("% 14.7Le ",rccs.values[j]);
+ }
+ printf("\n");
+ }
+ }
+
+ if(display_mode==DISPLAY_NUMERICAL){
+ // print labels
+ printf("\n");
+ printf("%5s ","n");
+ for(j=0;j<rccs.length;j++){
+ print_label(rccs.indices[j], labels);
+ }
+ printf("\n\n");
+ }
+
+ if(display_mode==DISPLAY_FINAL){
+ RCC_print(rccs);
+ }
+
+ return(0);
+}
+
+// single step in the flow no exponentials
+// inputs: flow_equation, tol
+// input/outputs: rccs
+int step_flow(RCC* rccs, Grouped_Polynomial flow_equation, long double tol){
+ int i;
+ long double* new_rccs=calloc((*rccs).length,sizeof(long double));
+ Int_Array computed;
+
+ init_Int_Array(&computed, (*rccs).length);
+
+ // initialize vectors to 0
+ for(i=0;i<(*rccs).length;i++){
+ new_rccs[i]=0.;
+ }
+
+ // compute the constants first
+ for(i=0;i<flow_equation.length;i++){
+ if(flow_equation.indices[i]<0){
+ evalcoef(*rccs, flow_equation.coefs[i], new_rccs+i);
+ // if the new rcc is too small, then ignore it
+ if(fabs(new_rccs[i])<tol){
+ new_rccs[i]=0.;
+ }
+ (*rccs).values[i]=new_rccs[i];
+ }
+ }
+
+ // for each equation
+ for(i=0;i<flow_equation.length;i++){
+ if(flow_equation.indices[i]>=0){
+ evalcoef(*rccs, flow_equation.coefs[i], new_rccs+i);
+ // if the new rcc is too small, then ignore it
+ if(fabs(new_rccs[i])<tol){
+ new_rccs[i]=0.;
+ }
+ }
+ }
+
+ // copy results to rccs
+ for(i=0;i<(*rccs).length;i++){
+ (*rccs).values[i]=new_rccs[i];
+ }
+
+ // free memory
+ free_Int_Array(computed);
+ free(new_rccs);
+ return(0);
+}
+
+
+// print the label of an rcc (takes constants and derivatives into account)
+int print_label(int index, Labels labels){
+ int i;
+ int nderivs;
+ int posin_labels;
+ Char_Array label;
+
+ // constant term
+ if(index<0){
+ nderivs=-index/DOFFSET;
+ for (i=0;i<12-nderivs;i++){
+ printf(" ");
+ }
+ for(i=0;i<nderivs;i++){
+ printf("d");
+ }
+ printf("C%d ",-index-nderivs*DOFFSET);
+ }
+ else{
+ nderivs=index/DOFFSET;
+ posin_labels=intlist_find_err(labels.indices, labels.length, index-nderivs*DOFFSET);
+ label=labels.labels[posin_labels];
+ for (i=0;i<14-label.length-nderivs;i++){
+ printf(" ");
+ }
+ for(i=0;i<nderivs;i++){
+ printf("d");
+ }
+ printf("%s ",char_array_to_str_noinit(labels.labels+posin_labels));
+ }
+
+ return(0);
+}
diff --git a/src/flow.h b/src/flow.h
new file mode 100644
index 0000000..baef992
--- /dev/null
+++ b/src/flow.h
@@ -0,0 +1,35 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+Compute flow numerically
+*/
+
+#ifndef NUMERICAL_FLOW_H
+#define NUMERICAL_FLOW_H
+
+
+#include "grouped_polynomial.h"
+#include "rcc.h"
+
+// compute flow
+int numerical_flow(Grouped_Polynomial flow_equation, RCC init, Labels labels, int niter, long double tol, int display_mode);
+// single step
+int step_flow(RCC* rccs, Grouped_Polynomial flow_equation, long double tol);
+
+// print the label of an rcc (takes constants and derivatives into account)
+int print_label(int index, Labels labels);
+#endif
diff --git a/src/grouped_polynomial.c b/src/grouped_polynomial.c
new file mode 100644
index 0000000..b7bea42
--- /dev/null
+++ b/src/grouped_polynomial.c
@@ -0,0 +1,765 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "grouped_polynomial.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include "definitions.cpp"
+#include "rational.h"
+#include "istring.h"
+#include "coefficient.h"
+#include "polynomial.h"
+#include "array.h"
+#include "number.h"
+#include "tools.h"
+
+
+// allocate memory
+int init_Grouped_Polynomial(Grouped_Polynomial* gpolynomial, int size){
+ (*gpolynomial).coefs=calloc(size,sizeof(Coefficient));
+ (*gpolynomial).indices=calloc(size,sizeof(int));
+ (*gpolynomial).length=0;
+ (*gpolynomial).memory=size;
+
+ return(0);
+}
+
+// free memory
+int free_Grouped_Polynomial(Grouped_Polynomial gpolynomial){
+ int i;
+ for(i=0;i<gpolynomial.length;i++){
+ free_Coefficient(gpolynomial.coefs[i]);
+ }
+ free(gpolynomial.coefs);
+ free(gpolynomial.indices);
+
+ return(0);
+}
+
+// resize the memory allocated to a grouped_polynomial
+int resize_grouped_polynomial(Grouped_Polynomial* grouped_polynomial,int new_size){
+ Grouped_Polynomial new_poly;
+ int i;
+
+ init_Grouped_Polynomial(&new_poly,new_size);
+ for(i=0;i<(*grouped_polynomial).length;i++){
+ new_poly.indices[i]=(*grouped_polynomial).indices[i];
+ new_poly.coefs[i]=(*grouped_polynomial).coefs[i];
+ }
+ new_poly.length=(*grouped_polynomial).length;
+
+ free((*grouped_polynomial).indices);
+ free((*grouped_polynomial).coefs);
+
+ *grouped_polynomial=new_poly;
+ return(0);
+}
+
+// copy a grouped_polynomial
+int grouped_polynomial_cpy(Grouped_Polynomial input, Grouped_Polynomial* output){
+ init_Grouped_Polynomial(output,input.length);
+ grouped_polynomial_cpy_noinit(input,output);
+ return(0);
+}
+int grouped_polynomial_cpy_noinit(Grouped_Polynomial input, Grouped_Polynomial* output){
+ int i;
+ if((*output).memory<input.length){
+ fprintf(stderr,"error: trying to copy a grouped polynomial of length %d to another with memory %d\n",input.length,(*output).memory);
+ exit(-1);
+ }
+ for(i=0;i<input.length;i++){
+ (*output).indices[i]=input.indices[i];
+ coefficient_cpy(input.coefs[i], (*output).coefs+i);
+ }
+ (*output).length=input.length;
+
+ return(0);
+}
+
+// append an element to a grouped_polynomial
+int grouped_polynomial_append(int index, Coefficient coef, Grouped_Polynomial* output){
+ int offset=(*output).length;
+
+ if((*output).length>=(*output).memory){
+ resize_grouped_polynomial(output,2*(*output).memory+1);
+ }
+
+ // copy and allocate
+ (*output).indices[offset]=index;
+ coefficient_cpy(coef, (*output).coefs+offset);
+ //increment length
+ (*output).length++;
+
+ return(0);
+}
+// append an element to a grouped_polynomial without allocating memory
+int grouped_polynomial_append_noinit(int index, Coefficient coef, Grouped_Polynomial* output){
+ int offset=(*output).length;
+
+ if((*output).length>=(*output).memory){
+ resize_grouped_polynomial(output,2*(*output).memory+1);
+ }
+
+ // copy without allocating
+ (*output).indices[offset]=index;
+ (*output).coefs[offset]=coef;
+ // increment length
+ (*output).length++;
+ return(0);
+}
+
+// concatenate two grouped_polynomials
+int grouped_polynomial_concat(Grouped_Polynomial input, Grouped_Polynomial* output){
+ int i;
+ for(i=0;i<input.length;i++){
+ grouped_polynomial_append(input.indices[i],input.coefs[i],output);
+ }
+ return(0);
+}
+int grouped_polynomial_concat_noinit(Grouped_Polynomial input, Grouped_Polynomial* output){
+ int i;
+ for(i=0;i<input.length;i++){
+ grouped_polynomial_append_noinit(input.indices[i],input.coefs[i],output);
+ }
+
+ // free input arrays
+ free(input.indices);
+ free(input.coefs);
+ return(0);
+}
+
+
+// construct a grouped polynomial from a polynomial, grouping together the terms specified in the id table
+// robust algorithm: allows for a term in the polynomial to contribute to several id table entries
+int group_polynomial(Polynomial polynomial, Grouped_Polynomial* grouped_polynomial, Id_Table idtable, Fields_Table fields){
+ int i,j;
+ // what is left to group
+ Polynomial remainder;
+ int index;
+ Number ratio;
+ Number num;
+ Int_Array factor;
+ int security=0;
+ int pos;
+ coef_denom denom;
+
+ // init remainder
+ polynomial_cpy(polynomial, &remainder);
+
+ // allocate memory
+ init_Grouped_Polynomial(grouped_polynomial, idtable.length+1);
+
+ // copy indices from idtable and allocate
+ // the constant term
+ (*grouped_polynomial).indices[0]=-1;
+ init_Coefficient((*grouped_polynomial).coefs, COEF_SIZE);
+ for(i=1;i<=idtable.length;i++){
+ (*grouped_polynomial).indices[i]=idtable.indices[i-1];
+ init_Coefficient((*grouped_polynomial).coefs+i, COEF_SIZE);
+ }
+ (*grouped_polynomial).length=idtable.length+1;
+
+ // keep on going as long as there are terms in the remainder
+ while(remainder.length>0){
+ // stop if the number of iterations exceeds 100 times the length of the polynomial
+ if(security >= 100*polynomial.length){
+ fprintf(stderr,"error: polynomial could not be grouped in less than %d groupings\n", 100*polynomial.length);
+ exit(-1);
+ }
+ security++;
+
+ // index of the last element
+ i=remainder.length-1;
+
+ // find entry
+ if(remainder.monomials[i].length==0){
+ // constant
+ index=-1;
+ }
+ else{
+ // loop over entries
+ for(j=0,index=-2;j<idtable.length && index==-2;j++){
+ // loop over terms in the polynomial
+ for(pos=0;pos<idtable.polynomials[j].length;pos++){
+ if(int_array_cmp(idtable.polynomials[j].monomials[pos],remainder.monomials[i])==0){
+ index=j;
+ break;
+ }
+ }
+ }
+ }
+
+ if(index==-2){
+ fprintf(stderr,"error: monomial (");
+ for(j=0;j<polynomial.monomials[i].length;j++){
+ fprintf(stderr,"%d", polynomial.monomials[i].values[j]);
+ if(j<polynomial.monomials[i].length-1){
+ fprintf(stderr,",");
+ }
+ }
+ fprintf(stderr,") not found in idtable\n");
+ exit(-1);
+ }
+
+ // if not constant
+ if(index>=0){
+ ratio=number_quot_ret(remainder.nums[i],idtable.polynomials[index].nums[pos]);
+ factor=remainder.factors[i];
+ // add to coefficient
+ denom.index=-1;
+ denom.power=1;
+ coefficient_append(factor, ratio, denom, (*grouped_polynomial).coefs+index+1);
+
+ // remove from remainder
+ free_Int_Array(remainder.monomials[i]);
+ // do not free factor yet
+ free_Number(remainder.nums[i]);
+ remainder.length--;
+
+ // add terms from idtable with minus sign
+ for(j=0;j<idtable.polynomials[index].length;j++){
+ if(j!=pos){
+ num=number_prod_ret(ratio, idtable.polynomials[index].nums[j]);
+ number_Qprod_chain(quot(-1,1),&num);
+ polynomial_append(idtable.polynomials[index].monomials[j], factor, num, &remainder);
+ free_Number(num);
+ }
+ }
+
+ free_Int_Array(factor);
+ free_Number(ratio);
+
+ // simplify remainder
+ polynomial_simplify(&remainder, fields);
+ }
+ // constant
+ else if(index==-1){
+ // add to coefficient
+ denom.index=-1;
+ denom.power=0;
+ coefficient_append(remainder.factors[i], remainder.nums[i], denom, (*grouped_polynomial).coefs);
+ // remove from remainder
+ free_Int_Array(remainder.monomials[i]);
+ free_Int_Array(remainder.factors[i]);
+ free_Number(remainder.nums[i]);
+ remainder.length--;
+ }
+ }
+
+ // simplify the result
+ simplify_grouped_polynomial(grouped_polynomial);
+
+ free_Polynomial(remainder);
+ return(0);
+}
+
+
+// construct a grouped polynomial from a polynomial, grouping together the terms specified in the id table.
+// identifies sub-polynomials in the polynomial corresponding to the entire rhs of an entry in the id table.
+// requires the polynomial and the idtable to be sorted
+// can only treat cases in which monomials in different polynomials of the idtable are distinct
+int group_polynomial_pickandchoose(Polynomial polynomial, Grouped_Polynomial* grouped_polynomial, Id_Table idtable){
+ int i,j,k;
+ // a mask specifying which terms of the polynomial have already been grouped
+ int* mask=calloc(polynomial.length, sizeof(int));
+ int index;
+ Number ratio, ratio_check;
+ // whether ratio was ever allocated
+ int alloc_ratio=0;
+ // whether the correct index was found
+ int found_index;
+ int start_index_search;
+ Int_Array mask_tmp_flips;
+ coef_denom denom;
+
+ // allocate memory
+ init_Grouped_Polynomial(grouped_polynomial, idtable.length+1);
+
+ // copy indices from idtable and allocate
+ // the constant term
+ (*grouped_polynomial).indices[0]=-1;
+ init_Coefficient((*grouped_polynomial).coefs, COEF_SIZE);
+ for(i=1;i<=idtable.length;i++){
+ (*grouped_polynomial).indices[i]=idtable.indices[i-1];
+ init_Coefficient((*grouped_polynomial).coefs+i, COEF_SIZE);
+ }
+ (*grouped_polynomial).length=idtable.length+1;
+
+ // loop over monomials
+ for(i=0;i<polynomial.length;i++){
+ // check that the term hasn't already been added
+ if(mask[i]==0){
+ // loop until the correct index is found (the polynomial must contain all the terms in the index and the numerical factors must match)
+ found_index=0;
+ start_index_search=0;
+ while(found_index==0){
+ found_index=1;
+ // find entry
+ index=find_id(polynomial.monomials[i], idtable,start_index_search);
+ // easier to debug if the error is here instead of inside find_id
+ if(index==-2){
+ fprintf(stderr,"error: monomial not found in idtable\n");
+ exit(-1);
+ }
+
+ // if not constant
+ if(index>=0){
+ // a vector in which to store the indices that were masked
+ init_Int_Array(&mask_tmp_flips,idtable.polynomials[index].length);
+
+ // loop over all monomials in that entry of the idtable
+ for(j=0;j<idtable.polynomials[index].length && found_index==1;j++){
+ // find the monomial in the polynomial
+ for(k=i;k<polynomial.length;k++){
+ // only check if mask==0
+ // only check if the factors are correct
+ if(mask[k]==0 && int_array_cmp(polynomial.factors[i],polynomial.factors[k])==0 && int_array_cmp(idtable.polynomials[index].monomials[j],polynomial.monomials[k])==0){
+ ratio_check=number_quot_ret(polynomial.nums[k],idtable.polynomials[index].nums[j]);
+
+ // if the factors don't factor
+ if(alloc_ratio!=0 && number_compare(ratio,ratio_check)==0){
+ found_index=0;
+ break;
+ }
+ // check that ratio was allocated
+ if(alloc_ratio!=0){
+ free_Number(ratio);
+ }
+ ratio=ratio_check;
+ alloc_ratio=1;
+
+ // added to polynomial
+ mask[k]=1;
+ // keep track of the flips so that they can be undone if the index turns out to be incorrect
+ int_array_append(k,&mask_tmp_flips);
+ break;
+ }
+ }
+
+ // error if the monomial could not be found
+ if(k==polynomial.length){
+ found_index=0;
+ }
+ }
+
+ // if the index was incorrect
+ if(found_index==0){
+ // reset mask
+ for(j=0;j<mask_tmp_flips.length;j++){
+ mask[mask_tmp_flips.values[j]]=0;
+ }
+ // start index search at next item
+ start_index_search=index+1;
+ }
+ else{
+ // add to grouped polynomial
+ denom.index=-1;
+ denom.power=1;
+ coefficient_append(polynomial.factors[i], ratio, denom, (*grouped_polynomial).coefs+index+1);
+ }
+
+ if(alloc_ratio==1){
+ free_Number(ratio);
+ alloc_ratio=0;
+ }
+ free_Int_Array(mask_tmp_flips);
+ }
+ // constant
+ else if(index==-1){
+ mask[i]=1;
+ denom.index=-1;
+ denom.power=0;
+ coefficient_append(polynomial.factors[i], polynomial.nums[i], denom, (*grouped_polynomial).coefs);
+ }
+ }
+ }
+ }
+
+ // check all the terms were grouped
+ for(i=0;i<polynomial.length;i++){
+ if(mask[i]==0){
+ fprintf(stderr,"error: this polynomial could not be grouped: no matches were found for some of the terms\n");
+ exit(-1);
+ }
+ }
+
+ free(mask);
+ return(0);
+}
+
+
+// find the entry in the idtable containing monomial
+// start search at the specified index
+int find_id(Int_Array monomial, Id_Table idtable, int start){
+ int i,j;
+
+ // constant
+ if(monomial.length==0){
+ return(-1);
+ }
+
+ // loop over entries
+ for(i=start;i<idtable.length;i++){
+ // loop over terms in the polynomial
+ for(j=0;j<idtable.polynomials[i].length;j++){
+ if(int_array_cmp(idtable.polynomials[i].monomials[j],monomial)==0){
+ return(i);
+ }
+ }
+ }
+
+ return(-2);
+}
+
+
+// simplify grouped polynomial
+int simplify_grouped_polynomial(Grouped_Polynomial* polynomial){
+ int i;
+ for(i=0;i<(*polynomial).length;i++){
+ coefficient_simplify((*polynomial).coefs+i);
+ }
+ return(0);
+}
+
+
+// derive a flow equation with respect to an unknown variable
+// equivalent to DB.dl where dl are symbols for the derivatives of the indices in the flow equation with respect to the unknown variable
+// indices specifies the list of indices that depend on the variable
+int flow_equation_derivx(Grouped_Polynomial flow_equation, Int_Array indices, Grouped_Polynomial* dflow){
+ int i,j,k;
+ Coefficient tmp_coef;
+
+ // alloc
+ init_Grouped_Polynomial(dflow, flow_equation.length);
+
+ // for each equation
+ for(i=0;i<flow_equation.length;i++){
+ // copy indices
+ if(flow_equation.indices[i]>=0){
+ (*dflow).indices[i]=flow_equation.indices[i]+DOFFSET;
+ }
+ else{
+ (*dflow).indices[i]=flow_equation.indices[i]-DOFFSET;
+ }
+
+ init_Coefficient((*dflow).coefs+i, COEF_SIZE);
+ // for each index
+ for(j=0;j<indices.length;j++){
+ coefficient_deriv(flow_equation.coefs[i], indices.values[j], &tmp_coef);
+ // multiply each coefficient by the appropriate dl[j]
+ for(k=0;k<tmp_coef.length;k++){
+ // only in non-trivial cases
+ if(number_is_zero(tmp_coef.nums[k])==0){
+ // non-constants
+ if(indices.values[j]>=0){
+ int_array_append(DOFFSET + indices.values[j], tmp_coef.factors+k);
+ }
+ // constants are offset with -doffset (so that the derivatives of constants also have a negative index)
+ else{
+ int_array_append(-DOFFSET + indices.values[j], tmp_coef.factors+k);
+ }
+ }
+ }
+
+ // add to output
+ coefficient_concat_noinit(tmp_coef, (*dflow).coefs+i);
+ }
+ }
+
+ (*dflow).length=flow_equation.length;
+
+ return(0);
+}
+
+
+/*
+// derive a flow equation with respect to an index
+int flow_equation_deriv(Grouped_Polynomial flow_equation, int index, Grouped_Polynomial* output){
+ int i,k;
+ // temp list of indices
+ Int_Array factor;
+ // number of times index was found
+ int match_count;
+ coef_denom denom;
+ // store the computation of the derivative of the constant
+ int previous_constant_index=0;
+ Coefficient dC;
+ Coefficient tmp_coef;
+
+ init_Grouped_Polynomial(output, flow_equation.length);
+
+ // loop over equations
+ for(k=0;k<flow_equation.length;k++){
+ init_Coefficient((*output).coefs+k, COEF_SIZE);
+
+ // loop over monomials
+ for(i=0;i<flow_equation.coefs[k].length;i++){
+
+ // derivative of the numerator
+ monomial_deriv(flow_equation.coefs[k].factors[i], index, &factor, &match_count);
+
+ // if the derivative doesn't vanish, add it to the coefficient
+ if(match_count>0){
+ coefficient_append_noinit(factor,number_Qprod_ret(quot(match_count,1),flow_equation.coefs[k].nums[i]), flow_equation.coefs[k].denoms[i], (*output).coefs+k);
+ }
+ else{
+ free_Int_Array(factor);
+ }
+
+ // derivative of the denominator
+ if(flow_equation.coefs[k].denoms[i].power>0){
+ // check whether the derivative was already computed
+ if(flow_equation.coefs[k].denoms[i].index!=previous_constant_index){
+ // if not first, then free
+ if(previous_constant_index!=0){
+ free_Coefficient(dC);
+ previous_constant_index=0;
+ }
+ init_Coefficient(&dC,COEF_SIZE);
+ coefficient_deriv_noinit(flow_equation.coefs[intlist_find_err(flow_equation.indices, flow_equation.length, flow_equation.coefs[k].denoms[i].index)], index, &dC);
+ previous_constant_index=flow_equation.coefs[k].denoms[i].index;
+ }
+
+ init_Coefficient(&tmp_coef, dC.length);
+ coefficient_append(flow_equation.coefs[k].factors[i], number_Qprod_ret(quot(-flow_equation.coefs[k].denoms[i].power,1), flow_equation.coefs[k].nums[i]), flow_equation.coefs[k].denoms[i], &tmp_coef);
+ (tmp_coef.denoms[0].power)++;
+
+ coefficient_prod_chain(dC, &tmp_coef);
+
+ coefficient_concat_noinit(tmp_coef, (*output).coefs+k);
+ }
+ }
+
+ // memory safe
+ if((*output).coefs[k].length>0){
+ coefficient_simplify((*output).coefs+k);
+ }
+ else{
+ // add a trivial element to the coefficient
+ init_Int_Array(&factor,0);
+ denom.index=-1;
+ denom.power=0;
+ coefficient_append_noinit(factor,number_zero(),denom,(*output).coefs+k);
+ }
+ }
+
+ free_Coefficient(dC);
+ return(0);
+}
+*/
+
+
+// print a grouped polynomial
+// prepend the indices on the left side with lhs_pre, and those on the right by rhs_pre
+int grouped_polynomial_print(Grouped_Polynomial grouped_polynomial, char lhs_pre, char rhs_pre){
+ int i,j;
+ Char_Array buffer;
+ int dcount;
+
+ // for each equation
+ for(i=0;i<grouped_polynomial.length;i++){
+ //print lhs
+ // negative indices are constants
+ if(grouped_polynomial.indices[i]<0){
+ // count derivatives
+ dcount=-grouped_polynomial.indices[i]/DOFFSET;
+ for(j=0;j<3-dcount;j++){
+ printf(" ");
+ }
+ printf("[");
+ for(j=0;j<dcount;j++){
+ printf("d");
+ }
+ printf("C%d] =",-grouped_polynomial.indices[i]-dcount*DOFFSET);
+ }
+ else{
+ // count derivatives
+ dcount=grouped_polynomial.indices[i]/DOFFSET;
+ for(j=0;j<2-dcount;j++){
+ printf(" ");
+ }
+ printf("[");
+ for(j=0;j<dcount;j++){
+ printf("d");
+ }
+ printf("%c%2d] =",lhs_pre,grouped_polynomial.indices[i]-dcount*DOFFSET);
+ }
+
+ // rhs
+ init_Char_Array(&buffer, STR_SIZE);
+ coefficient_sprint(grouped_polynomial.coefs[i],&buffer,9,rhs_pre);
+ if(buffer.length>0){
+ printf("%s",buffer.str);
+ }
+ free_Char_Array(buffer);
+
+ if(i<grouped_polynomial.length-1){
+ printf(",");
+ }
+ // extra \n
+ printf("\n");
+ }
+ return(0);
+}
+
+// read from string
+#define PP_NULL_MODE 0
+#define PP_COEF_MODE 1
+#define PP_INDEX_MODE 3
+#define PP_COMMENT_MODE 4
+#define PP_BRACKET_MODE 5
+#define PP_CONSTANT_MODE 6
+int char_array_to_Grouped_Polynomial(Char_Array str, Grouped_Polynomial* output){
+ // buffer
+ char* buffer=calloc(str.length+1,sizeof(char));
+ char* buffer_ptr=buffer;
+ int index=-2;
+ Coefficient coef;
+ int i,j;
+ int mode;
+ int dcount=0;
+
+ init_Grouped_Polynomial(output, EQUATION_SIZE);
+
+ // loop over input
+ mode=PP_NULL_MODE;
+ for(j=0;j<str.length;j++){
+ if(mode==PP_COMMENT_MODE){
+ if(str.str[j]=='\n'){
+ mode=PP_NULL_MODE;
+ }
+ }
+ // stay in polynomial mode until ','
+ else if(mode==PP_COEF_MODE){
+ if(str.str[j]==','){
+ // parse polynomial
+ str_to_Coefficient(buffer, &coef);
+ // write index and polynomial
+ grouped_polynomial_append_noinit(index, coef, output);
+ mode=PP_NULL_MODE;
+ }
+ else{
+ buffer_ptr=str_addchar(buffer_ptr,str.str[j]);
+ }
+ }
+ else{
+ switch(str.str[j]){
+ // index
+ case '[':
+ if(mode==PP_NULL_MODE){
+ mode=PP_BRACKET_MODE;
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ // reset derivatives count
+ dcount=0;
+ }
+ break;
+ case '%':
+ if(mode==PP_BRACKET_MODE){
+ mode=PP_INDEX_MODE;
+ }
+ break;
+ // constant term
+ case 'C':
+ if(mode==PP_BRACKET_MODE){
+ mode=PP_CONSTANT_MODE;
+ }
+ break;
+ // derivatives
+ case 'd':
+ if(mode==PP_BRACKET_MODE || mode==PP_INDEX_MODE || mode==PP_CONSTANT_MODE){
+ dcount++;
+ }
+ break;
+ // write index
+ case ']':
+ sscanf(buffer,"%d",&i);
+ if(mode==PP_INDEX_MODE){
+ index=i+dcount*DOFFSET;
+ }
+ else if(mode==PP_CONSTANT_MODE){
+ index=-i-dcount*DOFFSET;
+ }
+ mode=PP_NULL_MODE;
+
+ break;
+
+ // coef mode
+ case '=':
+ if(mode==PP_NULL_MODE){
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ mode=PP_COEF_MODE;
+ }
+ break;
+
+ // comment
+ case '#':
+ mode=PP_COMMENT_MODE;
+ break;
+
+ default:
+ if(mode!=PP_NULL_MODE){
+ buffer_ptr=str_addchar(buffer_ptr,str.str[j]);
+ }
+ break;
+ }
+ }
+ }
+
+ // last step
+ if(mode==PP_COEF_MODE){
+ str_to_Coefficient(buffer, &coef);
+ grouped_polynomial_append_noinit(index, coef, output);
+ }
+
+ free(buffer);
+ return(0);
+}
+
+
+// evaluate an equation on a vector
+int evaleq(RCC* rccs, Grouped_Polynomial poly){
+ int i;
+ long double* res=calloc((*rccs).length,sizeof(long double));
+
+ if((*rccs).length!=poly.length){
+ fprintf(stderr, "error: trying to evaluate an flow equation with %d components on an rcc with %d\n",poly.length,(*rccs).length);
+ exit(-1);
+ }
+
+ // initialize vectors to 0
+ for(i=0;i<(*rccs).length;i++){
+ res[i]=0.;
+ }
+
+ // for each equation
+ for(i=0;i<poly.length;i++){
+ evalcoef(*rccs, poly.coefs[i], res+i);
+ }
+
+ // copy res to rccs
+ for(i=0;i<(*rccs).length;i++){
+ (*rccs).values[i]=res[i];
+ }
+
+ // free memory
+ free(res);
+ return(0);
+
+}
+
diff --git a/src/grouped_polynomial.h b/src/grouped_polynomial.h
new file mode 100644
index 0000000..3c38f1b
--- /dev/null
+++ b/src/grouped_polynomial.h
@@ -0,0 +1,74 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+Polynomials can be represented in a grouped way, by putting the terms
+ proportional to the same monomial together.
+
+The main part of a grouped polynomial is the list of coefficients,
+ each of which stands for the set of terms proportional to the
+ corresponding monomial, specified in indices and labels.
+
+*/
+
+#ifndef GROUPED_POLYNOMIAL_H
+#define GROUPED_POLYNOMIAL_H
+
+#include "types.h"
+
+// memory
+int init_Grouped_Polynomial(Grouped_Polynomial* gpolynomial, int size);
+int free_Grouped_Polynomial(Grouped_Polynomial gpolynomial);
+
+// resize the memory allocated to a grouped polynomial
+int resize_grouped_polynomial(Grouped_Polynomial* grouped_polynomial,int new_size);
+
+// copy a grouped polynomial
+int grouped_polynomial_cpy(Grouped_Polynomial input, Grouped_Polynomial* output);
+int grouped_polynomial_cpy_noinit(Grouped_Polynomial input, Grouped_Polynomial* output);
+
+// append an element to a polynomial
+int grouped_polynomial_append(int index, Coefficient coef, Grouped_Polynomial* output);
+int grouped_polynomial_append_noinit(int index, Coefficient coef, Grouped_Polynomial* output);
+
+// concatenate two polynomials
+int grouped_polynomial_concat(Grouped_Polynomial input, Grouped_Polynomial* output);
+int grouped_polynomial_concat_noinit(Grouped_Polynomial input, Grouped_Polynomial* output);
+
+// construct a grouped polynomial from a polynomial, grouping together the terms specified in the id table.
+int group_polynomial(Polynomial polynomial, Grouped_Polynomial* grouped_polynomial, Id_Table idtable, Fields_Table fields);
+// more naive and faster version in which the terms in polynomial corresponding to a polynomial in the id table are grouped together (does not allow parts of terms to be grouped together)
+int group_polynomial_pickandchoose(Polynomial polynomial, Grouped_Polynomial* grouped_polynomial, Id_Table idtable);
+
+// find the entry in the idtable containing monomial
+int find_id(Int_Array monomial, Id_Table idtable, int start);
+
+// simplify grouped polynomial
+int simplify_grouped_polynomial(Grouped_Polynomial* polynomial);
+
+// derive a flow equation with respect to an unknown variable
+int flow_equation_derivx(Grouped_Polynomial flow_equation, Int_Array indices, Grouped_Polynomial* dflow);
+
+// print a grouped polynomial
+int grouped_polynomial_print(Grouped_Polynomial grouped_polynomial, char lhs_pre, char rhs_pre);
+
+// read from string
+int char_array_to_Grouped_Polynomial(Char_Array str, Grouped_Polynomial* output);
+
+// evaluate an equation on an RCC
+int evaleq(RCC* rccs, Grouped_Polynomial poly);
+
+#endif
diff --git a/src/idtable.c b/src/idtable.c
new file mode 100644
index 0000000..fe409c2
--- /dev/null
+++ b/src/idtable.c
@@ -0,0 +1,122 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "idtable.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include "array.h"
+#include "polynomial.h"
+
+// allocate memory
+int init_Id_Table(Id_Table* idtable,int size){
+ (*idtable).indices=calloc(size,sizeof(int));
+ (*idtable).polynomials=calloc(size,sizeof(Polynomial));
+ (*idtable).length=0;
+ (*idtable).memory=size;
+ return(0);
+}
+
+// free memory
+int free_Id_Table(Id_Table idtable){
+ int i;
+ for(i=0;i<idtable.length;i++){
+ free_Polynomial(idtable.polynomials[i]);
+ }
+ free(idtable.indices);
+ free(idtable.polynomials);
+
+ return(0);
+}
+
+// resize the memory allocated to a idtable
+int resize_idtable(Id_Table* idtable,int new_size){
+ Id_Table new_idtable;
+ int i;
+
+ init_Id_Table(&new_idtable,new_size);
+ for(i=0;i<(*idtable).length;i++){
+ new_idtable.indices[i]=(*idtable).indices[i];
+ new_idtable.polynomials[i]=(*idtable).polynomials[i];
+ }
+ new_idtable.length=(*idtable).length;
+
+ free((*idtable).indices);
+ free((*idtable).polynomials);
+
+ *idtable=new_idtable;
+ return(0);
+}
+
+// copy an idtable
+int idtable_cpy(Id_Table input, Id_Table* output){
+ init_Id_Table(output,input.length);
+ idtable_cpy_noinit(input,output);
+ return(0);
+}
+int idtable_cpy_noinit(Id_Table input, Id_Table* output){
+ int i;
+ if((*output).memory<input.length){
+ fprintf(stderr,"error: trying to copy an idtable of length %d to another with memory %d\n",input.length,(*output).memory);
+ exit(-1);
+ }
+ for(i=0;i<input.length;i++){
+ (*output).indices[i]=input.indices[i];
+ polynomial_cpy(input.polynomials[i],(*output).polynomials+i);
+ }
+ (*output).length=input.length;
+
+ return(0);
+}
+
+// append an element to a idtable
+int idtable_append(int index, Polynomial polynomial, Id_Table* output){
+ int offset=(*output).length;
+
+ if((*output).length>=(*output).memory){
+ resize_idtable(output,2*(*output).memory);
+ }
+
+ // copy and allocate
+ polynomial_cpy(polynomial,(*output).polynomials+offset);
+ (*output).indices[offset]=index;
+ // increment length
+ (*output).length++;
+ return(0);
+}
+// append an element to a idtable without allocating memory
+int idtable_append_noinit(int index, Polynomial polynomial, Id_Table* output){
+ int offset=(*output).length;
+
+ if((*output).length>=(*output).memory){
+ resize_idtable(output,2*(*output).memory);
+ }
+
+ // copy without allocating
+ (*output).indices[offset]=index;
+ (*output).polynomials[offset]=polynomial;
+ // increment length
+ (*output).length++;
+ return(0);
+}
+
+// concatenate two idtables
+int idtable_concat(Id_Table input, Id_Table* output){
+ int i;
+ for(i=0;i<input.length;i++){
+ idtable_append(input.indices[i],input.polynomials[i],output);
+ }
+ return(0);
+}
diff --git a/src/idtable.h b/src/idtable.h
new file mode 100644
index 0000000..38ab249
--- /dev/null
+++ b/src/idtable.h
@@ -0,0 +1,44 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/* correspondence table to group a polynomial into a flow equation */
+
+#ifndef IDTABLE_H
+#define IDTABLE_H
+
+#include "types.h"
+
+// allocate memory
+int init_Id_Table(Id_Table* idtable,int size);
+// free memory
+int free_Id_Table(Id_Table idtable);
+
+// resize the memory allocated to a idtable
+int resize_idtable(Id_Table* idtable,int new_size);
+
+// copy an idtable
+int idtable_cpy(Id_Table input, Id_Table* output);
+int idtable_cpy_noinit(Id_Table input, Id_Table* output);
+
+// append an element to a idtable
+int idtable_append(int index, Polynomial polynomial, Id_Table* output);
+int idtable_append_noinit(int index, Polynomial polynomial, Id_Table* output);
+
+// concatenate two idtables
+int idtable_concat(Id_Table input, Id_Table* output);
+
+#define IDTABLE_H_DONE
+#endif
diff --git a/src/istring.c b/src/istring.c
new file mode 100644
index 0000000..663c06a
--- /dev/null
+++ b/src/istring.c
@@ -0,0 +1,99 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include <stdlib.h>
+#include "istring.h"
+
+char* str_concat(char* ptr, const char* str){
+ char* str_ptr=(char*)str;
+
+ while(*str_ptr!='\0'){
+ *ptr=*str_ptr;
+ ptr++;
+ str_ptr++;
+ }
+ *ptr='\0';
+ return(ptr);
+}
+
+int str_concat_memorysafe(char** str_out, int pos, const char* str, int* memory){
+ char* out_ptr;
+
+ if(str_len((char*)str)+pos>=*memory){
+ *memory=*memory+str_len((char*)str)+pos+1;
+ resize_str(str_out,*memory);
+ }
+ out_ptr=*str_out+pos;
+ str_concat(out_ptr,str);
+ return(0);
+}
+
+int resize_str(char** out, int memory){
+ char* tmp_str=calloc(memory,sizeof(char));
+ char* tmp_ptr=tmp_str;
+ char* out_ptr=*out;
+
+ for(;*out_ptr!='\0';out_ptr++,tmp_ptr++){
+ *tmp_ptr=*out_ptr;
+ }
+ *tmp_ptr='\0';
+
+ free(*out);
+ *out=tmp_str;
+ return(0);
+}
+
+char* str_addchar(char* ptr, const char c){
+ *ptr=c;
+ ptr++;
+ *ptr='\0';
+ return(ptr);
+}
+
+int str_len(char* str){
+ char* ptr=str;
+ int ret=0;
+ while(*ptr!='\0'){ret++;ptr++;}
+ return(ret);
+}
+
+int str_cmp(char* str1, char* str2){
+ char* ptr1=str1;
+ char* ptr2=str2;
+ while(*ptr1==*ptr2 && *ptr1!='\0' && *ptr2!='\0'){
+ ptr1++;
+ ptr2++;
+ }
+ if(*ptr1=='\0' && *ptr2=='\0'){
+ return(1);
+ }
+ else{
+ return(0);
+ }
+}
+
+
+int str_cpy_noalloc(char* input, char* output){
+ char* ptr;
+ char* out_ptr;
+
+ for(ptr=input,out_ptr=output;*ptr!='\0';ptr++,out_ptr++){
+ *out_ptr=*ptr;
+ }
+ *out_ptr='\0';
+ return(0);
+}
+
diff --git a/src/istring.h b/src/istring.h
new file mode 100644
index 0000000..5b47b9b
--- /dev/null
+++ b/src/istring.h
@@ -0,0 +1,40 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+String manipulation
+*/
+
+#ifndef ISTRING_H
+#define ISTRING_H
+
+// concatenate str at the position pointed to by ptr, and return a pointer
+// to the end of the new string
+char* str_concat(char* ptr, const char* str);
+// concatenate strings and resize them if necessary
+int str_concat_memorysafe(char** str_out, int pos, const char* str, int* memory);
+// resize a string
+int resize_str(char** out, int memory);
+// idem with a single character
+char* str_addchar(char* ptr, const char c);
+// string length
+int str_len(char* str);
+// compare strings
+int str_cmp(char* str1, char* str2);
+// copy a string to another without allocating memory
+int str_cpy_noalloc(char* input, char* output);
+
+#endif
diff --git a/src/kondo.c b/src/kondo.c
new file mode 100644
index 0000000..c86b4b3
--- /dev/null
+++ b/src/kondo.c
@@ -0,0 +1,1449 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "kondo.h"
+#include <stdlib.h>
+#include <stdio.h>
+
+#include "idtable.h"
+#include "array.h"
+#include "number.h"
+#include "istring.h"
+#include "cli_parser.h"
+#include "fields.h"
+#include "parse_file.h"
+#include "polynomial.h"
+#include "definitions.cpp"
+#include "rational.h"
+
+// dimension of A, B and h (must be <10)
+#define KONDO_DIM 3
+// number of spin components
+#define KONDO_SPIN 2
+
+// offsets for indices of A, B and h
+// order matters for symbols table
+#define KONDO_A_OFFSET 1
+#define KONDO_B_OFFSET 2
+#define KONDO_H_OFFSET 3
+
+// parsing modes (from parse_file.c)
+#define PP_NULL_MODE 0
+// when reading a factor
+#define PP_FACTOR_MODE 1
+// reading a monomial
+#define PP_MONOMIAL_MODE 2
+// reading a numerator and denominator
+#define PP_NUMBER_MODE 3
+// types of fields
+#define PP_FIELD_MODE 6
+#define PP_PARAMETER_MODE 7
+#define PP_EXTERNAL_MODE 8
+#define PP_INTERNAL_MODE 9
+// indices
+#define PP_INDEX_MODE 10
+// factors or monomials
+#define PP_BRACKET_MODE 11
+// labels
+#define PP_LABEL_MODE 12
+// polynomial
+#define PP_POLYNOMIAL_MODE 13
+// field scalar product
+#define PP_FIELD_SCALAR_MODE 14
+#define PP_FIELD_VECTOR_PROD_MODE 15
+
+
+
+// generate configuration file
+int kondo_generate_conf(Str_Array* str_args, int box_count){
+ Str_Array new_args;
+ Fields_Table fields;
+ Char_Array tmp_str;
+ int arg_index;
+ int i;
+ Char_Array title;
+
+ init_Str_Array(&new_args,8);
+
+ // fields
+ kondo_fields_table(box_count, &tmp_str, &fields);
+ str_array_append_noinit(tmp_str, &new_args);
+
+ // symbols
+ kondo_symbols(&tmp_str, box_count, &fields);
+ arg_index=find_str_arg("symbols", *str_args);
+ if(arg_index>=0){
+ if(tmp_str.length>0){
+ char_array_snprintf(&tmp_str,",\n");
+ }
+ char_array_concat((*str_args).strs[arg_index], &tmp_str);
+ }
+ parse_input_symbols(tmp_str, &fields);
+ str_array_append_noinit(tmp_str, &new_args);
+
+ // identities
+ kondo_identities(&tmp_str);
+ arg_index=find_str_arg("identities", *str_args);
+ if(arg_index>=0){
+ if(tmp_str.length>0){
+ char_array_snprintf(&tmp_str,",\n");
+ }
+ char_array_concat((*str_args).strs[arg_index], &tmp_str);
+ }
+ parse_input_identities(tmp_str, &fields);
+ str_array_append_noinit(tmp_str, &new_args);
+
+ // groups
+ kondo_groups(&tmp_str, box_count);
+ str_array_append_noinit(tmp_str, &new_args);
+
+
+ // propagator
+ arg_index=find_str_arg("propagator", *str_args);
+ if(arg_index>=0){
+ kondo_propagator((*str_args).strs[arg_index], &tmp_str);
+ str_array_append_noinit(tmp_str, &new_args);
+ }
+
+ // input polynomial
+ arg_index=find_str_arg("input_polynomial", *str_args);
+ if(arg_index>=0){
+ kondo_input_polynomial((*str_args).strs[arg_index], &tmp_str, fields, box_count);
+ str_array_append_noinit(tmp_str, &new_args);
+ }
+
+ // id table
+ arg_index=find_str_arg("id_table", *str_args);
+ if(arg_index>=0){
+ kondo_idtable((*str_args).strs[arg_index], &tmp_str, fields);
+ str_array_append_noinit(tmp_str, &new_args);
+ }
+
+ // copy remaining entries
+ for(i=0;i<(*str_args).length;i++){
+ get_str_arg_title((*str_args).strs[i], &title);
+ if(str_cmp(title.str, "symbols")==0 &&\
+ str_cmp(title.str, "identities")==0 &&\
+ str_cmp(title.str, "propagator")==0 &&\
+ str_cmp(title.str, "input_polynomial")==0 &&\
+ str_cmp(title.str, "id_table")==0 ){
+
+ char_array_cpy((*str_args).strs[i], &tmp_str);
+ str_array_append_noinit(tmp_str, &new_args);
+ }
+ free_Char_Array(title);
+ }
+
+ free_Fields_Table(fields);
+ free_Str_Array(*str_args);
+ *str_args=new_args;
+
+ return(0);
+}
+
+
+// generate the Kondo fields table
+int kondo_fields_table(int box_count, Char_Array* str_fields, Fields_Table* fields){
+ int i,j;
+
+ init_Char_Array(str_fields,STR_SIZE);
+ char_array_snprintf(str_fields, "#!fields\n");
+
+ // external fields
+ char_array_append_str("x:",str_fields);
+ for(i=0;i<KONDO_SPIN;i++){
+ char_array_snprintf(str_fields, "%d,%d", 10*(i+10*KONDO_A_OFFSET), 10*(i+10*KONDO_B_OFFSET));
+ if(i<KONDO_SPIN-1){
+ char_array_append(',',str_fields);
+ }
+ }
+ char_array_append('\n',str_fields);
+
+ // internal fields: A
+ char_array_append_str("i:",str_fields);
+ for(i=0;i<KONDO_SPIN;i++){
+ for(j=1;j<=box_count;j++){
+ char_array_snprintf(str_fields, "%d", 10*(i+10*KONDO_A_OFFSET)+j);
+ char_array_append(',',str_fields);
+ }
+ }
+ // B
+ for(i=0;i<KONDO_SPIN;i++){
+ for(j=1;j<=2;j++){
+ char_array_snprintf(str_fields, "%d", 10*(i+10*KONDO_B_OFFSET)+j);
+ if(i<KONDO_SPIN-1 || j<2){
+ char_array_append(',',str_fields);
+ }
+ }
+ }
+ char_array_append('\n',str_fields);
+
+ // parameters
+ char_array_append_str("h:",str_fields);
+ for(i=0;i<KONDO_DIM;i++){
+ char_array_snprintf(str_fields, "%d", 10*(i+10*KONDO_H_OFFSET));
+ if(i<KONDO_DIM-1){
+ char_array_append(',',str_fields);
+ }
+ }
+ char_array_append('\n',str_fields);
+
+ // declare Fermions
+ char_array_append_str("f:",str_fields);
+ // external fields
+ for(i=0;i<KONDO_SPIN;i++){
+ char_array_snprintf(str_fields, "%d,%d", 10*(i+10*KONDO_A_OFFSET), 10*(i+10*KONDO_B_OFFSET));
+ char_array_append(',',str_fields);
+ }
+ // internal fields: A
+ for(i=0;i<KONDO_SPIN;i++){
+ for(j=1;j<=box_count;j++){
+ char_array_snprintf(str_fields, "%d", 10*(i+10*KONDO_A_OFFSET)+j);
+ char_array_append(',',str_fields);
+ }
+ }
+ // B
+ for(i=0;i<KONDO_SPIN;i++){
+ for(j=1;j<=2;j++){
+ char_array_snprintf(str_fields, "%d", 10*(i+10*KONDO_B_OFFSET)+j);
+ if(i<KONDO_SPIN-1 || j<2){
+ char_array_append(',',str_fields);
+ }
+ }
+ }
+ char_array_append('\n',str_fields);
+
+ // parse fields table
+ parse_input_fields(*str_fields, fields);
+
+ return(0);
+}
+
+
+// generate Kondo symbols
+int kondo_symbols(Char_Array* str_symbols, int box_count, Fields_Table* fields){
+ int i,j,k,l;
+ Char_Array tmp_str;
+ Polynomial poly;
+ char letters[3]={'A','B','h'};
+
+ init_Char_Array(str_symbols, STR_SIZE);
+ char_array_snprintf(str_symbols, "#!symbols\n");
+
+ // loop over box index
+ for(i=1;i<=box_count;i++){
+ // loop over letters
+ for(j=0;j<2;j++){
+ // loop over space dimension
+ for(k=0;k<KONDO_DIM;k++){
+ // write index
+ char_array_snprintf(str_symbols, "%d=", 100*(10*(KONDO_A_OFFSET+j)+k)+i);
+ // write the name of the scalar product
+ init_Char_Array(&tmp_str, 6);
+ char_array_snprintf(&tmp_str, "%c%d%d", letters[j], k, i);
+ // compute corresponding polynomial
+ kondo_resolve_ABh(tmp_str.str, &poly, *fields);
+ free_Char_Array(tmp_str);
+ // write to output
+ polynomial_sprint(poly, str_symbols);
+ free_Polynomial(poly);
+ // add ,
+ char_array_snprintf(str_symbols,",\n");
+ }
+ }
+ }
+
+ // scalar products
+ // loop over box index
+ for(i=1;i<=box_count;i++){
+ // loop over letters
+ for(j=0;j<3;j++){
+ for(k=0;k<3;k++){
+ // write index
+ char_array_snprintf(str_symbols, "%d=", 1000*(10*(KONDO_A_OFFSET+j)+KONDO_A_OFFSET+k)+i);
+ for(l=0;l<KONDO_DIM;l++){
+ char_array_snprintf(str_symbols, "(1)");
+ if(j<2){
+ char_array_snprintf(str_symbols,"[f%d]", 100*(10*(KONDO_A_OFFSET+j)+l)+i);
+ }
+ else{
+ char_array_snprintf(str_symbols,"[f%d]", 10*(10*(KONDO_A_OFFSET+j)+l));
+ }
+ if(k<2){
+ char_array_snprintf(str_symbols,"[f%d]", 100*(10*(KONDO_A_OFFSET+k)+l)+i);
+ }
+ else{
+ char_array_snprintf(str_symbols,"[f%d]", 10*(10*(KONDO_A_OFFSET+k)+l));
+ }
+
+ if(l<KONDO_DIM-1){
+ char_array_append('+',str_symbols);
+ }
+ }
+ // add ,
+ char_array_snprintf(str_symbols,",\n");
+ }
+ }
+ }
+
+ // vector products
+ for(i=1;i<=box_count;i++){
+ char_array_snprintf(str_symbols, "%d=", 100*(100*(KONDO_A_OFFSET)+10*KONDO_B_OFFSET+KONDO_H_OFFSET)+i);
+ for(l=0;l<KONDO_DIM;l++){
+ // remember (-1 %3 = -1)
+ char_array_snprintf(str_symbols, "(1)[f%d][f%d][f%d]+(-1)[f%d][f%d][f%d]", 100*(10*KONDO_A_OFFSET+((l+1)%KONDO_DIM))+i, 100*(10*KONDO_B_OFFSET+((l+2)%KONDO_DIM))+i, 10*(10*KONDO_H_OFFSET+l), 100*(10*KONDO_A_OFFSET+((l+2)%KONDO_DIM))+i, 100*(10*KONDO_B_OFFSET+((l+1)%KONDO_DIM))+i, 10*(10*KONDO_H_OFFSET+l));
+ if(l<KONDO_DIM-1){
+ char_array_append('+',str_symbols);
+ }
+ }
+
+ // add ,
+ if(i<box_count){
+ char_array_snprintf(str_symbols,",\n");
+ }
+ }
+
+
+ return(0);
+}
+
+// generate Kondo symbols (older method: one symbol for each scalar product)
+int kondo_symbols_scalarprod(Char_Array* str_symbols, int box_count, Fields_Table* fields){
+ int i,j,k;
+ Char_Array tmp_str;
+ Polynomial poly;
+ char letters[3]={'A','B','h'};
+
+ init_Char_Array(str_symbols, STR_SIZE);
+ char_array_snprintf(str_symbols, "#!symbols\n");
+
+ // loop over box index
+ for(i=1;i<=box_count;i++){
+ // loop over letters
+ for(j=0;j<3;j++){
+ for(k=0;k<3;k++){
+ // write index
+ char_array_snprintf(str_symbols, "%d=", 100*(10*(KONDO_A_OFFSET+j)+KONDO_A_OFFSET+k)+i);
+ // write the name of the scalar product
+ init_Char_Array(&tmp_str, 6);
+ char_array_snprintf(&tmp_str, "%c%d.%c%d", letters[j], i, letters[k], i);
+ // compute corresponding polynomial
+ kondo_resolve_scalar_prod(tmp_str.str, &poly, *fields);
+ free_Char_Array(tmp_str);
+ // write to output
+ polynomial_sprint(poly, str_symbols);
+ free_Polynomial(poly);
+ // add ,
+ if(i<box_count || j<2 || k<2){
+ char_array_snprintf(str_symbols,",\n");
+ }
+ }
+ }
+ }
+
+ parse_input_symbols(*str_symbols, fields);
+
+ return(0);
+}
+
+
+// generate Kondo groups (groups of independent variables)
+int kondo_groups(Char_Array* str_groups, int box_count){
+ int i,j;
+
+ init_Char_Array(str_groups, STR_SIZE);
+ char_array_snprintf(str_groups, "#!groups\n");
+ char_array_append('(',str_groups);
+ for(i=0;i<KONDO_DIM;i++){
+ for(j=1;j<=box_count;j++){
+ char_array_snprintf(str_groups, "%d",100*(10*KONDO_A_OFFSET+i)+j);
+ if(j<box_count || i<KONDO_DIM-1){
+ char_array_append(',',str_groups);
+ }
+ }
+ }
+ char_array_append(')',str_groups);
+ char_array_append('\n',str_groups);
+
+ char_array_append('(',str_groups);
+ for(i=0;i<KONDO_DIM;i++){
+ for(j=1;j<=box_count;j++){
+ char_array_snprintf(str_groups, "%d",100*(10*KONDO_B_OFFSET+i)+j);
+ if(j<box_count || i<KONDO_DIM-1){
+ char_array_append(',',str_groups);
+ }
+ }
+ }
+ char_array_append(')',str_groups);
+ char_array_append('\n',str_groups);
+ return(0);
+}
+
+
+// generate Kondo identities
+// h_3^2=1-h_1^2-h_2^2
+int kondo_identities(Char_Array* str_identities){
+ int i;
+
+ init_Char_Array(str_identities,STR_SIZE);
+ char_array_snprintf(str_identities, "#!identities\n");
+
+ char_array_snprintf(str_identities, "[f%d][f%d]=(1)",10*(KONDO_DIM-1+10*KONDO_H_OFFSET),10*(KONDO_DIM-1+10*KONDO_H_OFFSET));
+ for(i=0;i<KONDO_DIM-1;i++){
+ char_array_snprintf(str_identities, "+(-1)[f%d][f%d]",10*(i+10*KONDO_H_OFFSET),10*(i+10*KONDO_H_OFFSET));
+ }
+
+ return(0);
+}
+
+
+// convert the Kondo propagator
+int kondo_propagator(Char_Array str_kondo_propagator, Char_Array* str_propagator){
+ int i,j;
+ // buffer
+ char* buffer=calloc(str_kondo_propagator.length+1,sizeof(char));
+ char* buffer_ptr=buffer;
+ // offset and index for each element
+ int offset[2]={-1,-1};
+ int index[2]={-1,-1};
+ int mode;
+ int comment=0;
+
+ // allocate memory
+ init_Char_Array(str_propagator,STR_SIZE);
+
+ // reproduce the loop from parse_input_propagatore but merely copy values, and replace indices
+ mode=PP_INDEX_MODE;
+ for(j=0;j<str_kondo_propagator.length;j++){
+ if(comment==1){
+ // write comments to str
+ char_array_append(str_kondo_propagator.str[j],str_propagator);
+ if(str_kondo_propagator.str[j]=='\n'){
+ comment=0;
+ }
+ }
+ else{
+ switch(str_kondo_propagator.str[j]){
+ // indices
+ case ';':
+ if(mode==PP_INDEX_MODE){
+ get_offset_index(buffer,offset,index);
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ break;
+ case ':':
+ if(mode==PP_INDEX_MODE){
+ get_offset_index(buffer,offset+1,index+1);
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ mode=PP_NUMBER_MODE;
+ }
+ break;
+
+ // num
+ case ',':
+ if(mode==PP_NUMBER_MODE && offset[0]>=0 && offset[1]>=0 && index[0]>=0 && index[1]>=0){
+ // write indices and num
+ for(i=0;i<KONDO_SPIN;i++){
+ char_array_snprintf(str_propagator,"%d;%d:%s,",10*(i+10*offset[0])+index[0], 10*(i+10*offset[1])+index[1], buffer);
+ }
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ mode=PP_INDEX_MODE;
+ }
+ break;
+
+ // comment
+ case '#':
+ comment=1;
+ char_array_append(str_kondo_propagator.str[j],str_propagator);
+ break;
+
+ // ignore line breaks
+ case '\n': break;
+
+ default:
+ buffer_ptr=str_addchar(buffer_ptr,str_kondo_propagator.str[j]);
+ break;
+ }
+ }
+ }
+
+ // last step
+ if(mode==PP_NUMBER_MODE){
+ for(i=0;i<KONDO_SPIN;i++){
+ char_array_snprintf(str_propagator,"%d;%d:%s",10*(i+10*offset[0])+index[0], 10*(i+10*offset[1])+index[1], buffer);
+ if(i<KONDO_SPIN-1){
+ char_array_append(',',str_propagator);
+ }
+ }
+ }
+
+ free(buffer);
+ return(0);
+
+}
+
+
+// convert Kondo input polynomial
+int kondo_input_polynomial(Char_Array str_kondo_polynomial, Char_Array* str_polynomial, Fields_Table fields, int box_count){
+ Polynomial tmp_poly;
+ Polynomial out_poly;
+ Char_Array tmp_str_kondo_polynomial;
+ int i;
+ // whether there is a '%' in the input polynomial
+ int star=0;
+
+ init_Char_Array(str_polynomial, STR_SIZE);
+ char_array_snprintf(str_polynomial, "#!input_polynomial\n");
+
+ // check for a '%'
+ for(i=0;i<str_kondo_polynomial.length;i++){
+ if(str_kondo_polynomial.str[i]=='%'){
+ star=1;
+ break;
+ }
+ }
+
+ // if there is a '%', then take a product over boxes
+ if(star==1){
+ // product over i from 1 to box_count
+ for(i=1;i<=box_count;i++){
+ // replace '%' with the appropriate index
+ replace_star('0'+i,str_kondo_polynomial, &tmp_str_kondo_polynomial);
+ // read polynomial
+ parse_kondo_polynomial_factors(tmp_str_kondo_polynomial, &tmp_poly, fields);
+
+ // product
+ if(i==1){
+ polynomial_cpy(tmp_poly,&out_poly);
+ }
+ else{
+ polynomial_prod_chain(tmp_poly,&out_poly, fields);
+ }
+
+ free_Polynomial(tmp_poly);
+ free_Char_Array(tmp_str_kondo_polynomial);
+ }
+ }
+ // if no '%' then read polynomial as is
+ else{
+ parse_kondo_polynomial_factors(str_kondo_polynomial, &out_poly, fields);
+ }
+
+ // useful simplification
+ remove_unmatched_plusminus(&out_poly, fields);
+ polynomial_sprint(out_poly, str_polynomial);
+ free_Polynomial(out_poly);
+ return(0);
+}
+
+
+// convert the Kondo idtable
+int kondo_idtable(Char_Array str_kondo_idtable, Char_Array* str_idtable, Fields_Table fields){
+ int j;
+ // buffer
+ char* buffer=calloc(str_kondo_idtable.length+1,sizeof(char));
+ char* buffer_ptr=buffer;
+ Polynomial tmp_poly;
+ int mode;
+
+ // allocate memory
+ init_Char_Array(str_idtable,STR_SIZE);
+
+ // reproduce the loop from parse_input_id_table but merely copy labels and indices, and replace Kondo polynomials
+ mode=PP_INDEX_MODE;
+ for(j=0;j<str_kondo_idtable.length;j++){
+ // unless inside a polynomial write to output
+ if(mode!=PP_POLYNOMIAL_MODE){
+ char_array_append(str_kondo_idtable.str[j],str_idtable);
+ }
+
+ switch(str_kondo_idtable.str[j]){
+ // end polynomial mode
+ case ',':
+ if(mode==PP_POLYNOMIAL_MODE){
+ mode=PP_INDEX_MODE;
+ // write polynomial
+ parse_kondo_polynomial_str(buffer, &tmp_poly, fields);
+ polynomial_sprint(tmp_poly, str_idtable);
+ free_Polynomial(tmp_poly);
+ char_array_append(',',str_idtable);
+ }
+ break;
+
+ case ':':
+ if(mode==PP_INDEX_MODE){
+ mode=PP_POLYNOMIAL_MODE;
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ break;
+
+ default:
+ if(mode==PP_POLYNOMIAL_MODE){
+ buffer_ptr=str_addchar(buffer_ptr,str_kondo_idtable.str[j]);
+ }
+ break;
+ }
+ }
+
+ //last step
+ if(mode==PP_POLYNOMIAL_MODE){
+ parse_kondo_polynomial_str(buffer, &tmp_poly, fields);
+ polynomial_sprint(tmp_poly, str_idtable);
+ free_Polynomial(tmp_poly);
+ }
+
+ free(buffer);
+ return(0);
+}
+
+// read a product of polynomials
+int parse_kondo_polynomial_factors(Char_Array str_polynomial, Polynomial* output, Fields_Table fields){
+ int j;
+ // buffer
+ char* buffer=calloc(str_polynomial.length+1,sizeof(char));
+ char* buffer_ptr=buffer;
+ Polynomial tmp_poly;
+
+ // allocate memory
+ init_Polynomial(output,POLY_SIZE);
+
+ for(j=0;j<str_polynomial.length;j++){
+ switch(str_polynomial.str[j]){
+ case '*':
+ parse_kondo_polynomial_str(buffer, &tmp_poly, fields);
+ if((*output).length==0){
+ polynomial_concat(tmp_poly, output);
+ }
+ else{
+ polynomial_prod_chain(tmp_poly, output, fields);
+ }
+ free_Polynomial(tmp_poly);
+
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ break;
+
+ default:
+ buffer_ptr=str_addchar(buffer_ptr,str_polynomial.str[j]);
+ break;
+ }
+ }
+
+ //last step
+ parse_kondo_polynomial_str(buffer, &tmp_poly, fields);
+ if((*output).length==0){
+ polynomial_concat(tmp_poly, output);
+ }
+ else{
+ polynomial_prod_chain(tmp_poly, output, fields);
+ }
+ free_Polynomial(tmp_poly);
+
+ free(buffer);
+ return(0);
+}
+
+
+// read a kondo polynomial and convert it to a polynomial expressed in terms of the fields in the fields table
+int parse_kondo_polynomial_str(char* str_polynomial, Polynomial* output, Fields_Table fields){
+ // input pointer
+ char* polynomial_ptr;
+ // buffer
+ char* buffer=calloc(str_len(str_polynomial),sizeof(char));
+ char* buffer_ptr=buffer;
+ int mode;
+ int comment=0;
+ int parenthesis_count=0;
+ int i;
+ int offset1, offset2;
+ int index;
+ Polynomial tmp_poly;
+ Number tmp_num, tmp1_num;
+ Int_Array tmp_factor, tmp_monomial, dummy_factor;
+ Polynomial scalar_prod_poly;
+
+ // allocate memory
+ init_Polynomial(output,POLY_SIZE);
+
+ init_Polynomial(&tmp_poly,MONOMIAL_SIZE);
+ tmp_num=number_one();
+ init_Int_Array(&tmp_factor, MONOMIAL_SIZE);
+
+ *buffer_ptr='\0';
+ // loop over the input polynomial
+ // start in null mode
+ mode=PP_NULL_MODE;
+ for(polynomial_ptr=str_polynomial;*polynomial_ptr!='\0';polynomial_ptr++){
+ if(comment==1){
+ if(*polynomial_ptr=='\n'){
+ comment=0;
+ }
+ }
+ else{
+ switch(*polynomial_ptr){
+ // new monomial
+ case '+':
+ if(mode==PP_NULL_MODE){
+ // if not a constant
+ if(tmp_poly.length>0){
+ // write num
+ polynomial_multiply_scalar(tmp_poly, tmp_num);
+ // replace factor
+ for(i=0;i<tmp_poly.length;i++){
+ free_Int_Array(tmp_poly.factors[i]);
+ int_array_cpy(tmp_factor,tmp_poly.factors+i);
+ }
+ }
+ // if constant
+ else{
+ init_Int_Array(&tmp_monomial,1);
+ polynomial_append(tmp_monomial,tmp_factor,tmp_num,&tmp_poly);
+ free_Int_Array(tmp_monomial);
+ }
+ free_Int_Array(tmp_factor);
+ free_Number(tmp_num);
+ // write polynomial
+ polynomial_concat_noinit(tmp_poly, output);
+ // reset tmp_poly
+ init_Polynomial(&tmp_poly,MONOMIAL_SIZE);
+ tmp_num=number_one();
+ init_Int_Array(&tmp_factor,MONOMIAL_SIZE);
+ }
+ break;
+
+ // numerical pre-factor
+ case '(':
+ if(mode==PP_NULL_MODE){
+ mode=PP_NUMBER_MODE;
+ parenthesis_count=0;
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ else if(mode==PP_NUMBER_MODE){
+ // match parentheses
+ parenthesis_count++;
+ }
+ break;
+ case ')':
+ if(mode==PP_NUMBER_MODE){
+ if(parenthesis_count==0){
+ // write num
+ str_to_Number(buffer,&tmp1_num);
+ number_prod_chain(tmp1_num,&tmp_num);
+ free_Number(tmp1_num);
+ // back to null mode
+ mode=PP_NULL_MODE;
+ }
+ else{
+ parenthesis_count--;
+ }
+ }
+ break;
+
+ // enter factor mode
+ case '[':
+ if(mode==PP_NULL_MODE){
+ mode=PP_BRACKET_MODE;
+ }
+ break;
+ // factor mode
+ case 'l':
+ if(mode==PP_BRACKET_MODE){
+ mode=PP_FACTOR_MODE;
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ break;
+ // symbol mode
+ case 'f':
+ if(mode==PP_BRACKET_MODE){
+ mode=PP_FIELD_MODE;
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ break;
+ // read factor
+ case ']':
+ // factor
+ if(mode==PP_FACTOR_MODE){
+ sscanf(buffer,"%d",&i);
+ int_array_append(i,&tmp_factor);
+ }
+ // symbol
+ else if(mode==PP_FIELD_MODE){
+ // if polynomial exists, add to each monomial
+ if(tmp_poly.length>0){
+ for(i=0;i<tmp_poly.length;i++){
+ int_array_append(get_symbol_index(buffer), tmp_poly.monomials+i);
+ }
+ }
+ // if not, create a new term in the polynomial
+ else{
+ init_Int_Array(&tmp_monomial, MONOMIAL_SIZE);
+ int_array_append(get_symbol_index(buffer), &tmp_monomial);
+ init_Int_Array(&dummy_factor, 1);
+ polynomial_append_noinit(tmp_monomial, dummy_factor, number_one(), &tmp_poly);
+ }
+ }
+ // scalar product of symbols
+ else if(mode==PP_FIELD_SCALAR_MODE || mode==PP_FIELD_VECTOR_PROD_MODE){
+ get_offsets_index(buffer, &offset1, &offset2, &index);
+ // if polynomial exists, add to each monomial
+ if(tmp_poly.length>0){
+ for(i=0;i<tmp_poly.length;i++){
+ if(mode==PP_FIELD_SCALAR_MODE){
+ if(offset1!=KONDO_H_OFFSET || offset2!=KONDO_H_OFFSET){
+ int_array_append(1000*(10*offset1+offset2)+index, tmp_poly.monomials+i);
+ }
+ }
+ else{
+ int_array_append(100*(100*KONDO_A_OFFSET+10*KONDO_B_OFFSET+KONDO_H_OFFSET)+index, tmp_poly.monomials+i);
+ }
+ }
+ }
+ // if not, create a new term in the polynomial
+ else{
+ init_Int_Array(&tmp_monomial, MONOMIAL_SIZE);
+ if(mode==PP_FIELD_SCALAR_MODE){
+ if(offset1!=KONDO_H_OFFSET || offset2!=KONDO_H_OFFSET){
+ int_array_append(1000*(10*offset1+offset2)+index, &tmp_monomial);
+ }
+ }
+ else{
+ int_array_append(100*(100*KONDO_A_OFFSET+10*KONDO_B_OFFSET+KONDO_H_OFFSET)+index, &tmp_monomial);
+ }
+ init_Int_Array(&dummy_factor, 1);
+ polynomial_append_noinit(tmp_monomial, dummy_factor, number_one(), &tmp_poly);
+ }
+ /* // older method in which a scalar product was expanded in A, B and h
+ // resolve scalar product
+ kondo_resolve_scalar_prod_symbols(buffer, &scalar_prod_poly);
+ // add to tmp_poly
+ if(tmp_poly.length==0){
+ polynomial_concat(scalar_prod_poly,&tmp_poly);
+ }
+ else{
+ polynomial_prod_chain(scalar_prod_poly,&tmp_poly,fields);
+ }
+ free_Polynomial(scalar_prod_poly);
+ */
+ }
+ // switch back to null mode
+ mode=PP_NULL_MODE;
+ break;
+
+ // symbol scalar product
+ case '.':
+ if(mode==PP_FIELD_MODE){
+ mode=PP_FIELD_SCALAR_MODE;
+ }
+ buffer_ptr=str_addchar(buffer_ptr,*polynomial_ptr);
+ break;
+ case 'x':
+ if(mode==PP_FIELD_MODE){
+ mode=PP_FIELD_VECTOR_PROD_MODE;
+ }
+ buffer_ptr=str_addchar(buffer_ptr,*polynomial_ptr);
+ break;
+
+ // scalar product
+ case '<':
+ if(mode==PP_NULL_MODE){
+ mode=PP_MONOMIAL_MODE;
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ break;
+ case '>':
+ if(mode==PP_MONOMIAL_MODE){
+ // resolve scalar product
+ kondo_resolve_scalar_prod(buffer, &scalar_prod_poly, fields);
+ // add to tmp_poly
+ if(tmp_poly.length==0){
+ polynomial_concat(scalar_prod_poly,&tmp_poly);
+ }
+ else{
+ polynomial_prod_chain(scalar_prod_poly,&tmp_poly,fields);
+ }
+ free_Polynomial(scalar_prod_poly);
+
+ mode=PP_NULL_MODE;
+ }
+ break;
+
+ // characters to ignore
+ case ' ':break;
+ case '&':break;
+ case '\n':break;
+
+ // comments
+ case '#':
+ comment=1;
+ break;
+
+ default:
+ if(mode!=PP_NULL_MODE){
+ // write to buffer
+ buffer_ptr=str_addchar(buffer_ptr,*polynomial_ptr);
+ }
+ break;
+ }
+ }
+ }
+
+ // last term
+ if(tmp_poly.length>0){
+ polynomial_multiply_scalar(tmp_poly,tmp_num);
+ for(i=0;i<tmp_poly.length;i++){
+ free_Int_Array(tmp_poly.factors[i]);
+ int_array_cpy(tmp_factor,tmp_poly.factors+i);
+ }
+ }
+ else{
+ init_Int_Array(&tmp_monomial,1);
+ polynomial_append(tmp_monomial,tmp_factor,tmp_num,&tmp_poly);
+ }
+ free_Int_Array(tmp_factor);
+ free_Number(tmp_num);
+ polynomial_concat_noinit(tmp_poly, output);
+
+ // simplify
+ polynomial_simplify(output, fields);
+
+ free(buffer);
+ return(0);
+}
+
+// as Char_Array
+int parse_kondo_polynomial(Char_Array kondo_polynomial_str, Polynomial* polynomial, Fields_Table fields){
+ char* str;
+ char_array_to_str(kondo_polynomial_str, &str);
+ parse_kondo_polynomial_str(str, polynomial, fields);
+ free(str);
+ return(0);
+}
+
+
+// read Aij, Bij, hi where i is a space dimension and j is a box index
+int kondo_resolve_ABh(char* str, Polynomial* output, Fields_Table fields){
+ char* ptr;
+ // offset (A,B or H)
+ int offset=-1;
+ // dimension
+ int dim=-1;
+ // box index
+ int index=-1;
+ // polynomial for each term
+ Polynomial psi[KONDO_SPIN];
+ Polynomial poly_conjugate;
+ Int_Array monomial;
+ Int_Array factor;
+ Number_Matrix pauli_mat;
+ int i,a,b;
+
+ // memory
+ init_Polynomial(output, MONOMIAL_SIZE);
+
+ for(ptr=str;*ptr!='\0';ptr++){
+ switch(*ptr){
+ case 'A':
+ offset=KONDO_A_OFFSET;
+ break;
+ case 'a':
+ offset=KONDO_A_OFFSET;
+ break;
+ case 'B':
+ offset=KONDO_B_OFFSET;
+ break;
+ case 'b':
+ offset=KONDO_B_OFFSET;
+ break;
+ case 'h':
+ offset=KONDO_H_OFFSET;
+ break;
+ default:
+ // set index if dim was already set
+ if(dim>=0){
+ index=*ptr-'0';
+ }
+ else{
+ dim=*ptr-'0';
+ }
+ }
+ }
+
+ // turn B3 into B2 and B4 into B1
+ if(offset==KONDO_B_OFFSET){
+ switch(index){
+ case 3:
+ index=2;
+ break;
+ case 4:
+ index=1;
+ break;
+ }
+ }
+
+ // h's
+ if(offset==KONDO_H_OFFSET){
+ // external field
+ init_Int_Array(&monomial,1);
+ init_Int_Array(&factor,1);
+ int_array_append(10*(dim+10*offset), &monomial);
+ polynomial_append_noinit(monomial, factor, number_one(), output);
+ }
+ // psi's
+ else{
+ // construct spin indices
+ for(i=0;i<KONDO_SPIN;i++){
+ init_Polynomial(psi+i,2);
+
+ // external field
+ init_Int_Array(&monomial,1);
+ init_Int_Array(&factor,1);
+ int_array_append(10*(i+10*offset), &monomial);
+ polynomial_append_noinit(monomial, factor, number_one(), psi+i);
+
+ // internal field if applicable
+ if(index>0){
+ init_Int_Array(&monomial,1);
+ init_Int_Array(&factor,1);
+
+ int_array_append(10*(i+10*offset)+index, &monomial);
+ polynomial_append_noinit(monomial, factor, number_one(), psi+i);
+ }
+ }
+
+ // multiply by Pauli matrices
+ Pauli_matrix(dim+1,&pauli_mat);
+ for(a=0;a<KONDO_SPIN;a++){
+ for(b=0;b<KONDO_SPIN;b++){
+ polynomial_cpy(psi[b],&poly_conjugate);
+ polynomial_conjugate(poly_conjugate);
+ polynomial_multiply_scalar(poly_conjugate, pauli_mat.matrix[a][b]);
+ polynomial_prod_chain(psi[a],&poly_conjugate,fields);
+ // add to poly
+ polynomial_concat_noinit(poly_conjugate, output);
+ }
+ }
+
+ free_Number_Matrix(pauli_mat);
+
+ // free spin indices
+ for(i=0;i<KONDO_SPIN;i++){
+ free_Polynomial(psi[i]);
+ }
+ }
+
+ return(0);
+}
+
+#define K_VECT_PROD 1
+#define K_SCALAR_PROD 2
+// read a Kondo scalar product (generalized to vector products as well)
+int kondo_resolve_scalar_prod(char* str, Polynomial* output, Fields_Table fields){
+ char* ptr;
+ // offset of each term (A,B or H)
+ int offset=-1;
+ // index of each term (0,...,box_count)
+ int index=0;
+ int i;
+ int operation=0;
+ Polynomial poly_vect1[KONDO_DIM];
+ Polynomial poly_vect2[KONDO_DIM];
+
+ // memory
+ init_Polynomial(output, MONOMIAL_SIZE);
+
+ for(ptr=str;*ptr!='\0';ptr++){
+ switch(*ptr){
+ case 'A':
+ offset=KONDO_A_OFFSET;
+ break;
+ case 'a':
+ offset=KONDO_A_OFFSET;
+ break;
+ case 'B':
+ offset=KONDO_B_OFFSET;
+ break;
+ case 'b':
+ offset=KONDO_B_OFFSET;
+ break;
+ case 'h':
+ offset=KONDO_H_OFFSET;
+ break;
+
+ // scalar product
+ case '.':
+ // if no previous vector product
+ if(operation!=K_VECT_PROD){
+ kondo_polynomial_vector(offset, index, &poly_vect1, fields);
+ }
+ // compute vector product
+ else{
+ kondo_polynomial_vector(offset, index, &poly_vect2, fields);
+ kondo_polynomial_vector_product(&poly_vect1, poly_vect2, fields);
+ }
+ operation=K_SCALAR_PROD;
+ break;
+
+ // vector product
+ case 'x':
+ if(offset>=0){
+ kondo_polynomial_vector(offset, index, &poly_vect1, fields);
+ operation=K_VECT_PROD;
+ }
+ break;
+
+ // index
+ default:
+ // char to int
+ index=*ptr-'0';
+ }
+ }
+
+ // final scalar product
+ if(operation==K_SCALAR_PROD){
+ if(offset>=0){
+ kondo_polynomial_vector(offset, index, &poly_vect2, fields);
+ kondo_polynomial_scalar_product(poly_vect1, poly_vect2, output, fields);
+ }
+ }
+
+ // free memory
+ for(i=0;i<KONDO_DIM;i++){
+ free_Polynomial(poly_vect1[i]);
+ free_Polynomial(poly_vect2[i]);
+ }
+
+ return(0);
+}
+
+// compute a scalar product of polynomial vectors
+int kondo_polynomial_scalar_product(Polynomial poly_vect1[3], Polynomial poly_vect2[3], Polynomial* output, Fields_Table fields){
+ int i;
+ Polynomial tmp_poly;
+
+ for(i=0;i<KONDO_DIM;i++){
+ polynomial_prod(poly_vect1[i],poly_vect2[i],&tmp_poly,fields);
+
+ // add to output
+ polynomial_concat_noinit(tmp_poly, output);
+ }
+
+ polynomial_simplify(output, fields);
+
+ return(0);
+}
+
+// compute a vector product of polynomial vectors
+int kondo_polynomial_vector_product(Polynomial (*poly_vect1)[3], Polynomial poly_vect2[3], Fields_Table fields){
+ int i;
+ Polynomial out[3];
+ Polynomial tmp_poly;
+
+ for(i=0;i<3;i++){
+ init_Polynomial(out+i, POLY_SIZE);
+
+ polynomial_prod((*poly_vect1)[(i+1)%3],poly_vect2[(i+2)%3], &tmp_poly, fields);
+ polynomial_concat_noinit(tmp_poly, out+i);
+
+ polynomial_prod((*poly_vect1)[(i+2)%3],poly_vect2[(i+1)%3], &tmp_poly, fields);
+ polynomial_multiply_Qscalar(tmp_poly,quot(-1,1));
+ polynomial_concat_noinit(tmp_poly, out+i);
+ }
+
+ for(i=0;i<3;i++){
+ free_Polynomial((*poly_vect1)[i]);
+ (*poly_vect1)[i]=out[i];
+ }
+
+ return(0);
+}
+
+// compute the 3 components of a kondo vector
+int kondo_polynomial_vector(int offset, int index, Polynomial (*polys)[3], Fields_Table fields){
+ int i,a,b;
+ // polynomial for each term
+ Polynomial psi[KONDO_SPIN];
+ Polynomial poly_conjugate;
+ Int_Array monomial;
+ Int_Array factor;
+ Number_Matrix pauli_mat;
+
+ for(i=0;i<KONDO_DIM;i++){
+ // memory
+ init_Polynomial((*polys)+i,POLY_SIZE);
+ }
+
+ // h's
+ if(offset==KONDO_H_OFFSET){
+ // construct every component field
+ for(i=0;i<KONDO_DIM;i++){
+ // external field
+ init_Int_Array(&monomial,1);
+ init_Int_Array(&factor,1);
+ int_array_append(10*(i+10*offset), &monomial);
+ polynomial_append_noinit(monomial, factor, number_one(), (*polys)+i);
+ }
+ }
+ // psi's
+ else{
+ // construct spin indices
+ for(i=0;i<KONDO_SPIN;i++){
+ init_Polynomial(psi+i,2);
+
+ // external field
+ init_Int_Array(&monomial,1);
+ init_Int_Array(&factor,1);
+ int_array_append(10*(i+10*offset), &monomial);
+ polynomial_append_noinit(monomial, factor, number_one(), psi+i);
+
+ // internal field if applicable
+ if(index>0){
+ init_Int_Array(&monomial,1);
+ init_Int_Array(&factor,1);
+
+ int_array_append(10*(i+10*offset)+index, &monomial);
+ polynomial_append_noinit(monomial, factor, number_one(), psi+i);
+ }
+ }
+
+ // multiply by Pauli matrices
+ for(i=0;i<KONDO_DIM;i++){
+ Pauli_matrix(i+1,&pauli_mat);
+ for(a=0;a<KONDO_SPIN;a++){
+ for(b=0;b<KONDO_SPIN;b++){
+ polynomial_cpy(psi[b],&poly_conjugate);
+ polynomial_conjugate(poly_conjugate);
+ polynomial_multiply_scalar(poly_conjugate, pauli_mat.matrix[a][b]);
+ polynomial_prod_chain(psi[a],&poly_conjugate,fields);
+ // add to polys[j]
+ polynomial_concat_noinit(poly_conjugate, (*polys)+i);
+ }
+ }
+
+ free_Number_Matrix(pauli_mat);
+ }
+
+ // free spin indices
+ for(i=0;i<KONDO_SPIN;i++){
+ free_Polynomial(psi[i]);
+ }
+ }
+
+ return(0);
+}
+
+// read a scalar product of symbols
+int kondo_resolve_scalar_prod_symbols(char* str, Polynomial* output){
+ char* ptr;
+ // first or second term
+ int term=0;
+ // offset of each term (A,B or H)
+ int offset[2];
+ // index of each term (0,...,box_count)
+ int index[2]={0,0};
+ Int_Array monomial;
+ Int_Array factor;
+ int i;
+
+ // memory
+ init_Polynomial(output, KONDO_DIM);
+
+ for(ptr=str;*ptr!='\0';ptr++){
+ switch(*ptr){
+ case 'A':
+ offset[term]=KONDO_A_OFFSET;
+ break;
+ case 'a':
+ offset[term]=KONDO_A_OFFSET;
+ break;
+ case 'B':
+ offset[term]=KONDO_B_OFFSET;
+ break;
+ case 'b':
+ offset[term]=KONDO_B_OFFSET;
+ break;
+ case 'h':
+ offset[term]=KONDO_H_OFFSET;
+ break;
+ // switch term
+ case '.':
+ term=1-term;
+ break;
+ default:
+ // char to int
+ index[term]=*ptr-'0';
+ }
+ }
+
+ // scalar product
+ for(i=0;i<KONDO_DIM;i++){
+ init_Int_Array(&monomial,2);
+ init_Int_Array(&factor, 1);
+
+ if(offset[0]==KONDO_H_OFFSET){
+ int_array_append(10*(10*offset[0]+i)+index[0], &monomial);
+ }
+ else{
+ int_array_append(100*(10*offset[0]+i)+index[0], &monomial);
+ }
+ if(offset[1]==KONDO_H_OFFSET){
+ int_array_append(10*(10*offset[1]+i)+index[1], &monomial);
+ }
+ else{
+ int_array_append(100*(10*offset[1]+i)+index[1], &monomial);
+ }
+
+ polynomial_append_noinit(monomial, factor, number_one(), output);
+ }
+ return(0);
+}
+
+// get the offset and index of a monomial term
+// (e.g. A1 yields KONDO_A_OFFSET and 1)
+int get_offset_index(char* str, int* offset, int* index){
+ char* ptr;
+
+ for(ptr=str;*ptr!='\0';ptr++){
+ switch(*ptr){
+ case 'A':
+ *offset=KONDO_A_OFFSET;
+ break;
+ case 'a':
+ *offset=KONDO_A_OFFSET;
+ break;
+ case 'B':
+ *offset=KONDO_B_OFFSET;
+ break;
+ case 'b':
+ *offset=KONDO_B_OFFSET;
+ break;
+ case 'h':
+ *offset=KONDO_H_OFFSET;
+ break;
+ default:
+ // char to int
+ *index=*ptr-'0';
+ }
+ }
+
+ return(0);
+}
+
+// get the offsets and index of a scalar product
+int get_offsets_index(char* str, int* offset1, int* offset2, int* index){
+ int offset[2]={-1,-1};
+ char* ptr;
+ int term=0;
+
+ *index=-1;
+
+ for(ptr=str;*ptr!='\0';ptr++){
+ switch(*ptr){
+ case 'A':
+ offset[term]=KONDO_A_OFFSET;
+ break;
+ case 'a':
+ offset[term]=KONDO_A_OFFSET;
+ break;
+ case 'B':
+ offset[term]=KONDO_B_OFFSET;
+ break;
+ case 'b':
+ offset[term]=KONDO_B_OFFSET;
+ break;
+ case 'h':
+ offset[term]=KONDO_H_OFFSET;
+ break;
+ // switch term
+ case '.':
+ term=1-term;
+ break;
+ default:
+ // char to int
+ *index=*ptr-'0';
+ }
+ }
+
+ *offset1=offset[0];
+ *offset2=offset[1];
+
+ return(0);
+}
+
+// get the index of the symbol corresponding to a given string
+int get_symbol_index(char* str){
+ char* ptr;
+ int offset=-1;
+ int index=0;
+ int dim=-1;
+
+ // first check whether the field already is an index
+ for(ptr=str;*ptr!='\0';ptr++){
+ if((*ptr-'0'>=10 || *ptr-'0'<0) && (*ptr!='-')){
+ break;
+ }
+ }
+ if(*ptr=='\0'){
+ sscanf(str,"%d",&index);
+ return(index);
+ }
+
+ for(ptr=str;*ptr!='\0';ptr++){
+ switch(*ptr){
+ case 'A':
+ offset=KONDO_A_OFFSET;
+ break;
+ case 'a':
+ offset=KONDO_A_OFFSET;
+ break;
+ case 'B':
+ offset=KONDO_B_OFFSET;
+ break;
+ case 'b':
+ offset=KONDO_B_OFFSET;
+ break;
+ case 'h':
+ offset=KONDO_H_OFFSET;
+ break;
+ default:
+ // set index if dim was already set
+ if(dim>=0){
+ index=*ptr-'0';
+ }
+ else{
+ dim=*ptr-'0';
+ }
+ }
+ }
+
+ if(offset==-1){
+ return(-1);
+ }
+ // no symbol for h
+ if(offset==KONDO_H_OFFSET){
+ return(10*(10*offset+dim));
+ }
+ else{
+ return(100*(10*offset+dim)+index);
+ }
+}
diff --git a/src/kondo.h b/src/kondo.h
new file mode 100644
index 0000000..23756ad
--- /dev/null
+++ b/src/kondo.h
@@ -0,0 +1,76 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/* Generate configuration files specific to the Kondo model */
+
+#ifndef KONDO_H
+#define KONDO_H
+
+#include "types.h"
+
+// generate configuration file
+int kondo_generate_conf(Str_Array* str_args, int box_count);
+
+// generate the Kondo fields table
+int kondo_fields_table(int box_count, Char_Array* str_fields, Fields_Table* fields);
+
+// generate Kondo symbols
+int kondo_symbols(Char_Array* str_symbols, int box_count, Fields_Table* fields);
+// generate Kondo symbols (older method: one symbol for each scalar product)
+int kondo_symbols_scalarprod(Char_Array* str_symbols, int box_count, Fields_Table* fields);
+
+// generate Kondo groups (groups of independent variables)
+int kondo_groups(Char_Array* str_groups, int box_count);
+
+// generate Kondo identities
+int kondo_identities(Char_Array* str_identities);
+
+// convert the Kondo propagator
+int kondo_propagator(Char_Array str_kondo_propagator, Char_Array* str_propagator);
+
+// read a product of polynomials
+int parse_kondo_polynomial_factors(Char_Array str_polynomial, Polynomial* output, Fields_Table fields);
+
+// convert Kondo input polynomial
+int kondo_input_polynomial(Char_Array str_kondo_polynomial, Char_Array* str_polynomial, Fields_Table fields, int box_count);
+
+// convert the Kondo idtable
+int kondo_idtable(Char_Array str_kondo_idtable, Char_Array* str_idtable, Fields_Table fields);
+
+// read a kondo polynomial and convert it to a polynomial expressed in terms of the fields in the fields table
+int parse_kondo_polynomial_str(char* str_polynomial, Polynomial* output, Fields_Table fields);
+int parse_kondo_polynomial(Char_Array kondo_polynomial_str, Polynomial* polynomial, Fields_Table fields);
+
+// read Aij, Bij, hi where i is a space dimension and j is a box index
+int kondo_resolve_ABh(char* str, Polynomial* output, Fields_Table fields);
+// read a Kondo scalar product
+int kondo_resolve_scalar_prod(char* str, Polynomial* output, Fields_Table fields);
+// compute a scalar product of polynomial vectors
+int kondo_polynomial_scalar_product(Polynomial poly_vect1[3], Polynomial poly_vect2[3], Polynomial* output, Fields_Table fields);
+// compute a vector product of polynomial vectors
+int kondo_polynomial_vector_product(Polynomial (*poly_vect1)[3], Polynomial poly_vect2[3], Fields_Table fields);
+// compute the 3 components of a kondo vector
+int kondo_polynomial_vector(int offset, int index, Polynomial (*polys)[3], Fields_Table fields);
+// read a scalar product of symbols
+int kondo_resolve_scalar_prod_symbols(char* str, Polynomial* output);
+
+// get the offset and index of a monomial term
+int get_offset_index(char* str, int* offset, int* index);
+// get the offsets and index of a scalar product
+int get_offsets_index(char* str, int* offset1, int* offset2, int* index);
+// get the index of the symbol corresponding to a given string
+int get_symbol_index(char* str);
+#endif
diff --git a/src/kondo_preprocess.c b/src/kondo_preprocess.c
new file mode 100644
index 0000000..3371014
--- /dev/null
+++ b/src/kondo_preprocess.c
@@ -0,0 +1,126 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+kondo_preprocess
+
+Generate configuration files for the Kondo problem
+
+*/
+
+
+#include <stdio.h>
+#include <stdlib.h>
+
+#include "definitions.cpp"
+#include "kondo.h"
+#include "cli_parser.h"
+#include "array.h"
+
+
+// read cli arguments
+int read_args_kondo_pp(int argc,const char* argv[], Str_Array* str_args, Kondopp_Options* opts);
+// print usage message
+int print_usage_kondo_pp();
+
+int main (int argc, const char* argv[]){
+ int i;
+ // string arguments
+ Str_Array str_args;
+ // options
+ Kondopp_Options opts;
+
+ // read command-line arguments
+ read_args_kondo_pp(argc,argv,&str_args,&opts);
+
+ kondo_generate_conf(&str_args, 2*opts.dimension);
+ for(i=0;i<str_args.length;i++){
+ printf("%s\n",str_args.strs[i].str);
+ if(i<str_args.length-1){
+ printf("&\n");
+ }
+ }
+
+ //free memory
+ free_Str_Array(str_args);
+ return(0);
+}
+
+
+// read cli arguments
+#define CP_FLAG_DIMENSION 1
+int read_args_kondo_pp(int argc,const char* argv[], Str_Array* str_args, Kondopp_Options* opts){
+ int i;
+ // pointers
+ char* ptr;
+ // file to read the polynomial from in flow mode
+ const char* file="";
+ // flag that indicates what argument is being read
+ int flag=0;
+ // whether a file was specified on the command-line
+ int exists_file=0;
+
+
+ // if there are no arguments
+ if(argc==1){
+ print_usage_kondo_pp();
+ exit(-1);
+ }
+
+ // defaults
+ // dimensions (including time)
+ (*opts).dimension=2;
+
+// loop over arguments
+for(i=1;i<argc;i++){
+ // flag
+ if(argv[i][0]=='-'){
+ for(ptr=((char*)argv[i])+1;*ptr!='\0';ptr++){
+ switch(*ptr){
+ case 'd':
+ flag=CP_FLAG_DIMENSION;
+ break;
+ // print version
+ case 'v':
+ printf("kondo_preprocess " VERSION "\n");
+ exit(1);
+ break;
+ }
+ }
+ }
+ // number of dimensions
+ else if (flag==CP_FLAG_DIMENSION){
+ sscanf(argv[i],"%d",&((*opts).dimension));
+ flag=0;
+ }
+ // read file name from command-line
+ else{
+ file=argv[i];
+ exists_file=1;
+ }
+ }
+
+ read_config_file(str_args, file, 1-exists_file);
+
+ return(0);
+}
+
+// print usage message
+int print_usage_kondo_pp(){
+ printf("\nusage:\n kondo_preprocess [-d dimension] <filename>\n\n");
+ return(0);
+}
+
diff --git a/src/mean.c b/src/mean.c
new file mode 100644
index 0000000..aad7a5a
--- /dev/null
+++ b/src/mean.c
@@ -0,0 +1,793 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+As of version 1.0, the mean of a monomial is computed directly
+*/
+
+#include "mean.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <pthread.h>
+#include "definitions.cpp"
+#include "tools.h"
+#include "polynomial.h"
+#include "rational.h"
+#include "array.h"
+#include "fields.h"
+#include "number.h"
+
+// mean of a monomial
+int mean(Int_Array monomial, Polynomial* out, Fields_Table fields, Polynomial_Matrix propagator){
+ int sign=1;
+ // +/- internal fields
+ Int_Array internal_plus;
+ Int_Array internal_minus;
+
+ // init out
+ *out=polynomial_one();
+
+ // sort first
+ monomial_sort(monomial, 0, monomial.length-1, fields, &sign);
+ polynomial_multiply_Qscalar(*out, quot(sign,1));
+ // get internals
+ // (*out).monomials is the first element of out but it only has 1 element
+ // first, free (*out).monomials[0]
+ free_Int_Array((*out).monomials[0]);
+ get_internals(monomial, &internal_plus, &internal_minus, (*out).monomials, fields);
+
+ if(internal_plus.length>0 && internal_minus.length>0){
+ mean_internal(internal_plus, internal_minus, out, propagator, fields);
+ }
+
+ free_Int_Array(internal_plus);
+ free_Int_Array(internal_minus);
+ return(0);
+}
+
+// compute the mean of a monomial of internal fields (with split + and -)
+int mean_internal(Int_Array internal_plus, Int_Array internal_minus, Polynomial* out, Polynomial_Matrix propagator, Fields_Table fields){
+ if(internal_plus.length!=internal_minus.length){
+ fprintf(stderr,"error: monomial contains unmatched +/- fields\n");
+ exit(-1);
+ }
+ int n=internal_minus.length;
+ // pairing as an array of positions
+ int* pairing=calloc(n,sizeof(int));
+ // specifies which indices are available for pairing
+ int* mask=calloc(n,sizeof(int));
+ // signature of the permutation
+ int pairing_sign;
+ // sign from mixing - and + together
+ int mixing_sign;
+ Polynomial num;
+ Polynomial num_summed=polynomial_zero();
+ // propagator matrix indices
+ int* indices_minus=calloc(n,sizeof(int));
+ int* indices_plus=calloc(n,sizeof(int));
+ int i;
+ // whether the next pairing exists
+ int exists_next=0;
+
+ // indices
+ for(i=0;i<n;i++){
+ indices_plus[i]=intlist_find_err(propagator.indices, propagator.length, internal_plus.values[i]);
+ indices_minus[i]=intlist_find_err(propagator.indices, propagator.length, -internal_minus.values[i]);
+ }
+
+ // init pairing and mask
+ exists_next=init_pairing(pairing, mask, n, propagator, indices_plus, indices_minus)+1;
+
+ // initial sign
+ pairing_sign=permutation_signature(pairing,n);
+
+ // mixing sign (from ordering psi+psi-): (-1)^{n(n+1)/2}
+ if((n*(n+1))/2 %2 ==0){
+ mixing_sign=1;
+ }
+ else{
+ mixing_sign=-1;
+ }
+
+ // loop over pairings
+ // loop ends when the first pairing leaves the array
+ while(exists_next==1){
+ num=polynomial_one();
+ // propagator product for the current pairing (only simplify after all pairings)
+ for(i=0;i<n;i++){
+ polynomial_prod_chain_nosimplify(propagator.matrix[indices_plus[i]][indices_minus[pairing[i]]],&num, fields);
+ }
+ polynomial_multiply_Qscalar(num,quot(mixing_sign*pairing_sign,1));
+ polynomial_concat_noinit_inplace(num,&num_summed);
+
+ exists_next=next_pairing(pairing, mask, n, propagator, indices_plus, indices_minus)+1;
+ pairing_sign=permutation_signature(pairing,n);
+ }
+
+ // only simplify in mean_symbols
+ polynomial_prod_chain_nosimplify(num_summed,out,fields);
+ free_Polynomial(num_summed);
+ free(pairing);
+ free(mask);
+ free(indices_plus);
+ free(indices_minus);
+ return(0);
+}
+
+// first pairing with a non-vanishing propagator
+int init_pairing(int* pairing, int* mask, int n, Polynomial_Matrix propagator, int* indices_plus, int* indices_minus){
+ // index we want to increment
+ int move=0;
+ int i;
+ for(i=0;i<n;i++){
+ pairing[i]=-1;
+ mask[i]=0;
+ }
+
+ // loop until move is out of range
+ while(move>=0 && move<n){
+ // move
+ pairing[move]=next_wick(move, pairing[move], mask, n, propagator, indices_plus, indices_minus);
+ // if the next term does not exist, then move previous index
+ if(pairing[move]==-1){
+ move--;
+ }
+ // else move next index
+ else{
+ move++;
+ }
+ }
+
+ // if move==-1, then there is no first term, return -1
+ if(move==-1){
+ return(-1);
+ }
+ // if the first term exists
+ return(0);
+}
+
+// next pairing with a non-vanishing propagator
+int next_pairing(int* pairing, int* mask, int n, Polynomial_Matrix propagator, int* indices_plus, int* indices_minus){
+ // index we want to increment
+ int move=n-1;
+
+ // last index
+ mask[pairing[n-1]]=0;
+
+ // loop until move is out of range
+ while(move>=0 && move<n){
+ // move
+ pairing[move]=next_wick(move, pairing[move], mask, n, propagator, indices_plus, indices_minus);
+ // if the next term does not exist, then move previous index
+ if(pairing[move]==-1){
+ move--;
+ }
+ // else move next index
+ else{
+ move++;
+ }
+ }
+
+ // if move==-1, then there is no next term, return -1
+ if(move==-1){
+ return(-1);
+ }
+ // if the next term exists
+ return(0);
+}
+
+// next term in the Wick expansion
+int next_wick(int index, int start, int* mask, int n, Polynomial_Matrix propagator, int* indices_plus, int* indices_minus){
+ int i;
+ // unset mask
+ if(start>=0 && start<n){
+ mask[start]=0;
+ }
+ // find next position
+ for(i=start+1;i<n;i++){
+ // if the propagator doesn't vanish
+ if(mask[i]==0 && polynomial_is_zero(propagator.matrix[indices_plus[index]][indices_minus[i]])==0){
+ mask[i]=1;
+ return(i);
+ }
+ }
+ // no next term
+ return(-1);
+}
+
+
+/* Older function: propagator as number
+// compute the mean of a monomial of internal fields (with split + and -)
+// compute all contractions
+int mean_internal_slow(Int_Array internal_plus, Int_Array internal_minus, Number* outnum, Polynomial_Matrix propagator){
+ if(internal_plus.length!=internal_minus.length){
+ fprintf(stderr,"error: monomial contains unmatched +/- fields\n");
+ exit(-1);
+ }
+ int n=internal_minus.length;
+ // pairing as an array of positions
+ int* pairing=calloc(n,sizeof(int));
+ // specifies which indices are available for pairing
+ int* mask=calloc(n,sizeof(int));
+ // signature of the permutation
+ int pairing_sign;
+ // sign from mixing - and + together
+ int mixing_sign;
+ Number num;
+ Number num_summed=number_zero();
+ // propagator matrix indices
+ int index1, index2;
+ int i,j,k,l;
+
+ // init pairing and mask
+ for(i=0;i<n-1;i++){
+ pairing[i]=i;
+ mask[i]=1;
+ }
+ pairing[n-1]=n-1;
+ pairing_sign=1;
+
+ // mixing sign: (-1)^{n(n+1)/2}
+ if((n*(n+1))/2 %2 ==0){
+ mixing_sign=1;
+ }
+ else{
+ mixing_sign=-1;
+ }
+
+ // loop over pairings
+ // loop ends when the first pairing leaves the array
+ while(pairing[0]<n){
+ num=number_one();
+ // propagator product for the current pairing
+ for(i=0;i<n;i++){
+ // indices within the propagator matrix
+ index1=intlist_find_err(propagator.indices, propagator.length, internal_plus.values[i]);
+ index2=intlist_find_err(propagator.indices, propagator.length, -internal_minus.values[pairing[i]]);
+
+ number_prod_chain(propagator.matrix[index1][index2],&num);
+ }
+ number_Qprod_chain(quot(mixing_sign*pairing_sign,1),&num);
+ number_add_chain(num,&num_summed);
+ free_Number(num);
+
+ // next pairing
+ // last element of the pairing that we can move
+ for(i=n-1;i>=0;i--){
+ // move i-th
+ mask[pairing[i]]=0;
+ // search for next possible position
+ for(j=pairing[i]+1;j<n;j++){
+ if(mask[j]==0){
+ break;
+ }
+ }
+
+ // if the next position exists
+ if(j<n){
+ // sign correction: change sign by (-1)^{1+(n-i)(n-i-1)/2}
+ // actually (-1)^{1+(n-1-i)(n-1-i-1)/2
+ if(((n-i-1)*(n-i-2))/2 % 2==0){
+ pairing_sign*=-1;
+ }
+
+ pairing[i]=j;
+ mask[j]=1;
+ // put the remaining pairings at their left-most possible values
+ if(i<n-1){
+ k=i+1;
+ for(l=0;l<n;l++){
+ if(mask[l]==0){
+ mask[l]=1;
+ pairing[k]=l;
+ k++;
+ // if exhausted all indices
+ if(k>=n){
+ break;
+ }
+ }
+ }
+ }
+ // if the next position was found, then don't try to move the previous pairings
+ break;
+ }
+ // if no next position is found, store the pairing outside the array (so the algorithm stops when the first pairing is outside the array)
+ else{
+ pairing[i]=n;
+ }
+ }
+ }
+
+ number_prod_chain(num_summed,outnum);
+ free_Number(num_summed);
+ free(pairing);
+ free(mask);
+ return(0);
+}
+*/
+
+
+// get lists of internal fields from a monomial (separate + and -)
+// requires the monomial to be sorted (for the sign to be correct)
+int get_internals(Int_Array monomial, Int_Array* internal_plus, Int_Array* internal_minus, Int_Array* others, Fields_Table fields){
+ int i;
+ init_Int_Array(internal_plus, monomial.length);
+ init_Int_Array(internal_minus, monomial.length);
+ init_Int_Array(others, monomial.length);
+ for (i=0;i<monomial.length;i++){
+ if(int_array_find(abs(monomial.values[i]),fields.internal)>=0){
+ // split +/- fields
+ if(monomial.values[i]>0){
+ int_array_append(monomial.values[i],internal_plus);
+ }
+ else{
+ int_array_append(monomial.values[i],internal_minus);
+ }
+ }
+ else{
+ int_array_append(monomial.values[i], others);
+ }
+ }
+ return(0);
+}
+
+
+// compute the mean of a monomial containing symbolic expressions
+// keep track of which means were already computed
+int mean_symbols(Int_Array monomial, Polynomial* output, Fields_Table fields, Polynomial_Matrix propagator, Groups groups, Identities* computed){
+ Int_Array symbol_list;
+ int i;
+ int power;
+ int* current_term;
+ Polynomial mean_num;
+ Int_Array tmp_monomial;
+ Number tmp_num;
+ Int_Array base_monomial;
+ int sign;
+ // whether or not the next term exists
+ int exists_next=0;
+ // simplify polynomial periodically
+ int simplify_freq=1;
+ Polynomial mean_poly;
+
+ init_Polynomial(output, POLY_SIZE);
+
+ // check whether the mean was already computed
+ for(i=0;i<(*computed).length;i++){
+ if(int_array_cmp((*computed).lhs[i], monomial)==0){
+ // write polynomial
+ polynomial_concat((*computed).rhs[i], output);
+ return(0);
+ }
+ }
+
+ init_Int_Array(&symbol_list, monomial.length);
+ init_Int_Array(&base_monomial, monomial.length);
+
+ // generate symbols list
+ for(i=0;i<monomial.length;i++){
+ if(field_type(monomial.values[i], fields)==FIELD_SYMBOL){
+ int_array_append(intlist_find_err(fields.symbols.indices, fields.symbols.length, monomial.values[i]), &symbol_list);
+ }
+ else{
+ int_array_append(monomial.values[i], &base_monomial);
+ }
+ }
+ power=symbol_list.length;
+
+ // trivial case
+ if(power==0){
+ mean(monomial, &mean_num, fields, propagator);
+ polynomial_concat_noinit(mean_num, output);
+
+ free_Int_Array(symbol_list);
+ free_Int_Array(base_monomial);
+ return(0);
+ }
+ else{
+ // initialize current term to a position that has no repetitions
+ current_term=calloc(power,sizeof(int));
+ exists_next=init_prod(current_term, symbol_list, fields, power, base_monomial)+1;
+ }
+
+ // loop over terms; the loop stops when all the pointers are at the end of the first symbol
+ while(exists_next==1){
+ // construct monomial
+ int_array_cpy(base_monomial, &tmp_monomial);
+ tmp_num=number_one();
+ for(i=0;i<power;i++){
+ int_array_concat(fields.symbols.expr[symbol_list.values[i]].monomials[current_term[i]], &tmp_monomial);
+ number_prod_chain(fields.symbols.expr[symbol_list.values[i]].nums[current_term[i]], &tmp_num);
+ }
+ // check whether the monomial vanishes
+ if(check_monomial_match(tmp_monomial, fields)==1){
+ // sort monomial
+ sign=1;
+ monomial_sort(tmp_monomial, 0, tmp_monomial.length-1, fields, &sign);
+ number_Qprod_chain(quot(sign,1), &tmp_num);
+
+ // mean
+ mean_groups(tmp_monomial, &mean_poly, fields, propagator, groups, computed);
+
+ // write to output
+ polynomial_multiply_scalar(mean_poly,tmp_num);
+ polynomial_concat_noinit_inplace(mean_poly, output);
+ }
+
+ free_Number(tmp_num);
+ free_Int_Array(tmp_monomial);
+
+ // next term
+ exists_next=next_prod(current_term, symbol_list, fields, power, base_monomial)+1;
+
+
+ // simplfiy every 25 steps (improves both memory usage and performance)
+ if(simplify_freq %25 ==0){
+ polynomial_simplify(output, fields);
+ simplify_freq=0;
+ }
+ simplify_freq++;
+ }
+
+ // simplify
+ polynomial_simplify(output, fields);
+
+ // write computed
+ identities_append(monomial, *output, computed);
+
+ // free memory
+ free(current_term);
+ free_Int_Array(symbol_list);
+ free_Int_Array(base_monomial);
+ return(0);
+}
+
+// first term in product with no repetitions
+int init_prod(int* current_term, Int_Array symbol_list, Fields_Table fields, int power, Int_Array base_monomial){
+ // index we want to increment
+ int move=0;
+ // tmp monomial
+ Int_Array monomial;
+ int i;
+
+ init_Int_Array(&monomial, base_monomial.length+5*power);
+ int_array_cpy_noinit(base_monomial, &monomial);
+ // init current term
+ for(i=0;i<power;i++){
+ current_term[i]=-1;
+ }
+
+ // loop until move is out of range
+ while(move>=0 && move<power){
+ // move
+ current_term[move]=next_term_norepeat(current_term[move], fields.symbols.expr[symbol_list.values[move]], &monomial, fields);
+ // if the next term does not exist, then move previous index
+ if(current_term[move]==-1){
+ move--;
+ }
+ // else move next index
+ else{
+ move++;
+ }
+ }
+
+ free_Int_Array(monomial);
+ // if move==-1, then there is no first term, return -1
+ if(move==-1){
+ return(-1);
+ }
+ // if the next term exists
+ return(0);
+}
+
+// next term in product with no repetitions
+int next_prod(int* current_term, Int_Array symbol_list, Fields_Table fields, int power, Int_Array base_monomial){
+ // index we want to increment
+ int move=power-1;
+ // tmp monomial
+ Int_Array monomial;
+ int i;
+
+ // init monomial
+ init_Int_Array(&monomial, base_monomial.length+5*power);
+ int_array_cpy_noinit(base_monomial, &monomial);
+ for(i=0;i<=move;i++){
+ int_array_concat(fields.symbols.expr[symbol_list.values[i]].monomials[current_term[i]],&monomial);
+ }
+
+ // loop until move is out of range
+ while(move>=0 && move<power){
+ // move
+ current_term[move]=next_term_norepeat(current_term[move], fields.symbols.expr[symbol_list.values[move]], &monomial, fields);
+ // if the next term does not exist, then move previous index
+ if(current_term[move]==-1){
+ move--;
+ }
+ // else move next index
+ else{
+ move++;
+ }
+ }
+
+ free_Int_Array(monomial);
+ // if move==-1, then there is no next term, return -1
+ if(move==-1){
+ return(-1);
+ }
+ // if the next term exists
+ return(0);
+}
+
+// find the next term in a polynomial that can be multiplied to a given monomial and add it to the monomial
+int next_term_norepeat(int start, Polynomial polynomial, Int_Array* monomial, Fields_Table fields){
+ int i;
+ // remove last term from monomial
+ if(start>=0 && start<polynomial.length){
+ (*monomial).length-=polynomial.monomials[start].length;
+ }
+ // find next position
+ for(i=start+1;i<polynomial.length;i++){
+ // if no repetitions
+ if(check_monomial_addterm(*monomial,polynomial.monomials[i],fields)==1){
+ // append to monomial
+ int_array_concat(polynomial.monomials[i], monomial);
+ return(i);
+ }
+ }
+ // no next term
+ return(-1);
+}
+
+
+// signature of a permutation
+int permutation_signature(int* permutation, int n){
+ int* tmp_array=calloc(n,sizeof(int));
+ int i;
+ int ret=1;
+ for(i=0;i<n;i++){
+ tmp_array[i]=permutation[i];
+ }
+ sort_fermions(tmp_array, 0, n-1, &ret);
+ free(tmp_array);
+ return(ret);
+}
+
+// sort a list of anti-commuting variables
+int sort_fermions(int* array, int begin, int end, int* sign){
+ int i;
+ int tmp;
+ int index;
+ // the pivot: middle of the monomial
+ int pivot=(begin+end)/2;
+
+ // if the monomial is non trivial
+ if(begin<end){
+ // send pivot to the end
+ if(pivot!=end){
+ tmp=array[end];
+ array[end]=array[pivot];
+ array[pivot]=tmp;
+ *sign*=-1;
+ }
+
+ // loop over the others
+ for(i=begin, index=begin;i<end;i++){
+ // compare with pivot
+ if(array[i]<array[end]){
+ // if smaller, exchange with reference index
+ if(i!=index){
+ tmp=array[i];
+ array[i]=array[index];
+ array[index]=tmp;
+ *sign*=-1;
+ }
+ // move reference index
+ index++;
+ }
+ }
+ // put pivot (which we had sent to the end) in the right place
+ if(end!=index){
+ tmp=array[end];
+ array[end]=array[index];
+ array[index]=tmp;
+ *sign*=-1;
+ }
+
+ // recurse
+ sort_fermions(array, begin, index-1, sign);
+ sort_fermions(array, index+1, end, sign);
+ }
+ return(0);
+}
+
+
+// mean while factoring groups out
+int mean_groups(Int_Array monomial, Polynomial* output, Fields_Table fields, Polynomial_Matrix propagator, Groups groups, Identities* computed){
+ Polynomial num_mean;
+ Int_Array tmp_monomial;
+ int i;
+ int group=-2;
+ int next_group=-2;
+ Polynomial tmp_poly;
+ int sign;
+
+ init_Polynomial(output, MONOMIAL_SIZE);
+
+ // check whether there are symbols
+ // requires the symbols to be at the end of the monomial
+ if(monomial.length==0 || field_type(monomial.values[monomial.length-1], fields)!=FIELD_SYMBOL){
+ // mean
+ mean(monomial, &num_mean, fields, propagator);
+ // add to output
+ polynomial_concat_noinit(num_mean,output);
+ }
+ else{
+ // sort into groups
+ if(groups.length>0){
+ sign=1;
+ monomial_sort_groups(monomial, 0, monomial.length-1, fields, groups, &sign);
+ }
+ // construct groups and take mean
+ init_Int_Array(&tmp_monomial, MONOMIAL_SIZE);
+ for(i=0;i<=monomial.length;i++){
+ // new group
+ if(i<monomial.length){
+ next_group=find_group(monomial.values[i], groups);
+ }
+ // if group changes, take mean
+ if((i>0 && next_group!=group) || i==monomial.length){
+ mean_symbols(tmp_monomial, &tmp_poly, fields, propagator, groups, computed);
+ // if zero
+ if(polynomial_is_zero(tmp_poly)==1){
+ // set output to 0
+ free_Polynomial(*output);
+ init_Polynomial(output, 1);
+ free_Polynomial(tmp_poly);
+ break;
+ }
+ // add to output
+ if(polynomial_is_zero(*output)==1){
+ polynomial_concat(tmp_poly, output);
+ }
+ else{
+ polynomial_prod_chain_nosimplify(tmp_poly, output, fields);
+ }
+ free_Polynomial(tmp_poly);
+
+ // reset tmp_monomial
+ free_Int_Array(tmp_monomial);
+ init_Int_Array(&tmp_monomial, MONOMIAL_SIZE);
+ }
+
+ // add to monomial
+ if(i<monomial.length){
+ int_array_append(monomial.values[i], &tmp_monomial);
+ }
+ group=next_group;
+ }
+
+ // sign correction
+ if(sign==-1){
+ polynomial_multiply_Qscalar(*output,quot(sign,1));
+ }
+
+ free_Int_Array(tmp_monomial);
+
+ }
+
+ return(0);
+}
+
+
+
+// mean of a polynomial
+
+// argument struct for multithreaded mean
+struct mean_args{
+ Polynomial* polynomial;
+ Fields_Table fields;
+ Polynomial_Matrix propagator;
+ Groups groups;
+};
+
+// multithreaded
+int polynomial_mean_multithread(Polynomial* polynomial, Fields_Table fields, Polynomial_Matrix propagator, Groups groups, int threads){
+ int i;
+ Polynomial thread_polys[threads];
+ pthread_t thread_ids[threads];
+ struct mean_args args[threads];
+ int len=(*polynomial).length;
+
+
+ // alloc
+ for(i=0;i<threads;i++){
+ init_Polynomial(thread_polys+i,(*polynomial).length/threads+1);
+ // arguments
+ args[i].fields=fields;
+ args[i].propagator=propagator;
+ args[i].groups=groups;
+ }
+
+ // split polynomial
+ for(i=0;i<len;i++){
+ polynomial_append((*polynomial).monomials[i], (*polynomial).factors[i], (*polynomial).nums[i], thread_polys+(i % threads));
+ }
+
+ // start threads
+ for(i=0;i<threads;i++){
+ args[i].polynomial=thread_polys+i;
+ pthread_create(thread_ids+i, NULL, polynomial_mean_thread, (void*)(args+i));
+ }
+
+ free_Polynomial(*polynomial);
+ init_Polynomial(polynomial, len);
+
+ // wait for completion and join
+ for(i=0;i<threads;i++){
+ pthread_join(thread_ids[i], NULL);
+ polynomial_concat_noinit(thread_polys[i], polynomial);
+ }
+
+ polynomial_simplify(polynomial, fields);
+
+ return(0);
+}
+
+// mean for one of the threads
+void* polynomial_mean_thread(void* mean_args){
+ struct mean_args *args=mean_args;
+ polynomial_mean((*args).polynomial,(*args).fields,(*args).propagator,(*args).groups);
+ return(NULL);
+}
+
+// single threaded version
+int polynomial_mean(Polynomial* polynomial, Fields_Table fields, Polynomial_Matrix propagator, Groups groups){
+ int i,j;
+ Polynomial output;
+ Polynomial tmp_poly;
+ // a list of already computed means
+ Identities computed;
+
+ init_Polynomial(&output, (*polynomial).length);
+ init_Identities(&computed, EQUATION_SIZE);
+
+ remove_unmatched_plusminus(polynomial, fields);
+
+ // mean of each monomial
+ for(i=0;i<(*polynomial).length;i++){
+ fprintf(stderr,"computing %d of %d means\n",i,(*polynomial).length-1);
+ mean_groups((*polynomial).monomials[i], &tmp_poly, fields, propagator, groups, &computed);
+
+ // write factors
+ for(j=0;j<tmp_poly.length;j++){
+ int_array_concat((*polynomial).factors[i], tmp_poly.factors+j);
+ number_prod_chain((*polynomial).nums[i], tmp_poly.nums+j);
+ }
+
+ // add to output
+ polynomial_concat_noinit(tmp_poly, &output);
+ // simplify (simplify here in order to keep memory usage low)
+ polynomial_simplify(&output, fields);
+ }
+ free_Identities(computed);
+
+ free_Polynomial(*polynomial);
+ *polynomial=output;
+
+ return(0);
+}
+
diff --git a/src/mean.h b/src/mean.h
new file mode 100644
index 0000000..34ec1d3
--- /dev/null
+++ b/src/mean.h
@@ -0,0 +1,70 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+Compute the mean of a monomial or a polynomial
+*/
+
+#ifndef MEAN_H
+#define MEAN_H
+
+#include "types.h"
+
+// mean of a monomial
+int mean(Int_Array monomial, Polynomial* out, Fields_Table fields, Polynomial_Matrix propagator);
+
+// compute the mean of a monomial of internal fields (with split + and -)
+int mean_internal(Int_Array internal_plus, Int_Array internal_minus, Polynomial* out, Polynomial_Matrix propagator, Fields_Table fields);
+// first pairing with a non-vanishing propagator
+int init_pairing(int* pairing, int* mask, int n, Polynomial_Matrix propagator, int* indices_plus, int* indices_minus);
+// next pairing with a non-vanishing propagator
+int next_pairing(int* pairing, int* mask, int n, Polynomial_Matrix propagator, int* indices_plus, int* indices_minus);
+// next term in the Wick expansion
+int next_wick(int index, int start, int* mask, int n, Polynomial_Matrix propagator, int* indices_plus, int* indices_minus);
+
+/*
+int mean_internal_slow(Int_Array internal_plus, Int_Array internal_minus, Number* outnum, Polynomial_Matrix propagator);
+*/
+
+// get lists of internal fields from a monomial (separate + and -)
+// requires the monomial to be sorted (for the sign to be correct)
+int get_internals(Int_Array monomial, Int_Array* internal_plus, Int_Array* internal_minus, Int_Array* others, Fields_Table fields);
+
+// compute the mean of a monomial containing symbolic expressions
+int mean_symbols(Int_Array monomial, Polynomial* output, Fields_Table fields, Polynomial_Matrix propagator, Groups groups, Identities* computed);
+// first term in product with no repetitions
+int init_prod(int* current_term, Int_Array symbol_list, Fields_Table fields, int power, Int_Array base_monomial);
+// next term in product with no repetitions
+int next_prod(int* current_term, Int_Array symbol_list, Fields_Table fields, int power, Int_Array base_monomial);
+// find the next term in a polynomial that can be multiplied to a given monomial and add it to the monomial
+int next_term_norepeat(int start, Polynomial polynomial, Int_Array* monomial, Fields_Table fields);
+
+// signature of a permutation
+int permutation_signature(int* permutation, int n);
+
+// sort a list of anti-commuting variables
+int sort_fermions(int* array, int begin, int end, int* sign);
+
+// mean while factoring groups out
+int mean_groups(Int_Array monomial, Polynomial* output, Fields_Table fields, Polynomial_Matrix propagator, Groups groups, Identities* computed);
+
+// compute the mean of a polynomial
+int polynomial_mean(Polynomial* polynomial, Fields_Table fields, Polynomial_Matrix propagator, Groups groups);
+// multithreaded
+int polynomial_mean_multithread(Polynomial* polynomial, Fields_Table fields, Polynomial_Matrix propagator, Groups groups, int threads);
+// single thread mean
+void* polynomial_mean_thread(void* mean_args);
+#endif
diff --git a/src/meankondo.c b/src/meankondo.c
new file mode 100644
index 0000000..1c976d4
--- /dev/null
+++ b/src/meankondo.c
@@ -0,0 +1,301 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+meankondo
+
+A simple tool to compute the renormalization group flow for Fermionic hierarchical models
+
+*/
+
+
+#include <stdio.h>
+#include <stdlib.h>
+
+// pre-compiler definitions
+#include "definitions.cpp"
+
+// various arrays
+#include "array.h"
+
+// list of fields
+#include "fields.h"
+// numbers
+#include "number.h"
+// polynomials
+#include "polynomial.h"
+// list of rccs
+#include "idtable.h"
+// grouped representation of polynomials
+#include "grouped_polynomial.h"
+// command line parser
+#include "cli_parser.h"
+// parse input file
+#include "parse_file.h"
+// means
+#include "mean.h"
+// various string operations
+#include "istring.h"
+
+// read cli arguments
+int read_args_meankondo(int argc,const char* argv[], Str_Array* str_args, Meankondo_Options* opts);
+// print usage message
+int print_usage_meankondo();
+// compute flow
+int compute_flow(Str_Array str_args, Meankondo_Options opts);
+// compute the flow equation
+int compute_flow_equation(Polynomial init_poly, Id_Table idtable, Fields_Table fields, Polynomial_Matrix propagator, Groups groups, int threads, Grouped_Polynomial* flow_equation);
+
+
+int main (int argc, const char* argv[]){
+ // string arguments
+ Str_Array str_args;
+ // options
+ Meankondo_Options opts;
+
+ // read command-line arguments
+ read_args_meankondo(argc,argv,&str_args,&opts);
+
+ // warning message if representing rational numbers as floats
+#ifdef RATIONAL_AS_FLOAT
+ fprintf(stderr,"info: representing rational numbers using floats\n");
+#endif
+
+ compute_flow(str_args, opts);
+
+ //free memory
+ free_Str_Array(str_args);
+ return(0);
+}
+
+
+// parse command-line arguments
+#define CP_FLAG_THREADS 1
+int read_args_meankondo(int argc,const char* argv[], Str_Array* str_args, Meankondo_Options* opts){
+ int i;
+ // pointers
+ char* ptr;
+ // file to read the polynomial from in flow mode
+ const char* file="";
+ // flag that indicates what argument is being read
+ int flag=0;
+ // whether a file was specified on the command-line
+ int exists_file=0;
+
+
+ // defaults
+ // single thread
+ (*opts).threads=1;
+ // do not chain
+ (*opts).chain=0;
+
+ // loop over arguments
+ for(i=1;i<argc;i++){
+ // flag
+ if(argv[i][0]=='-'){
+ for(ptr=((char*)argv[i])+1;*ptr!='\0';ptr++){
+ switch(*ptr){
+ // threads
+ case 't':
+ flag=CP_FLAG_THREADS;
+ break;
+ // chain
+ case 'C':
+ (*opts).chain=1;
+ break;
+ // print version
+ case 'v':
+ printf("meankondo " VERSION "\n");
+ exit(1);
+ break;
+ default:
+ print_usage_meankondo();
+ exit(-1);
+ break;
+ }
+ }
+ }
+ // threads
+ else if(flag==CP_FLAG_THREADS){
+ sscanf(argv[i],"%d",&((*opts).threads));
+ flag=0;
+ }
+ // read file name from command-line
+ else{
+ file=argv[i];
+ exists_file=1;
+ }
+ }
+
+ read_config_file(str_args, file, 1-exists_file);
+
+ return(0);
+}
+
+// print usage message
+int print_usage_meankondo(){
+ printf("\nusage:\n meankondo [-t threads] [-C] <filename>\n\n");
+ return(0);
+}
+
+
+// compute the renormalization group flow
+int compute_flow(Str_Array str_args, Meankondo_Options opts){
+ int i;
+ // index of the entry in the input file
+ int arg_index;
+ // header of the entry
+ Char_Array arg_header;
+ // list of fields
+ Fields_Table fields;
+ // their propagator
+ Polynomial_Matrix propagator;
+ // initial polynomial
+ Polynomial init_poly;
+ // list of rccs
+ Id_Table idtable;
+ // groups of independent fields
+ Groups groups;
+ // flow equation
+ Grouped_Polynomial flow_equation;
+
+
+ // parse fields
+ arg_index=find_str_arg("fields", str_args);
+ if(arg_index<0){
+ fprintf(stderr,"error: no fields entry in the configuration file\n");
+ exit(-1);
+ }
+ else{
+ parse_input_fields(str_args.strs[arg_index],&fields);
+ }
+
+ // parse id table
+ arg_index=find_str_arg("id_table", str_args);
+ if(arg_index<0){
+ fprintf(stderr,"error: no id table entry in the configuration file\n");
+ exit(-1);
+ }
+ else{
+ parse_input_id_table(str_args.strs[arg_index],&idtable, fields);
+ }
+
+ // parse symbols
+ arg_index=find_str_arg("symbols", str_args);
+ if(arg_index>=0){
+ parse_input_symbols(str_args.strs[arg_index],&fields);
+ }
+ else{
+ init_Symbols(&(fields.symbols),1);
+ }
+
+ // parse input polynomial
+ arg_index=find_str_arg("input_polynomial", str_args);
+ if(arg_index>=0){
+ parse_input_polynomial(str_args.strs[arg_index],&init_poly, fields);
+ }
+ else{
+ fprintf(stderr,"error: no input polynomial entry in the configuration file\n");
+ exit(-1);
+ }
+
+ // propagator
+ arg_index=find_str_arg("propagator", str_args);
+ if(arg_index<0){
+ fprintf(stderr,"error: no propagator entry in the configuration file\n");
+ exit(-1);
+ }
+ else{
+ parse_input_propagator(str_args.strs[arg_index],&propagator, fields);
+ }
+
+ // parse identities
+ arg_index=find_str_arg("identities", str_args);
+ if(arg_index>=0){
+ parse_input_identities(str_args.strs[arg_index],&fields);
+ }
+ else{
+ init_Identities(&(fields.ids),1);
+ }
+
+ // parse groups
+ arg_index=find_str_arg("groups", str_args);
+ if(arg_index>=0){
+ parse_input_groups(str_args.strs[arg_index],&groups);
+ }
+ else{
+ init_Groups(&groups, 1);
+ }
+
+ // flow equation
+ compute_flow_equation(init_poly, idtable, fields, propagator, groups, opts.threads, &flow_equation);
+ free_Polynomial(init_poly);
+ free_Polynomial_Matrix(propagator);
+ free_Fields_Table(fields);
+ free_Groups(groups);
+
+ // if chain then print config file
+ if(opts.chain==1){
+ for(i=0;i<str_args.length;i++){
+ // check whether to print the str_arg
+ get_str_arg_title(str_args.strs[i], &arg_header);
+ if (\
+ str_cmp(arg_header.str, "symbols")==0 &&\
+ str_cmp(arg_header.str, "groups")==0 &&\
+ str_cmp(arg_header.str, "fields")==0 &&\
+ str_cmp(arg_header.str, "identities")==0 &&\
+ str_cmp(arg_header.str, "propagator")==0 &&\
+ str_cmp(arg_header.str, "input_polynomial")==0 &&\
+ str_cmp(arg_header.str, "id_table")==0 ){
+ printf("%s\n&\n",str_args.strs[i].str);
+ }
+ free_Char_Array(arg_header);
+ }
+ // print flow equation
+ printf("#!flow_equation\n");
+ }
+
+ // print flow equation
+ grouped_polynomial_print(flow_equation,'%','%');
+
+ // free memory
+ free_Id_Table(idtable);
+ free_Grouped_Polynomial(flow_equation);
+ return(0);
+}
+
+
+// compute the flow equation
+int compute_flow_equation(Polynomial init_poly, Id_Table idtable, Fields_Table fields, Polynomial_Matrix propagator, Groups groups, int threads, Grouped_Polynomial* flow_equation){
+ // expectation
+ Polynomial exp_poly;
+
+ polynomial_cpy(init_poly,&exp_poly);
+
+ // average
+ if(threads>1){
+ polynomial_mean_multithread(&exp_poly, fields, propagator, groups, threads);
+ }
+ else{
+ polynomial_mean(&exp_poly, fields, propagator, groups);
+ }
+
+ // grouped representation of expanded_poly
+ group_polynomial(exp_poly,flow_equation,idtable, fields);
+ free_Polynomial(exp_poly);
+
+ return(0);
+}
diff --git a/src/meantools.c b/src/meantools.c
new file mode 100644
index 0000000..f45c376
--- /dev/null
+++ b/src/meantools.c
@@ -0,0 +1,116 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+meantools
+
+Utility to perform various operations on flow equations
+
+*/
+
+
+#include <stdio.h>
+#include <stdlib.h>
+
+// pre-compiler definitions
+#include "definitions.cpp"
+
+// grouped representation of polynomials
+#include "grouped_polynomial.h"
+// command line parser
+#include "cli_parser.h"
+// parse input file
+#include "parse_file.h"
+// arrays
+#include "array.h"
+// string functions
+#include "istring.h"
+// tools
+#include "meantools_exp.h"
+#include "meantools_deriv.h"
+#include "meantools_eval.h"
+
+#define EXP_COMMAND 1
+#define DERIV_COMMAND 2
+#define EVAL_COMMAND 3
+
+// read cli arguments
+int read_args_meantools(int argc,const char* argv[], Str_Array* str_args, Meantools_Options* opts);
+// print usage message
+int print_usage_meantools();
+
+
+int main (int argc, const char* argv[]){
+ // string arguments
+ Str_Array str_args;
+ // options
+ Meantools_Options opts;
+
+ // read command-line arguments
+ read_args_meantools(argc,argv,&str_args, &opts);
+
+ switch(opts.command){
+ case EXP_COMMAND: tool_exp(str_args);
+ break;
+ case DERIV_COMMAND: tool_deriv(str_args,opts);
+ break;
+ case EVAL_COMMAND: tool_eval(str_args,opts);
+ break;
+ }
+
+ //free memory
+ free_Str_Array(str_args);
+ return(0);
+}
+
+
+// parse command-line arguments
+int read_args_meantools(int argc,const char* argv[], Str_Array* str_args, Meantools_Options* opts){
+
+ // if there are no arguments
+ if(argc==1){
+ print_usage_meantools();
+ exit(-1);
+ }
+
+ if(str_cmp((char*)argv[1],"exp")==1){
+ (*opts).command=EXP_COMMAND;
+ tool_exp_read_args(argc, argv, str_args);
+ }
+ else if(str_cmp((char*)argv[1],"derive")==1){
+ (*opts).command=DERIV_COMMAND;
+ tool_deriv_read_args(argc, argv, str_args, opts);
+ }
+ else if(str_cmp((char*)argv[1],"eval")==1){
+ (*opts).command=EVAL_COMMAND;
+ tool_eval_read_args(argc, argv, str_args, opts);
+ }
+ else{
+ print_usage_meantools();
+ exit(-1);
+ }
+
+ return(0);
+}
+
+// print usage message
+int print_usage_meantools(){
+ printf("\nusage:\n meantools exp <filename>\n meantools derive [-d derivatives] -V <variables> <filename>\n meantools eval -R <rccs> <filename>\n\n");
+ return(0);
+}
+
+
+
diff --git a/src/meantools_deriv.c b/src/meantools_deriv.c
new file mode 100644
index 0000000..28d8641
--- /dev/null
+++ b/src/meantools_deriv.c
@@ -0,0 +1,195 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "meantools_deriv.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include "parse_file.h"
+#include "cli_parser.h"
+#include "istring.h"
+#include "definitions.cpp"
+#include "array.h"
+#include "grouped_polynomial.h"
+
+
+#define CP_FLAG_DERIVS 1
+#define CP_FLAG_VARS 2
+// read command line arguments
+int tool_deriv_read_args(int argc, const char* argv[], Str_Array* str_args, Meantools_Options* opts){
+ // file to read the polynomial from in flow mode
+ const char* file="";
+ // whether a file was specified on the command-line
+ int exists_file=0;
+ // flag
+ int flag=0;
+ // buffer in which to read the variables
+ Char_Array buffer;
+ int i;
+ char* ptr;
+
+ // defaults
+ // derive once
+ (*opts).deriv_derivs=1;
+ // derive with respect to all variables
+ (*opts).deriv_vars.length=-1;
+
+
+ // loop over arguments
+ for(i=2;i<argc;i++){
+ // flag
+ if(argv[i][0]=='-'){
+ for(ptr=((char*)argv[i])+1;*ptr!='\0';ptr++){
+ switch(*ptr){
+ // number of derivatives
+ case 'd':
+ flag=CP_FLAG_DERIVS;
+ break;
+ case 'V':
+ flag=CP_FLAG_VARS;
+ break;
+ }
+ }
+ }
+ // number of derivatives
+ else if(flag==CP_FLAG_DERIVS){
+ sscanf(argv[i],"%d",&((*opts).deriv_derivs));
+ flag=0;
+ }
+ // variables
+ else if(flag==CP_FLAG_VARS){
+ // if the argument is "all" then derive wrt all variables
+ if(str_cmp((char*)argv[i],"all")){
+ (*opts).deriv_vars.length=-2;
+ }
+ else{
+ str_to_char_array((char*)argv[i], &buffer);
+ int_array_read(buffer,&((*opts).deriv_vars));
+ free_Char_Array(buffer);
+ }
+ flag=0;
+ }
+ // read file name from command-line
+ else{
+ file=argv[i];
+ exists_file=1;
+ }
+ }
+
+ read_config_file(str_args, file, 1-exists_file);
+
+ return(0);
+}
+
+
+// derive a flow equation
+int tool_deriv(Str_Array str_args, Meantools_Options opts){
+ // index of the entry in the input file
+ int arg_index;
+ // flow equation
+ Grouped_Polynomial flow_equation;
+ // flow equation for the derivatives
+ Grouped_Polynomial flow_equation_deriv;
+ int i;
+
+
+ // parse flow equation
+ // if there is a unique argument, assume it is the flow equation
+ if(str_args.length==1){
+ char_array_to_Grouped_Polynomial(str_args.strs[0], &flow_equation);
+ }
+ else{
+ arg_index=find_str_arg("flow_equation", str_args);
+ if(arg_index<0){
+ fprintf(stderr,"error: no flow equation entry in the configuration file\n");
+ exit(-1);
+ }
+ else{
+ char_array_to_Grouped_Polynomial(str_args.strs[arg_index], &flow_equation);
+ }
+
+ // variables
+ // check they were not specified on the command line
+ if(opts.deriv_vars.length==-1){
+ arg_index=find_str_arg("variables", str_args);
+ if(arg_index>=0){
+ int_array_read(str_args.strs[arg_index],&(opts.deriv_vars));
+ }
+ }
+ }
+
+ // if variables length is negative then set the variables to all of the available ones
+ if(opts.deriv_vars.length<0){
+ init_Int_Array(&(opts.deriv_vars), flow_equation.length);
+ for(i=0;i<flow_equation.length;i++){
+ int_array_append(flow_equation.indices[i], &(opts.deriv_vars));
+ }
+ }
+
+ // compute derivatives
+ flow_equation_derivative(opts.deriv_derivs, opts.deriv_vars, flow_equation, &flow_equation_deriv);
+
+ grouped_polynomial_print(flow_equation_deriv,'%','%');
+
+ // free memory
+ free_Grouped_Polynomial(flow_equation);
+ free_Grouped_Polynomial(flow_equation_deriv);
+ free_Int_Array(opts.deriv_vars);
+ return(0);
+}
+
+
+// n first derivatives of a flow equation wrt to variables
+int flow_equation_derivative(int n, Int_Array variables, Grouped_Polynomial flow_equation, Grouped_Polynomial* flow_equation_derivs){
+ Grouped_Polynomial dflow;
+ Grouped_Polynomial tmpflow;
+ Int_Array indices;
+ int i,j;
+
+ int_array_cpy(variables, &indices);
+
+ // output polynomial
+ grouped_polynomial_cpy(flow_equation, flow_equation_derivs);
+
+ for(j=0,dflow=flow_equation;j<n;j++){
+ // tmp flow contains the result of the previous derivative
+ grouped_polynomial_cpy(dflow, &tmpflow);
+ // derive
+ flow_equation_derivx(tmpflow, indices, &dflow);
+ // free
+ free_Grouped_Polynomial(tmpflow);
+
+ // add the derived indices as variables for the next derivative
+ for(i=0;i<variables.length;i++){
+ if(variables.values[i]>=0){
+ int_array_append((j+1)*DOFFSET+variables.values[i], &indices);
+ }
+ // constants have a negative index
+ else{
+ int_array_append(-(j+1)*DOFFSET+variables.values[i], &indices);
+ }
+ }
+
+ // add to flow equation
+ grouped_polynomial_concat(dflow, flow_equation_derivs);
+ }
+
+ if(n>0){
+ free_Grouped_Polynomial(dflow);
+ }
+ free_Int_Array(indices);
+ return(0);
+}
diff --git a/src/meantools_deriv.h b/src/meantools_deriv.h
new file mode 100644
index 0000000..4ea36a9
--- /dev/null
+++ b/src/meantools_deriv.h
@@ -0,0 +1,30 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#ifndef MEANTOOLS_DERIV_H
+#define MEANTOOLS_DERIV_H
+
+#include "types.h"
+
+// read arguments
+int tool_deriv_read_args(int argc, const char* argv[], Str_Array* str_args, Meantools_Options* opts);
+// derive a flow equation
+int tool_deriv(Str_Array str_args, Meantools_Options opts);
+// n first derivatives of a flow equation wrt to variables
+int flow_equation_derivative(int n, Int_Array variables, Grouped_Polynomial flow_equation, Grouped_Polynomial* flow_equation_derivs);
+
+#endif
+
diff --git a/src/meantools_eval.c b/src/meantools_eval.c
new file mode 100644
index 0000000..50fff5b
--- /dev/null
+++ b/src/meantools_eval.c
@@ -0,0 +1,129 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "meantools_eval.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include "parse_file.h"
+#include "cli_parser.h"
+#include "grouped_polynomial.h"
+#include "array.h"
+#include "rcc.h"
+
+
+#define CP_FLAG_RCCS 1
+// read command line arguments
+int tool_eval_read_args(int argc, const char* argv[], Str_Array* str_args, Meantools_Options* opts){
+ // file to read the polynomial from in flow mode
+ const char* file="";
+ // whether a file was specified on the command-line
+ int exists_file=0;
+ // flag
+ int flag=0;
+ int i;
+ char* ptr;
+
+ // defaults
+ // mark rccstring so that it can be recognized whether it has been set or not
+ (*opts).eval_rccstring.length=-1;
+
+ // loop over arguments
+ for(i=2;i<argc;i++){
+ // flag
+ if(argv[i][0]=='-'){
+ for(ptr=((char*)argv[i])+1;*ptr!='\0';ptr++){
+ switch(*ptr){
+ // evaluate string
+ case 'R':
+ flag=CP_FLAG_RCCS;
+ break;
+ }
+ }
+ }
+ // rccs
+ else if(flag==CP_FLAG_RCCS){
+ str_to_char_array((char*)argv[i], &((*opts).eval_rccstring));
+ flag=0;
+ }
+ // read file name from command-line
+ else{
+ file=argv[i];
+ exists_file=1;
+ }
+ }
+
+ read_config_file(str_args, file, 1-exists_file);
+
+ return(0);
+}
+
+
+// evaluate a flow equation on a vector of rccs
+int tool_eval(Str_Array str_args, Meantools_Options opts){
+ // index of the entry in the input file
+ int arg_index;
+ // rccs
+ RCC rccs;
+ // flow equation
+ Grouped_Polynomial flow_equation;
+
+
+ // parse flow equation
+ // if there is a unique argument, assume it is the flow equation
+ if(str_args.length==1){
+ char_array_to_Grouped_Polynomial(str_args.strs[0], &flow_equation);
+ }
+ else{
+ arg_index=find_str_arg("flow_equation", str_args);
+ if(arg_index<0){
+ fprintf(stderr,"error: no flow equation entry in the configuration file\n");
+ exit(-1);
+ }
+ else{
+ char_array_to_Grouped_Polynomial(str_args.strs[arg_index], &flow_equation);
+ }
+
+ // rccs
+ // check they were not specified on the command line
+ if(opts.eval_rccstring.length==-1){
+ arg_index=find_str_arg("initial_condition", str_args);
+ if(arg_index>=0){
+ char_array_cpy(str_args.strs[arg_index],&(opts.eval_rccstring));
+ }
+ }
+ }
+
+ // initialize the rccs
+ prepare_init(flow_equation.indices,flow_equation.length,&rccs);
+ // read rccs from string
+ if(opts.eval_rccstring.length!=-1){
+ parse_init_cd(opts.eval_rccstring, &rccs);
+ free_Char_Array(opts.eval_rccstring);
+ }
+
+ // evaluate
+ evaleq(&rccs, flow_equation);
+
+ // print
+ RCC_print(rccs);
+
+ // free memory
+ free_Grouped_Polynomial(flow_equation);
+ free_RCC(rccs);
+ return(0);
+}
+
diff --git a/src/meantools_eval.h b/src/meantools_eval.h
new file mode 100644
index 0000000..518049d
--- /dev/null
+++ b/src/meantools_eval.h
@@ -0,0 +1,29 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#ifndef MEANTOOLS_EVAL_H
+#define MEANTOOLS_EVAL_H
+
+#include "types.h"
+
+// read arguments
+int tool_eval_read_args(int argc, const char* argv[], Str_Array* str_args, Meantools_Options* opts);
+// evaluate a flow equation
+int tool_eval(Str_Array str_args, Meantools_Options opts);
+
+#endif
+
+
diff --git a/src/meantools_exp.c b/src/meantools_exp.c
new file mode 100644
index 0000000..1aca928
--- /dev/null
+++ b/src/meantools_exp.c
@@ -0,0 +1,130 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "meantools_exp.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include "parse_file.h"
+#include "cli_parser.h"
+#include "polynomial.h"
+#include "fields.h"
+#include "grouped_polynomial.h"
+#include "idtable.h"
+
+// read command line arguments
+int tool_exp_read_args(int argc, const char* argv[], Str_Array* str_args){
+ // file to read the polynomial from in flow mode
+ const char* file="";
+ // whether a file was specified on the command-line
+ int exists_file=0;
+
+ if(argc>=3){
+ file=argv[2];
+ exists_file=1;
+ }
+ read_config_file(str_args, file, 1-exists_file);
+
+ return(0);
+}
+
+
+// compute the exponential of the input polynomial
+int tool_exp(Str_Array str_args){
+ // index of the entry in the input file
+ int arg_index;
+ // list of fields
+ Fields_Table fields;
+ // input polynomial
+ Polynomial poly;
+ // exp as a polynomial
+ Polynomial exp_poly;
+ // list of rccs
+ Id_Table idtable;
+ // exp
+ Grouped_Polynomial exp;
+ int i,j;
+
+ // parse fields
+ arg_index=find_str_arg("fields", str_args);
+ if(arg_index<0){
+ fprintf(stderr,"error: no fields entry in the configuration file\n");
+ exit(-1);
+ }
+ else{
+ parse_input_fields(str_args.strs[arg_index],&fields);
+ }
+
+ // parse id table
+ arg_index=find_str_arg("id_table", str_args);
+ if(arg_index<0){
+ fprintf(stderr,"error: no id table entry in the configuration file\n");
+ exit(-1);
+ }
+ else{
+ parse_input_id_table(str_args.strs[arg_index],&idtable, fields);
+ }
+
+ // parse input polynomial
+ arg_index=find_str_arg("input_polynomial", str_args);
+ if(arg_index>=0){
+ parse_input_polynomial(str_args.strs[arg_index],&poly, fields);
+ }
+ else{
+ fprintf(stderr,"error: no input polynomial entry in the configuration file\n");
+ exit(-1);
+ }
+
+ // parse symbols
+ arg_index=find_str_arg("symbols", str_args);
+ if(arg_index>=0){
+ parse_input_symbols(str_args.strs[arg_index],&fields);
+ }
+ else{
+ init_Symbols(&(fields.symbols),1);
+ }
+
+ // parse identities
+ arg_index=find_str_arg("identities", str_args);
+ if(arg_index>=0){
+ parse_input_identities(str_args.strs[arg_index],&fields);
+ }
+ else{
+ init_Identities(&(fields.ids),1);
+ }
+
+ // exp(V)
+ polynomial_exponential(poly,&exp_poly, fields);
+ // grouped representation
+ group_polynomial(exp_poly, &exp, idtable, fields);
+ free_Polynomial(exp_poly);
+ free_Polynomial(poly);
+
+ // no denominators
+ for(i=0;i<exp.length;i++){
+ for(j=0;j<exp.coefs[i].length;j++){
+ exp.coefs[i].denoms[j].power=0;
+ }
+ }
+
+ grouped_polynomial_print(exp,'%','%');
+
+ // free memory
+ free_Fields_Table(fields);
+ free_Id_Table(idtable);
+ free_Grouped_Polynomial(exp);
+ return(0);
+}
diff --git a/src/meantools_exp.h b/src/meantools_exp.h
new file mode 100644
index 0000000..f3f6666
--- /dev/null
+++ b/src/meantools_exp.h
@@ -0,0 +1,27 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#ifndef MEANTOOLS_EXP_H
+#define MEANTOOLS_EXP_H
+
+#include "types.h"
+
+// read arguments
+int tool_exp_read_args(int argc, const char* argv[], Str_Array* str_args);
+// compute the exponential of the input polynomial
+int tool_exp(Str_Array str_args);
+
+#endif
diff --git a/src/number.c b/src/number.c
new file mode 100644
index 0000000..5d4cd18
--- /dev/null
+++ b/src/number.c
@@ -0,0 +1,551 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "number.h"
+#include <stdlib.h>
+#include <stdio.h>
+#include <math.h>
+#include "istring.h"
+#include "definitions.cpp"
+#include "tools.h"
+#include "rational.h"
+#include "array.h"
+
+// init
+int init_Number(Number* number, int memory){
+ (*number).scalars=calloc(memory,sizeof(Q));
+ (*number).base=calloc(memory,sizeof(int));
+ (*number).memory=memory;
+ (*number).length=0;
+ return(0);
+}
+int free_Number(Number number){
+ free(number.scalars);
+ free(number.base);
+ return(0);
+}
+
+// copy
+int number_cpy(Number input, Number* output){
+ init_Number(output,input.length);
+ number_cpy_noinit(input,output);
+ return(0);
+}
+int number_cpy_noinit(Number input, Number* output){
+ int i;
+ if((*output).memory<input.length){
+ fprintf(stderr,"error: trying to copy a number of length %d to another with memory %d\n",input.length, (*output).memory);
+ exit(-1);
+ }
+ for(i=0;i<input.length;i++){
+ (*output).scalars[i]=input.scalars[i];
+ (*output).base[i]=input.base[i];
+ }
+ (*output).length=input.length;
+ return(0);
+}
+
+// resize memory
+int number_resize(Number* number, int newsize){
+ Number new_number;
+ init_Number(&new_number, newsize);
+ number_cpy_noinit(*number,&new_number);
+ free_Number(*number);
+ *number=new_number;
+ return(0);
+}
+
+// add a value
+int number_append(Q scalar, int base, Number* output){
+ if((*output).length>=(*output).memory){
+ number_resize(output,2*(*output).memory);
+ }
+ (*output).scalars[(*output).length]=scalar;
+ (*output).base[(*output).length]=base;
+ (*output).length++;
+ // not optimal
+ number_sort(*output,0,(*output).length-1);
+ return(0);
+}
+
+// concatenate
+int number_concat(Number input, Number* output){
+ int i;
+ int offset=(*output).length;
+ if((*output).length+input.length>(*output).memory){
+ // make it longer than needed by (*output).length (for speed)
+ number_resize(output,2*(*output).length+input.length);
+ }
+ for(i=0;i<input.length;i++){
+ (*output).scalars[offset+i]=input.scalars[i];
+ (*output).base[offset+i]=input.base[i];
+ }
+ (*output).length=offset+input.length;
+ return(0);
+}
+
+// special numbers
+Number number_zero(){
+ Number ret;
+ // don't allocate 0 memory since zero's will usually be used to add to
+ init_Number(&ret,NUMBER_SIZE);
+ return(ret);
+}
+Number number_one(){
+ Number ret=number_zero();
+ number_add_elem(quot(1,1),1,&ret);
+ return(ret);
+}
+
+// find a base element
+int number_find_base(int base, Number number){
+ return(intlist_find(number.base, number.length, base));
+}
+
+// sort
+int number_sort(Number number, int begin, int end){
+ int i;
+ int index;
+ // the pivot: middle of the array
+ int pivot=(begin+end)/2;
+ // if the array is non trivial
+ if(begin<end){
+ // send pivot to the end
+ number_exchange_terms(pivot, end, number);
+
+ // loop over the others
+ for(i=begin, index=begin;i<end;i++){
+ // compare with pivot
+ if(number.base[i]<number.base[end]){
+ // if smaller, exchange with reference index
+ number_exchange_terms(i, index, number);
+ // move reference index
+ index++;
+ }
+ }
+ // put pivot (which we had sent to the end) in the right place
+ number_exchange_terms(index, end, number);
+
+ // recurse
+ number_sort(number, begin, index-1);
+ number_sort(number, index+1, end);
+ }
+ return(0);
+}
+
+// exchange terms (for sorting)
+int number_exchange_terms(int index1, int index2, Number number){
+ Q qtmp;
+ int tmp;
+
+ qtmp=number.scalars[index1];
+ number.scalars[index1]=number.scalars[index2];
+ number.scalars[index2]=qtmp;
+
+ tmp=number.base[index1];
+ number.base[index1]=number.base[index2];
+ number.base[index2]=tmp;
+
+ return(0);
+}
+
+// checks whether two numbers are equal
+// requires both numbers to be sorted
+int number_compare(Number x1, Number x2){
+ int i;
+ if(x1.length!=x2.length){
+ return(0);
+ }
+ for(i=0;i<x1.length;i++){
+ if(x1.base[i]!=x2.base[i] || Q_cmp(x1.scalars[i],x2.scalars[i])!=0){
+ return(0);
+ }
+ }
+ return(1);
+}
+
+
+// add (write result to second element)
+int number_add_chain(Number input, Number* inout){
+ int i;
+ for(i=0;i<input.length;i++){
+ number_add_elem(input.scalars[i], input.base[i], inout);
+ }
+ return(0);
+}
+// add a single element
+int number_add_elem(Q scalar, int base, Number* inout){
+ int index;
+ index=number_find_base(base,*inout);
+ if(index>=0){
+ (*inout).scalars[index]=Q_add((*inout).scalars[index], scalar);
+ }
+ else{
+ number_append(scalar, base, inout);
+ }
+ return(0);
+}
+// create a new number
+int number_add(Number x1, Number x2, Number* out){
+ number_cpy(x1,out);
+ number_add_chain(x2,out);
+ return(0);
+}
+// return the number
+Number number_add_ret(Number x1, Number x2){
+ Number out;
+ number_add(x1,x2,&out);
+ return(out);
+}
+
+// multiply
+int number_prod(Number x1, Number x2, Number* out){
+ int i,j;
+ int div;
+ Q new_scalar;
+ int new_base;
+ init_Number(out, x1.length);
+ for(i=0;i<x1.length;i++){
+ for(j=0;j<x2.length;j++){
+ new_scalar=Q_prod(x1.scalars[i], x2.scalars[j]);
+ // simplify the base
+ div=gcd(x1.base[i], x2.base[j]);
+ new_base=(x1.base[i]/div)*(x2.base[j]/div);
+ new_scalar.numerator*=div;
+
+ number_add_elem(new_scalar, new_base, out);
+ }
+ }
+ return(0);
+}
+// write to second number
+int number_prod_chain(Number input, Number* inout){
+ Number tmp;
+ number_prod(input,*inout,&tmp);
+ free_Number(*inout);
+ *inout=tmp;
+ return(0);
+}
+// return result
+Number number_prod_ret(Number x1, Number x2){
+ Number ret;
+ number_prod(x1,x2,&ret);
+ return(ret);
+}
+
+// multiply by a rational
+int number_Qprod_chain(Q q, Number* inout){
+ int i;
+ for(i=0;i<(*inout).length;i++){
+ (*inout).scalars[i]=Q_prod(q,(*inout).scalars[i]);
+ }
+ return(0);
+}
+// write to output
+int number_Qprod(Q q, Number x, Number* inout){
+ number_cpy(x,inout);
+ number_Qprod_chain(q,inout);
+ return(0);
+}
+// return result
+Number number_Qprod_ret(Q q, Number x){
+ Number ret;
+ number_Qprod(q,x,&ret);
+ return(ret);
+}
+
+// inverse
+int number_inverse_inplace(Number* inout){
+ int i;
+ for(i=0;i<(*inout).length;i++){
+ if((*inout).base[i]>0){
+ (*inout).scalars[i]=Q_inverse((*inout).scalars[i]);
+ (*inout).scalars[i].denominator*=(*inout).base[i];
+ }
+ else if((*inout).base[i]<0){
+ (*inout).scalars[i]=Q_inverse((*inout).scalars[i]);
+ (*inout).scalars[i].denominator*=-(*inout).base[i];
+ (*inout).scalars[i].numerator*=-1;
+ }
+ else{
+ fprintf(stderr,"error: attempting to invert 0\n");
+ exit(-1);
+ }
+ }
+ return(0);
+}
+// write to output
+int number_inverse(Number input, Number* output){
+ number_cpy(input,output);
+ number_inverse_inplace(output);
+ return(0);
+}
+// return result
+Number number_inverse_ret(Number x){
+ Number ret;
+ number_inverse(x,&ret);
+ return(ret);
+}
+
+// quotient
+int number_quot(Number x1, Number x2, Number* output){
+ Number inv;
+ number_inverse(x2, &inv);
+ number_prod(x1, inv, output);
+ free_Number(inv);
+ return(0);
+}
+int number_quot_chain(Number x1, Number* inout){
+ number_inverse_inplace(inout);
+ number_prod_chain(x1, inout);
+ return(0);
+}
+Number number_quot_ret(Number x1, Number x2){
+ Number ret;
+ number_quot(x1, x2, &ret);
+ return(ret);
+}
+
+
+// remove 0's
+int number_simplify(Number in, Number* out){
+ int i;
+ init_Number(out, in.length);
+ for(i=0;i<in.length;i++){
+ if(in.scalars[i].numerator!=0){
+ number_append(in.scalars[i],in.base[i], out);
+ }
+ }
+ return(0);
+}
+
+
+// check whether a number is 0
+int number_is_zero(Number x){
+ int i;
+ for(i=0;i<x.length;i++){
+ if(x.scalars[i].numerator!=0 && x.base[i]!=0){
+ return(0);
+ }
+ }
+ return(1);
+}
+
+
+// approximate numerical expression
+long double number_double_val(Number x){
+ int i;
+ long double ret=0.;
+ long double b;
+ for(i=0;i<x.length;i++){
+ if(x.scalars[i].numerator!=0){
+ b=1.0*x.base[i];
+ ret+=Q_double_value(x.scalars[i])*sqrt(b);
+ }
+ }
+ return(ret);
+}
+
+
+// print to string
+int number_sprint(Number number, Char_Array* out){
+ int i;
+ Number simp;
+ number_simplify(number, &simp);
+ for(i=0;i<simp.length;i++){
+ if(i>0){
+ char_array_snprintf(out," + ");
+ }
+ if(simp.length>1 || (simp.length==1 && simp.base[0]!=1)){
+ char_array_append('(',out);
+ }
+ Q_sprint(simp.scalars[i], out);
+ if(simp.length>1 || (simp.length==1 && simp.base[0]!=1)){
+ char_array_append(')',out);
+ }
+
+ if(simp.base[i]!=1){
+ char_array_snprintf(out,"s{%d}",simp.base[i]);
+ }
+ }
+
+ free_Number(simp);
+ return(0);
+}
+
+// print to stdout
+int number_print(Number number){
+ Char_Array buffer;
+ init_Char_Array(&buffer,5*number.length);
+ number_sprint(number, &buffer);
+ printf("%s",buffer.str);
+ return(0);
+}
+
+#define PP_NULL_MODE 0
+#define PP_NUM_MODE 1
+#define PP_SQRT_MODE 2
+// read from a string
+int str_to_Number(char* str, Number* number){
+ char* ptr;
+ int mode;
+ char* buffer=calloc(str_len(str)+1,sizeof(char));
+ char* buffer_ptr=buffer;
+ Q num;
+ int base;
+ // whether there are parentheses in the string
+ int exist_parenthesis=0;
+
+ init_Number(number, NUMBER_SIZE);
+
+ // init num and base
+ // init to 0 so that if str is empty, then the number is set to 0
+ num=quot(0,1);
+ base=1;
+
+ mode=PP_NULL_MODE;
+ for(ptr=str;*ptr!='\0';ptr++){
+ switch(*ptr){
+ // read number
+ case '(':
+ if(mode==PP_NULL_MODE){
+ // init base
+ base=1;
+ mode=PP_NUM_MODE;
+ exist_parenthesis=1;
+ }
+ break;
+ case ')':
+ if(mode==PP_NUM_MODE){
+ str_to_Q(buffer,&num);
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ mode=PP_NULL_MODE;
+ }
+ break;
+
+ // read sqrt
+ case '{':
+ // init num
+ if(num.numerator==0){
+ num=quot(1,1);
+ }
+ if(mode==PP_NULL_MODE){
+ mode=PP_SQRT_MODE;
+ }
+ // if there is a square root, then do not read a fraction (see end of loop)
+ exist_parenthesis=1;
+ break;
+ case '}':
+ if(mode==PP_SQRT_MODE){
+ sscanf(buffer,"%d",&base);
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ mode=PP_NULL_MODE;
+ }
+ break;
+
+ // write num
+ case '+':
+ if(mode==PP_NULL_MODE){
+ number_add_elem(num, base, number);
+ // re-init num and base
+ num=quot(0,1);
+ base=1;
+ }
+ break;
+
+ default:
+ if(mode!=PP_NULL_MODE){
+ buffer_ptr=str_addchar(buffer_ptr,*ptr);
+ }
+ break;
+ }
+ }
+
+ // last step
+ if(mode==PP_NULL_MODE){
+ if(exist_parenthesis==0){
+ str_to_Q(str, &num);
+ }
+ number_add_elem(num, base, number);
+ }
+
+ free(buffer);
+ return(0);
+}
+
+// with Char_Array input
+int char_array_to_Number(Char_Array cstr_num,Number* output){
+ char* buffer;
+ char_array_to_str(cstr_num,&buffer);
+ str_to_Number(buffer, output);
+ free(buffer);
+ return(0);
+}
+
+
+// -------------------- Number_Matrix ---------------------
+
+// init
+int init_Number_Matrix(Number_Matrix* matrix, int length){
+ int i,j;
+ (*matrix).matrix=calloc(length,sizeof(Number*));
+ (*matrix).indices=calloc(length,sizeof(int));
+ for(i=0;i<length;i++){
+ (*matrix).matrix[i]=calloc(length,sizeof(Number));
+ for(j=0;j<length;j++){
+ (*matrix).matrix[i][j]=number_zero();
+ }
+ }
+ (*matrix).length=length;
+ return(0);
+}
+int free_Number_Matrix(Number_Matrix matrix){
+ int i,j;
+ for(i=0;i<matrix.length;i++){
+ for(j=0;j<matrix.length;j++){
+ free_Number(matrix.matrix[i][j]);
+ }
+ free(matrix.matrix[i]);
+ }
+ free(matrix.matrix);
+ free(matrix.indices);
+ return(0);
+}
+
+// Pauli matrices
+int Pauli_matrix(int i, Number_Matrix* output){
+ init_Number_Matrix(output,2);
+ switch(i){
+ case 1:
+ number_add_elem(quot(1,1),1,(*output).matrix[0]+1);
+ number_add_elem(quot(1,1),1,(*output).matrix[1]+0);
+ break;
+ case 2:
+ number_add_elem(quot(-1,1),-1,(*output).matrix[0]+1);
+ number_add_elem(quot(1,1),-1,(*output).matrix[1]+0);
+ break;
+ case 3:
+ number_add_elem(quot(1,1),1,(*output).matrix[0]+0);
+ number_add_elem(quot(-1,1),1,(*output).matrix[1]+1);
+ break;
+ default:
+ fprintf(stderr,"error: requested %d-th pauli matrix\n",i);
+ exit(-1);
+ }
+ return(0);
+}
diff --git a/src/number.h b/src/number.h
new file mode 100644
index 0000000..4095f9c
--- /dev/null
+++ b/src/number.h
@@ -0,0 +1,120 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+Numerical constants (rational numbers and their square roots (including \sqrt{-1}=i))
+*/
+
+#ifndef NUMBER_H
+#define NUMBER_H
+
+#include "types.h"
+
+// init
+int init_Number(Number* number, int memory);
+int free_Number(Number number);
+
+// copy
+int number_cpy(Number input, Number* output);
+int number_cpy_noinit(Number input, Number* output);
+
+// resize memory
+int number_resize(Number* number, int newsize);
+
+// add a value
+int number_append(Q scalar, int base, Number* output);
+
+// concatenate
+int number_concat(Number input, Number* output);
+
+// special numbers
+Number number_zero();
+Number number_one();
+
+// find a base element
+int number_find_base(int base, Number number);
+
+// sort
+int number_sort(Number number, int begin, int end);
+// exchange terms (for sorting)
+int number_exchange_terms(int index1, int index2, Number number);
+
+// checks whether two numbers are equal
+int number_compare(Number x1, Number x2);
+
+// add (write result to second element)
+int number_add_chain(Number input, Number* inout);
+// add a single element
+int number_add_elem(Q scalar, int base, Number* inout);
+// create a new number
+int number_add(Number x1, Number x2, Number* out);
+// return the number
+Number number_add_ret(Number x1, Number x_2);
+
+// multiply
+int number_prod(Number x1, Number x2, Number* out);
+// write to second number
+int number_prod_chain(Number input, Number* inout);
+// return result
+Number number_prod_ret(Number x1, Number x2);
+
+// multiply by a rational
+int number_Qprod_chain(Q q, Number* inout);
+// write to output
+int number_Qprod(Q q, Number x, Number* inout);
+// return result
+Number number_Qprod_ret(Q q, Number x);
+
+// inverse
+int number_inverse_inplace(Number* inout);
+// write to output
+int number_inverse(Number input, Number* output);
+// return result
+Number number_inverse_ret(Number x);
+
+// quotient
+int number_quot(Number x1, Number x2, Number* output);
+int number_quot_chain(Number x1, Number* inout);
+Number number_quot_ret(Number x1, Number x2);
+
+// remove 0's
+int number_simplify(Number in, Number* out);
+
+// check whether a number is 0
+int number_is_zero(Number x);
+
+// approximate numerical expression
+long double number_double_val(Number x);
+
+// print to string
+int number_sprint(Number number, Char_Array* out);
+// print to stdout
+int number_print(Number number);
+// read from a string
+int str_to_Number(char* str, Number* number);
+// char array input
+int char_array_to_Number(Char_Array cstr_num, Number* number);
+
+
+//------------------------ Number_Matrix --------------------------
+// init
+int init_Number_Matrix(Number_Matrix* matrix, int length);
+int free_Number_Matrix(Number_Matrix matrix);
+
+// Pauli matrices
+int Pauli_matrix(int i, Number_Matrix* output);
+
+#endif
diff --git a/src/numkondo.c b/src/numkondo.c
new file mode 100644
index 0000000..dce7de6
--- /dev/null
+++ b/src/numkondo.c
@@ -0,0 +1,226 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+numkondo
+
+Compute the flow of a flow equation numerically
+
+*/
+
+
+#include <stdio.h>
+#include <stdlib.h>
+
+// pre-compiler definitions
+#include "definitions.cpp"
+
+// rccs
+#include "rcc.h"
+// grouped representation of polynomials
+#include "grouped_polynomial.h"
+// command line parser
+#include "cli_parser.h"
+// parse input file
+#include "parse_file.h"
+// numerical flow
+#include "flow.h"
+// arrays
+#include "array.h"
+
+// read cli arguments
+int read_args_numkondo(int argc,const char* argv[], Str_Array* str_args, Numkondo_Options* opts);
+// print usage message
+int print_usage_numkondo();
+// compute flow
+int numflow(Str_Array str_args, Numkondo_Options opts);
+
+
+int main (int argc, const char* argv[]){
+ // string arguments
+ Str_Array str_args;
+ // options
+ Numkondo_Options opts;
+
+ // read command-line arguments
+ read_args_numkondo(argc,argv,&str_args,&opts);
+
+ numflow(str_args, opts);
+
+ //free memory
+ free_Str_Array(str_args);
+ return(0);
+}
+
+
+// parse command-line arguments
+#define CP_FLAG_NITER 1
+#define CP_FLAG_TOL 2
+#define CP_FLAG_RCCS 3
+int read_args_numkondo(int argc,const char* argv[], Str_Array* str_args, Numkondo_Options* opts){
+ int i;
+ // pointers
+ char* ptr;
+ // file to read the polynomial from in flow mode
+ const char* file="";
+ // flag that indicates what argument is being read
+ int flag=0;
+ // whether a file was specified on the command-line
+ int exists_file=0;
+
+ // if there are no arguments
+ if(argc==1){
+ print_usage_numkondo();
+ exit(-1);
+ }
+
+ // defaults
+ // display entire flow
+ (*opts).display_mode=DISPLAY_NUMERICAL;
+ // default niter
+ (*opts).niter=100;
+ // default to 0 tolerance
+ (*opts).tol=0;
+ // mark rccstring so that it can be recognized whether it has been set or not
+ (*opts).eval_rccstring.length=-1;
+
+// loop over arguments
+for(i=1;i<argc;i++){
+ // flag
+ if(argv[i][0]=='-'){
+ for(ptr=((char*)argv[i])+1;*ptr!='\0';ptr++){
+ switch(*ptr){
+ // final step: display the final step of the integration with maximal precision
+ case 'F':
+ (*opts).display_mode=DISPLAY_FINAL;
+ break;
+ // niter
+ case 'N':
+ flag=CP_FLAG_NITER;
+ break;
+ // tolerance
+ case 'D':
+ flag=CP_FLAG_TOL;
+ break;
+ // initial condition
+ case 'I':
+ flag=CP_FLAG_RCCS;
+ break;
+ // print version
+ case 'v':
+ printf("numkondo " VERSION "\n");
+ exit(1);
+ break;
+ }
+ }
+ }
+ // if the niter flag is up
+ else if (flag==CP_FLAG_NITER){
+ // read niter
+ sscanf(argv[i],"%d",&((*opts).niter));
+ // reset flag
+ flag=0;
+ }
+ // tolerance
+ else if (flag==CP_FLAG_TOL){
+ sscanf(argv[i],"%Lf",&((*opts).tol));
+ flag=0;
+ }
+ // init condition
+ else if(flag==CP_FLAG_RCCS){
+ str_to_char_array((char*)argv[i], &((*opts).eval_rccstring));
+ flag=0;
+ }
+ // read file name from command-line
+ else{
+ file=argv[i];
+ exists_file=1;
+ }
+ }
+
+ read_config_file(str_args, file, 1-exists_file);
+
+ return(0);
+}
+
+// print usage message
+int print_usage_numkondo(){
+ printf("\nusage:\n numkondo [-F] [-N niter] [-D tolerance] [-I initial_condition] <filename>\n\n");
+ return(0);
+}
+
+
+// numerical computation of the flow
+int numflow(Str_Array str_args, Numkondo_Options opts){
+ // index of the entry in the input file
+ int arg_index;
+ // list of rccs
+ Labels labels;
+ // initial condition
+ RCC init_cd;
+ // flow equation
+ Grouped_Polynomial flow_equation;
+
+ // parse id table
+ arg_index=find_str_arg("labels", str_args);
+ if(arg_index<0){
+ fprintf(stderr,"error: no labels entry in the configuration file\n");
+ exit(-1);
+ }
+ else{
+ parse_labels(str_args.strs[arg_index], &labels);
+ }
+
+ // parse flow equation
+ arg_index=find_str_arg("flow_equation", str_args);
+ if(arg_index<0){
+ fprintf(stderr,"error: no flow equation entry in the configuration file\n");
+ exit(-1);
+ }
+ else{
+ char_array_to_Grouped_Polynomial(str_args.strs[arg_index], &flow_equation);
+ }
+
+ // initial conditions
+ // check they were not specified on the command line
+ if(opts.eval_rccstring.length==-1){
+ arg_index=find_str_arg("initial_condition", str_args);
+ if(arg_index<0){
+ fprintf(stderr,"error: no initial condition in the configuration file or on the command line\n");
+ exit(-1);
+ }
+ else{
+ char_array_cpy(str_args.strs[arg_index],&(opts.eval_rccstring));
+ }
+ }
+ // initialize the rccs
+ prepare_init(flow_equation.indices,flow_equation.length,&init_cd);
+ // read rccs from string
+ if(opts.eval_rccstring.length!=-1){
+ parse_init_cd(opts.eval_rccstring, &init_cd);
+ free_Char_Array(opts.eval_rccstring);
+ }
+
+ numerical_flow(flow_equation, init_cd, labels, opts.niter, opts.tol, opts.display_mode);
+
+ free_RCC(init_cd);
+
+ // free memory
+ free_Labels(labels);
+ free_Grouped_Polynomial(flow_equation);
+ return(0);
+}
+
diff --git a/src/parse_file.c b/src/parse_file.c
new file mode 100644
index 0000000..6054372
--- /dev/null
+++ b/src/parse_file.c
@@ -0,0 +1,796 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "parse_file.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include "array.h"
+#include "fields.h"
+#include "rational.h"
+#include "number.h"
+#include "polynomial.h"
+#include "rcc.h"
+#include "definitions.cpp"
+#include "istring.h"
+#include "tools.h"
+#include "idtable.h"
+
+
+// parsing modes
+#define PP_NULL_MODE 0
+// when reading a factor
+#define PP_FACTOR_MODE 1
+// reading a monomial
+#define PP_MONOMIAL_MODE 2
+// reading a numerator and denominator
+#define PP_NUMBER_MODE 3
+// types of fields
+#define PP_FIELD_MODE 6
+#define PP_PARAMETER_MODE 7
+#define PP_EXTERNAL_MODE 8
+#define PP_INTERNAL_MODE 9
+#define PP_FERMIONS_MODE 10
+// indices
+#define PP_INDEX_MODE 11
+// factors or monomials
+#define PP_BRACKET_MODE 12
+// labels
+#define PP_LABEL_MODE 13
+// polynomial
+#define PP_POLYNOMIAL_MODE 14
+// group
+#define PP_GROUP_MODE 15
+
+
+// parse fields list
+int parse_input_fields(Char_Array str_fields, Fields_Table* fields){
+ // buffer
+ char* buffer=calloc(str_fields.length+1,sizeof(char));
+ char* buffer_ptr=buffer;
+ int i,j;
+ int mode;
+ int comment=0;
+
+ // allocate memory
+ init_Fields_Table(fields);
+
+ // loop over input
+ mode=PP_NULL_MODE;
+ for(j=0;j<str_fields.length;j++){
+ if(comment==1){
+ if(str_fields.str[j]=='\n'){
+ comment=0;
+ }
+ }
+ else{
+ switch(str_fields.str[j]){
+ // parameters
+ case 'h':
+ if(mode==PP_NULL_MODE){
+ mode=PP_PARAMETER_MODE;
+ }
+ break;
+ // external fields
+ case 'x':
+ if(mode==PP_NULL_MODE){
+ mode=PP_EXTERNAL_MODE;
+ }
+ break;
+ // internal fields
+ case 'i':
+ if(mode==PP_NULL_MODE){
+ mode=PP_INTERNAL_MODE;
+ }
+ break;
+ case 'f':
+ if(mode==PP_NULL_MODE){
+ mode=PP_FERMIONS_MODE;
+ }
+ break;
+
+ // reset buffer
+ case ':':
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ break;
+
+ // write to fields
+ case ',':
+ sscanf(buffer,"%d",&i);
+ if(mode==PP_PARAMETER_MODE){
+ int_array_append(i,&((*fields).parameter));
+ }
+ else if(mode==PP_EXTERNAL_MODE){
+ int_array_append(i,&((*fields).external));
+ }
+ else if(mode==PP_INTERNAL_MODE){
+ int_array_append(i,&((*fields).internal));
+ }
+ else if(mode==PP_FERMIONS_MODE){
+ int_array_append(i,&((*fields).fermions));
+ }
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ break;
+
+ // back to null mode
+ case '\n':
+ sscanf(buffer,"%d",&i);
+ if(mode==PP_PARAMETER_MODE){
+ int_array_append(i,&((*fields).parameter));
+ }
+ else if(mode==PP_EXTERNAL_MODE){
+ int_array_append(i,&((*fields).external));
+ }
+ else if(mode==PP_INTERNAL_MODE){
+ int_array_append(i,&((*fields).internal));
+ }
+ else if(mode==PP_FERMIONS_MODE){
+ int_array_append(i,&((*fields).fermions));
+ }
+ mode=PP_NULL_MODE;
+ break;
+
+ // comment
+ case '#':
+ comment=1;
+ break;
+
+ default:
+ if(mode!=PP_NULL_MODE){
+ buffer_ptr=str_addchar(buffer_ptr,str_fields.str[j]);
+ }
+ break;
+ }
+ }
+ }
+ free(buffer);
+ return(0);
+}
+
+
+// parse symbols list
+// write result to fields
+int parse_input_symbols(Char_Array str_symbols, Fields_Table* fields){
+ // buffer
+ char* buffer=calloc(str_symbols.length+1,sizeof(char));
+ char* buffer_ptr=buffer;
+ Polynomial polynomial;
+ int index;
+ int i,j;
+ int mode;
+ int comment=0;
+
+ // loop over input
+ mode=PP_INDEX_MODE;
+ for(j=0;j<str_symbols.length;j++){
+ if(comment==1){
+ if(str_symbols.str[j]=='\n'){
+ comment=0;
+ }
+ }
+ // stay in polynomial mode until ','
+ else if(mode==PP_POLYNOMIAL_MODE){
+ if(str_symbols.str[j]==','){
+ // parse polynomial
+ str_to_Polynomial(buffer, &polynomial);
+ // write index and polynomial
+ symbols_append_noinit(index, polynomial, &((*fields).symbols));
+ mode=PP_INDEX_MODE;
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ else{
+ buffer_ptr=str_addchar(buffer_ptr,str_symbols.str[j]);
+ }
+ }
+ else{
+ switch(str_symbols.str[j]){
+ // polynomial mode
+ case '=':
+ if(mode==PP_INDEX_MODE){
+ // read index
+ sscanf(buffer,"%d",&index);
+ // reset buffer
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ mode=PP_POLYNOMIAL_MODE;
+ }
+ break;
+
+ // comment
+ case '#':
+ comment=1;
+ break;
+
+ default:
+ buffer_ptr=str_addchar(buffer_ptr,str_symbols.str[j]);
+ break;
+ }
+ }
+ }
+
+ // last step
+ if(polynomial.length>0){
+ str_to_Polynomial(buffer, &polynomial);
+ symbols_append_noinit(index, polynomial, &((*fields).symbols));
+ }
+
+ // simplify
+ for(i=0;i<(*fields).symbols.length;i++){
+ polynomial_simplify((*fields).symbols.expr+i, *fields);
+ }
+
+ free(buffer);
+ return(0);
+}
+
+// parse groups of independent fields
+int parse_input_groups(Char_Array str_groups, Groups* groups){
+ // buffer
+ char* buffer=calloc(str_groups.length+1,sizeof(char));
+ char* buffer_ptr=buffer;
+ int index;
+ int j;
+ Int_Array group;
+ int mode;
+ int comment=0;
+
+ // alloc
+ init_Groups(groups, GROUP_SIZE);
+
+ // loop over input
+ mode=PP_NULL_MODE;
+ for(j=0;j<str_groups.length;j++){
+ if(comment==1){
+ if(str_groups.str[j]=='\n'){
+ comment=0;
+ }
+ }
+ else{
+ switch(str_groups.str[j]){
+ // group mode
+ case '(':
+ if(mode==PP_NULL_MODE){
+ // reset buffer
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ // init
+ init_Int_Array(&group, GROUP_SIZE);
+ mode=PP_GROUP_MODE;
+ }
+ break;
+ case')':
+ if(mode==PP_GROUP_MODE){
+ sscanf(buffer,"%d",&index);
+ int_array_append(index, &group);
+ groups_append_noinit(group, groups);
+ mode=PP_NULL_MODE;
+ }
+ break;
+
+ // read index
+ case',':
+ if(mode==PP_GROUP_MODE){
+ sscanf(buffer,"%d",&index);
+ int_array_append(index, &group);
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ break;
+
+ // comment
+ case '#':
+ comment=1;
+ break;
+
+ default:
+ if(mode!=PP_NULL_MODE){
+ buffer_ptr=str_addchar(buffer_ptr,str_groups.str[j]);
+ }
+ break;
+ }
+ }
+ }
+
+ free(buffer);
+ return(0);
+}
+
+
+// parse identities between fields
+// write result to fields
+int parse_input_identities(Char_Array str_identities, Fields_Table* fields){
+ // buffer
+ char* buffer=calloc(str_identities.length+1,sizeof(char));
+ char* buffer_ptr=buffer;
+ Int_Array monomial;
+ Polynomial polynomial;
+ int i,j;
+ int sign;
+ int tmp;
+ int mode;
+ int comment=0;
+
+ init_Int_Array(&monomial, MONOMIAL_SIZE);
+
+ // loop over input
+ mode=PP_NULL_MODE;
+ for(j=0;j<str_identities.length;j++){
+ if(comment==1){
+ if(str_identities.str[j]=='\n'){
+ comment=0;
+ }
+ }
+ // stay in polynomial mode until ','
+ else if(mode==PP_POLYNOMIAL_MODE){
+ if(str_identities.str[j]==','){
+ // parse polynomial
+ str_to_Polynomial(buffer, &polynomial);
+ // write monomial and polynomial
+ identities_append_noinit(monomial, polynomial, &((*fields).ids));
+ // realloc
+ init_Int_Array(&monomial, MONOMIAL_SIZE);
+ mode=PP_NULL_MODE;
+ }
+ else{
+ buffer_ptr=str_addchar(buffer_ptr,str_identities.str[j]);
+ }
+ }
+ else{
+ switch(str_identities.str[j]){
+ // monomial
+ case '[':
+ if(mode==PP_NULL_MODE){
+ mode=PP_INDEX_MODE;
+ }
+ if(mode==PP_INDEX_MODE){
+ mode=PP_BRACKET_MODE;
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ break;
+ // for notational homogeneity
+ case 'f':
+ if(mode==PP_BRACKET_MODE){
+ mode=PP_FIELD_MODE;
+ }
+ break;
+ // write monomial term
+ case ']':
+ if(mode==PP_FIELD_MODE){
+ sscanf(buffer,"%d",&i);
+ int_array_append(i,&monomial);
+ mode=PP_INDEX_MODE;
+ }
+ break;
+
+ // polynomial mode
+ case '=':
+ if(mode==PP_INDEX_MODE){
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ mode=PP_POLYNOMIAL_MODE;
+ }
+ break;
+
+ // comment
+ case '#':
+ comment=1;
+ break;
+
+ default:
+ if(mode!=PP_NULL_MODE){
+ buffer_ptr=str_addchar(buffer_ptr,str_identities.str[j]);
+ }
+ break;
+ }
+ }
+ }
+
+ // last step
+ if(mode==PP_POLYNOMIAL_MODE){
+ str_to_Polynomial(buffer, &polynomial);
+ identities_append_noinit(monomial, polynomial, &((*fields).ids));
+ }
+ else{
+ free_Int_Array(monomial);
+ }
+
+ // sort
+ // don't use the identities to simplify
+ tmp=(*fields).ids.length;
+ (*fields).ids.length=0;
+ for(i=0;i<tmp;i++){
+ sign=1;
+ monomial_sort((*fields).ids.lhs[i], 0, (*fields).ids.lhs[i].length-1, *fields, &sign);
+ polynomial_simplify((*fields).ids.rhs+i, *fields);
+ polynomial_multiply_Qscalar((*fields).ids.rhs[i],quot(sign,1));
+ }
+ (*fields).ids.length=tmp;
+
+ free(buffer);
+ return(0);
+}
+
+// parse propagator
+int parse_input_propagator(Char_Array str_propagator, Polynomial_Matrix* propagator, Fields_Table fields){
+ // buffer
+ char* buffer=calloc(str_propagator.length+1,sizeof(char));
+ char* buffer_ptr=buffer;
+ int i,j;
+ int index1=-1;
+ int index2=-1;
+ int mode;
+ int comment=0;
+
+ // allocate memory
+ init_Polynomial_Matrix(propagator, fields.internal.length);
+
+ // copy indices
+ for(i=0;i<fields.internal.length;i++){
+ (*propagator).indices[i]=fields.internal.values[i];
+ }
+
+ // loop over input
+ mode=PP_INDEX_MODE;
+ for(j=0;j<str_propagator.length;j++){
+ if(comment==1){
+ if(str_propagator.str[j]=='\n'){
+ comment=0;
+ }
+ }
+ else{
+ switch(str_propagator.str[j]){
+ // indices
+ case ';':
+ if(mode==PP_INDEX_MODE){
+ sscanf(buffer,"%d",&i);
+ index1=intlist_find_err((*propagator).indices, (*propagator).length, i);
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ break;
+ case ':':
+ if(mode==PP_INDEX_MODE){
+ sscanf(buffer,"%d",&i);
+ index2=intlist_find_err((*propagator).indices, (*propagator).length, i);
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ mode=PP_POLYNOMIAL_MODE;
+ }
+ break;
+
+ // num
+ case ',':
+ if(mode==PP_POLYNOMIAL_MODE && index1>=0 && index2>=0){
+ free_Polynomial((*propagator).matrix[index1][index2]);
+ str_to_Polynomial(buffer,(*propagator).matrix[index1]+index2);
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ mode=PP_INDEX_MODE;
+ }
+ break;
+
+ // comment
+ case '#':
+ comment=1;
+ break;
+
+ default:
+ buffer_ptr=str_addchar(buffer_ptr,str_propagator.str[j]);
+ break;
+ }
+ }
+ }
+
+ // last step
+ if(mode==PP_POLYNOMIAL_MODE){
+ free_Polynomial((*propagator).matrix[index1][index2]);
+ str_to_Polynomial(buffer,(*propagator).matrix[index1]+index2);
+ }
+
+ free(buffer);
+ return(0);
+}
+
+
+// parse input polynomial
+int parse_input_polynomial(Char_Array str_polynomial, Polynomial* output, Fields_Table fields){
+ int j;
+ // buffer
+ char* buffer=calloc(str_polynomial.length+1,sizeof(char));
+ char* buffer_ptr=buffer;
+ Polynomial tmp_poly;
+
+ // allocate memory
+ init_Polynomial(output,POLY_SIZE);
+
+ for(j=0;j<str_polynomial.length;j++){
+ switch(str_polynomial.str[j]){
+ case '*':
+ str_to_Polynomial(buffer, &tmp_poly);
+ if((*output).length==0){
+ polynomial_concat(tmp_poly, output);
+ }
+ else{
+ polynomial_prod_chain(tmp_poly, output, fields);
+ }
+ free_Polynomial(tmp_poly);
+
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ break;
+
+ default:
+ buffer_ptr=str_addchar(buffer_ptr,str_polynomial.str[j]);
+ break;
+ }
+ }
+
+ //last step
+ str_to_Polynomial(buffer, &tmp_poly);
+ if((*output).length==0){
+ polynomial_concat(tmp_poly, output);
+ }
+ else{
+ polynomial_prod_chain(tmp_poly, output, fields);
+ }
+ free_Polynomial(tmp_poly);
+
+ free(buffer);
+ return(0);
+}
+
+
+
+// parse id table
+// fields argument for sorting
+int parse_input_id_table(Char_Array str_idtable, Id_Table* idtable, Fields_Table fields){
+ // buffer
+ char* buffer=calloc(str_idtable.length+1,sizeof(char));
+ char* buffer_ptr=buffer;
+ int index;
+ Polynomial polynomial;
+ int j;
+ int mode;
+ int comment=0;
+
+ // allocate memory
+ init_Id_Table(idtable,EQUATION_SIZE);
+
+ // loop over input
+ mode=PP_INDEX_MODE;
+ for(j=0;j<str_idtable.length;j++){
+ if(comment==1){
+ if(str_idtable.str[j]=='\n'){
+ comment=0;
+ }
+ }
+ else{
+ switch(str_idtable.str[j]){
+ // end polynomial mode
+ case ',':
+ // write polynomial
+ if(mode==PP_POLYNOMIAL_MODE){
+ str_to_Polynomial(buffer,&polynomial);
+ // add to idtable
+ idtable_append_noinit(index,polynomial,idtable);
+ mode=PP_INDEX_MODE;
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ break;
+
+ case ':':
+ if(mode==PP_INDEX_MODE){
+ sscanf(buffer,"%d",&index);
+ mode=PP_POLYNOMIAL_MODE;
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ break;
+
+ // comment
+ case '#':
+ comment=1;
+ break;
+
+ default:
+ if(mode!=PP_NULL_MODE){
+ buffer_ptr=str_addchar(buffer_ptr,str_idtable.str[j]);
+ }
+ break;
+ }
+ }
+ }
+
+ //last step
+ if(mode==PP_POLYNOMIAL_MODE){
+ str_to_Polynomial(buffer,&polynomial);
+ idtable_append_noinit(index,polynomial,idtable);
+ }
+
+ // sort
+ for(j=0;j<(*idtable).length;j++){
+ polynomial_simplify((*idtable).polynomials+j, fields);
+ }
+
+ free(buffer);
+ return(0);
+}
+
+// parse a list of labels
+int parse_labels(Char_Array str_labels, Labels* labels){
+ // buffer
+ char* buffer=calloc(str_labels.length+1,sizeof(char));
+ char* buffer_ptr=buffer;
+ Char_Array label;
+ int index;
+ int j;
+ int mode;
+ int comment=0;
+
+ // allocate memory
+ init_Labels(labels,EQUATION_SIZE);
+
+ // loop over input
+ mode=PP_INDEX_MODE;
+ for(j=0;j<str_labels.length;j++){
+ if(comment==1){
+ if(str_labels.str[j]=='\n'){
+ comment=0;
+ }
+ }
+ else{
+ switch(str_labels.str[j]){
+ case '"':
+ if(mode==PP_INDEX_MODE){
+ mode=PP_LABEL_MODE;
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ // write
+ else if(mode==PP_LABEL_MODE){
+ str_to_char_array(buffer,&label);
+ labels_append_noinit(label,index,labels);
+ mode=PP_INDEX_MODE;
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ break;
+
+ case ':':
+ // write
+ if(mode==PP_INDEX_MODE){
+ sscanf(buffer,"%d",&index);
+ }
+ break;
+
+ // characters to ignore
+ case ' ':break;
+ case '&':break;
+ case '\n':break;
+ case ',':break;
+
+ // comment
+ case '#':
+ comment=1;
+ break;
+
+ default:
+ buffer_ptr=str_addchar(buffer_ptr,str_labels.str[j]);
+ break;
+ }
+ }
+ }
+
+ free(buffer);
+ return(0);
+}
+
+
+// read initial condition for numerical computation
+int parse_init_cd(Char_Array init_cd, RCC* init){
+ char* buffer=calloc(init_cd.length+1,sizeof(char));
+ char* buffer_ptr=buffer;
+ int index=0;
+ int i,j;
+ int comment_mode=0;
+ int dcount=0;
+
+ *buffer_ptr='\0';
+ // loop over the input
+ for(j=0;j<init_cd.length;j++){
+ if(comment_mode==1){
+ if(init_cd.str[j]=='\n'){
+ comment_mode=0;
+ }
+ }
+ else{
+ switch(init_cd.str[j]){
+ // new term
+ case ',':
+ // write init
+ sscanf(buffer,"%Lf",(*init).values+intlist_find_err((*init).indices,(*init).length,index));
+ // reset buffer
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ // reset derivatives counter
+ dcount=0;
+ break;
+ // separator
+ case ':':
+ // write index
+ sscanf(buffer,"%d",&i);
+ if(i<0){
+ index=i-dcount*DOFFSET;
+ }
+ else{
+ index=i+dcount*DOFFSET;
+ }
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ break;
+ // derivatives
+ case 'd':
+ dcount++;
+ break;
+
+ // characters to ignore
+ case ' ':break;
+ case '&':break;
+ case '\n':break;
+
+ // comments
+ case '#':
+ comment_mode=1;
+ break;
+
+ default:
+ // write to buffer
+ buffer_ptr=str_addchar(buffer_ptr,init_cd.str[j]);
+ break;
+ }
+ }
+ }
+
+ // write init
+ sscanf(buffer,"%Lf",(*init).values+unlist_find((*init).indices,(*init).length,index));
+
+ free(buffer);
+ return(0);
+}
+
+
+// set indices and length of init
+int prepare_init(int* indices, int length, RCC* init){
+ int i;
+ init_RCC(init, length);
+ for(i=0;i<length;i++){
+ (*init).indices[i]=indices[i];
+ // set constants to 1
+ if(indices[i]<0 && indices[i]>-DOFFSET){
+ (*init).values[i]=1.;
+ }
+ else{
+ (*init).values[i]=0.;
+ }
+
+ }
+ return(0);
+}
diff --git a/src/parse_file.h b/src/parse_file.h
new file mode 100644
index 0000000..b51103a
--- /dev/null
+++ b/src/parse_file.h
@@ -0,0 +1,56 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+Parse the input file
+*/
+
+#ifndef PARSE_FILE_H
+#define PARSE_FILE_H
+
+#include "types.h"
+
+// parse fields list
+int parse_input_fields(Char_Array str_fields, Fields_Table* fields);
+
+// parse symbols list
+int parse_input_symbols(Char_Array str_symbols, Fields_Table* fields);
+
+// parse groups of independent fields
+int parse_input_groups(Char_Array str_groups, Groups* groups);
+
+// parse identities between fields
+int parse_input_identities(Char_Array str_identities, Fields_Table* fields);
+
+// parse propagator
+int parse_input_propagator(Char_Array str_propagator, Polynomial_Matrix* propagator, Fields_Table fields);
+
+// parse input polynomial
+int parse_input_polynomial(Char_Array str_polynomial, Polynomial* output, Fields_Table fields);
+
+// parse id table
+int parse_input_id_table(Char_Array str_idtable, Id_Table* idtable, Fields_Table fields);
+
+// parse a list of labels
+int parse_labels(Char_Array str_labels, Labels* labels);
+
+// parse the initial condition
+int parse_init_cd(Char_Array init_cd, RCC* init);
+
+// set indices and length of init
+int prepare_init(int* indices, int length, RCC* init);
+
+#endif
diff --git a/src/polynomial.c b/src/polynomial.c
new file mode 100644
index 0000000..639728a
--- /dev/null
+++ b/src/polynomial.c
@@ -0,0 +1,1263 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "polynomial.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include "definitions.cpp"
+#include "rational.h"
+#include "tools.h"
+#include "mean.h"
+#include "coefficient.h"
+#include "istring.h"
+#include "array.h"
+#include "number.h"
+#include "fields.h"
+
+
+// allocate memory
+int init_Polynomial(Polynomial* polynomial,int size){
+ (*polynomial).monomials=calloc(size,sizeof(Int_Array));
+ (*polynomial).factors=calloc(size,sizeof(Int_Array));
+ (*polynomial).nums=calloc(size,sizeof(Number));
+ (*polynomial).length=0;
+ (*polynomial).memory=size;
+ return(0);
+}
+
+// free memory
+int free_Polynomial(Polynomial polynomial){
+ int i;
+ for(i=0;i<polynomial.length;i++){
+ free_Int_Array(polynomial.monomials[i]);
+ free_Int_Array(polynomial.factors[i]);
+ free_Number(polynomial.nums[i]);
+ }
+ free(polynomial.monomials);
+ free(polynomial.factors);
+ free(polynomial.nums);
+
+ return(0);
+}
+
+// resize the memory allocated to a polynomial
+int resize_polynomial(Polynomial* polynomial,int new_size){
+ Polynomial new_poly;
+ int i;
+
+ init_Polynomial(&new_poly,new_size);
+ for(i=0;i<(*polynomial).length;i++){
+ new_poly.monomials[i]=(*polynomial).monomials[i];
+ new_poly.factors[i]=(*polynomial).factors[i];
+ new_poly.nums[i]=(*polynomial).nums[i];
+ }
+ new_poly.length=(*polynomial).length;
+
+ free((*polynomial).monomials);
+ free((*polynomial).factors);
+ free((*polynomial).nums);
+
+ *polynomial=new_poly;
+ return(0);
+}
+
+// copy a polynomial
+int polynomial_cpy(Polynomial input, Polynomial* output){
+ init_Polynomial(output,input.length);
+ polynomial_cpy_noinit(input,output);
+ return(0);
+}
+int polynomial_cpy_noinit(Polynomial input, Polynomial* output){
+ int i;
+ if((*output).memory<input.length){
+ fprintf(stderr,"error: trying to copy a polynomial of length %d to another with memory %d\n",input.length,(*output).memory);
+ exit(-1);
+ }
+ for(i=0;i<input.length;i++){
+ int_array_cpy(input.monomials[i],(*output).monomials+i);
+ int_array_cpy(input.factors[i],(*output).factors+i);
+ number_cpy(input.nums[i],(*output).nums+i);
+ }
+ (*output).length=input.length;
+
+ return(0);
+}
+
+// append an element to a polynomial
+int polynomial_append(Int_Array monomial, Int_Array factor, Number num, Polynomial* output){
+ int offset=(*output).length;
+
+ if((*output).length>=(*output).memory){
+ resize_polynomial(output,2*(*output).memory+1);
+ }
+
+ // copy and allocate
+ int_array_cpy(monomial,(*output).monomials+offset);
+ int_array_cpy(factor,(*output).factors+offset);
+ number_cpy(num,(*output).nums+offset);
+ //increment length
+ (*output).length++;
+
+ return(0);
+}
+// append an element to a polynomial without allocating memory
+int polynomial_append_noinit(Int_Array monomial, Int_Array factor, Number num, Polynomial* output){
+ int offset=(*output).length;
+
+ if((*output).length>=(*output).memory){
+ resize_polynomial(output,2*(*output).memory+1);
+ }
+
+ // copy without allocating
+ (*output).monomials[offset]=monomial;
+ (*output).factors[offset]=factor;
+ (*output).nums[offset]=num;
+ // increment length
+ (*output).length++;
+ return(0);
+}
+// noinit, and if there already exists an element with the same monomial and factor, then just add numbers
+int polynomial_append_noinit_inplace(Int_Array monomial, Int_Array factor, Number num, Polynomial* output){
+ int i;
+ int foundit=0;
+ for(i=0;i<(*output).length;i++){
+ if(int_array_cmp(monomial, (*output).monomials[i])==0 && int_array_cmp(factor, (*output).factors[i])==0){
+ number_add_chain(num,(*output).nums+i);
+ foundit=1;
+ free_Number(num);
+ free_Int_Array(monomial);
+ free_Int_Array(factor);
+ break;
+ }
+ }
+ if(foundit==0){
+ polynomial_append_noinit(monomial, factor, num, output);
+ }
+ return(0);
+}
+
+// concatenate two polynomials
+int polynomial_concat(Polynomial input, Polynomial* output){
+ int i;
+ for(i=0;i<input.length;i++){
+ polynomial_append(input.monomials[i],input.factors[i],input.nums[i],output);
+ }
+ return(0);
+}
+// noinit
+int polynomial_concat_noinit(Polynomial input, Polynomial* output){
+ int i;
+ for(i=0;i<input.length;i++){
+ polynomial_append_noinit(input.monomials[i],input.factors[i],input.nums[i],output);
+ }
+
+ // free input arrays
+ free(input.monomials);
+ free(input.factors);
+ free(input.nums);
+ return(0);
+}
+// noinit, inplace
+int polynomial_concat_noinit_inplace(Polynomial input, Polynomial* output){
+ int i;
+ for(i=0;i<input.length;i++){
+ polynomial_append_noinit_inplace(input.monomials[i],input.factors[i],input.nums[i],output);
+ }
+
+ // free input arrays
+ free(input.monomials);
+ free(input.factors);
+ free(input.nums);
+ return(0);
+}
+
+// add polynomials
+int polynomial_add_chain(Polynomial input, Polynomial* inout, Fields_Table fields){
+ polynomial_concat(input,inout);
+ polynomial_simplify(inout, fields);
+ return(0);
+}
+// add polynomials (noinit)
+int polynomial_add_chain_noinit(Polynomial input, Polynomial* inout, Fields_Table fields){
+ polynomial_concat_noinit(input,inout);
+ polynomial_simplify(inout, fields);
+ return(0);
+}
+
+// multiply a polynomial by a scalar
+int polynomial_multiply_scalar(Polynomial polynomial, Number num){
+ int i;
+ for(i=0;i<polynomial.length;i++){
+ number_prod_chain(num,polynomial.nums+i);
+ }
+ return(0);
+}
+// multiply a polynomial by a rational number
+int polynomial_multiply_Qscalar(Polynomial polynomial, Q q){
+ int i;
+ for(i=0;i<polynomial.length;i++){
+ number_Qprod_chain(q,polynomial.nums+i);
+ }
+ return(0);
+}
+
+// change the sign of the monomials in a polynomial
+int polynomial_conjugate(Polynomial polynomial){
+ int i,j;
+ for(i=0;i<polynomial.length;i++){
+ for(j=0;j<polynomial.monomials[i].length;j++){
+ polynomial.monomials[i].values[j]*=-1;
+ }
+ }
+ return(0);
+}
+
+
+// returns an initialized polynomial, equal to 1
+Polynomial polynomial_one(){
+ Polynomial ret;
+ Int_Array dummy_monomial;
+ Int_Array dummy_factor;
+
+ init_Polynomial(&ret,1);
+ init_Int_Array(&dummy_monomial,1);
+ init_Int_Array(&dummy_factor,1);
+ polynomial_append_noinit(dummy_monomial,dummy_factor,number_one(),&ret);
+
+ return(ret);
+}
+
+// returns an initialized polynomial, equal to 0
+Polynomial polynomial_zero(){
+ Polynomial ret;
+ Int_Array dummy_monomial;
+ Int_Array dummy_factor;
+
+ init_Polynomial(&ret,1);
+ init_Int_Array(&dummy_monomial,1);
+ init_Int_Array(&dummy_factor,1);
+ polynomial_append_noinit(dummy_monomial,dummy_factor,number_zero(),&ret);
+
+ return(ret);
+}
+
+// check whether a polynomial is 0
+int polynomial_is_zero(Polynomial poly){
+ int i;
+ for(i=0;i<poly.length;i++){
+ if(number_is_zero(poly.nums[i])==0){
+ return(0);
+ }
+ }
+ return(1);
+}
+
+// compute V^p
+int polynomial_power(Polynomial input_polynomial, Polynomial* output, int power, Fields_Table fields){
+ int i,j;
+ int* current_term;
+ // out buffers: since we first check whether the monomial vanishes before adding it to the output,
+ // it is more efficient to concatenate the monomials in a separate variable, and then add it to the ouput
+ // instead of incrementally adding terms to the output
+ Int_Array out_monomial;
+ int monomial_size;
+ Int_Array out_factor;
+ int factor_size;
+ Number out_num;
+
+ init_Polynomial(output, POLY_SIZE);
+
+ // trivial case
+ if(power==0){
+ init_Int_Array(&out_monomial, 1);
+ init_Int_Array(&out_factor, 1);
+ polynomial_append_noinit(out_monomial, out_factor, number_one(), output);
+ return(0);
+ }
+
+ // initialize current term
+ current_term=calloc(power,sizeof(int));
+ for(i=0;i<power;i++){
+ current_term[i]=0;
+ }
+
+ // loop over terms; the loop stops when all the pointers in the list
+ // mentioned above are at the end of the input polynomial
+ while(current_term[0]<input_polynomial.length){
+ // compute the amount of memory to allocate
+ for(i=0,monomial_size=0,factor_size=0;i<power;i++){
+ monomial_size+=input_polynomial.monomials[current_term[i]].length;
+ factor_size+=input_polynomial.factors[current_term[i]].length;
+ }
+ // allocate
+ init_Int_Array(&out_monomial, monomial_size);
+ init_Int_Array(&out_factor, factor_size);
+ out_num=number_one();
+
+ // concatenate monomial and factor
+ for(i=0;i<power;i++){
+ int_array_concat(input_polynomial.monomials[current_term[i]],&out_monomial);
+ int_array_concat(input_polynomial.factors[current_term[i]],&out_factor);
+ number_prod_chain(input_polynomial.nums[current_term[i]], &out_num);
+ }
+
+ // check whether the monomial vanishes
+ if(check_monomial(out_monomial, fields)==1){
+ // multinomial combinatorial factor n!/(m1!m2!m3!...)
+ number_Qprod_chain(quot(factorial(power),multinomial(power,current_term)),&out_num);
+ // write monomials and factors
+ polynomial_append_noinit(out_monomial, out_factor, out_num, output);
+ }
+ else{
+ free_Int_Array(out_monomial);
+ free_Int_Array(out_factor);
+ free_Number(out_num);
+ }
+
+ // move to the next term of V^p by advancing the last pointer if possible,
+ // the next to last if not, and so forth, until all the pointers have
+ // reached the end of the input polynomial
+ (current_term[power-1])++;
+ // loop until the last pointer is in an adequate place or the first
+ // pointer has reached the end
+ for(i=power-2;current_term[0]<input_polynomial.length && current_term[power-1]>=input_polynomial.length;i--){
+ // try to advance pointer
+ (current_term[i])++;
+ // if the step fails, keep on looping, if not, set all the following
+ // pointers to the latest position
+ if(current_term[i]<input_polynomial.length){
+ for(j=i+1;j<power;j++){
+ current_term[j]=current_term[i];
+ }
+ }
+ }
+ }
+
+ polynomial_simplify(output, fields);
+
+ // free memory
+ free(current_term);
+ return(0);
+}
+
+
+// compute V*W
+int polynomial_prod(Polynomial input1, Polynomial input2, Polynomial* output, Fields_Table fields){
+ polynomial_cpy(input2,output);
+ polynomial_prod_chain(input1,output, fields);
+ return(0);
+}
+// chain
+int polynomial_prod_chain_nosimplify(Polynomial input, Polynomial* inout, Fields_Table fields){
+ // position in V and W
+ int pos1, pos2;
+ Int_Array out_monomial;
+ Int_Array out_factor;
+ Number out_num;
+ // save length of inout (which changes during the loop
+ int inout_length=(*inout).length;
+ // first position in input which can multiply a term of inout without vanishing
+ int firstpos;
+
+ // loop over terms
+ for(pos1=0;pos1<inout_length;pos1++){
+ // multiply first term of input to inout[pos1]
+ // search for the first possible product
+ firstpos=-1;
+ for(pos2=0; pos2<input.length; pos2++){
+ if(check_monomial_willnot_vanish((*inout).monomials[pos1],input.monomials[pos2],fields)==1){
+ firstpos=pos2;
+ pos2++;
+ break;
+ }
+ }
+
+ // if there was no possible product
+ if(firstpos==-1){
+ number_Qprod_chain(quot(0,1),(*inout).nums+pos1);
+ }
+ else{
+ // add other terms at the end of inout
+ for(;pos2<input.length;pos2++){
+ // check whether the term will vanish
+ if(check_monomial_willnot_vanish((*inout).monomials[pos1],input.monomials[pos2],fields)==1){
+ // allocate
+ init_Int_Array(&out_monomial, (*inout).monomials[pos1].length+input.monomials[pos2].length);
+ init_Int_Array(&out_factor, (*inout).factors[pos1].length+input.factors[pos2].length);
+
+ // concatenate monomial and factor
+ int_array_concat((*inout).monomials[pos1],&out_monomial);
+ int_array_concat(input.monomials[pos2],&out_monomial);
+ int_array_concat((*inout).factors[pos1],&out_factor);
+ int_array_concat(input.factors[pos2],&out_factor);
+ number_prod((*inout).nums[pos1],input.nums[pos2],&out_num);
+
+ // write monomials and factors
+ polynomial_append_noinit(out_monomial, out_factor, out_num, inout);
+ }
+ }
+ // first term
+ int_array_concat(input.monomials[firstpos],(*inout).monomials+pos1);
+ int_array_concat(input.factors[firstpos],(*inout).factors+pos1);
+ number_prod_chain(input.nums[firstpos],(*inout).nums+pos1);
+ }
+ }
+
+ return(0);
+}
+// simplify
+int polynomial_prod_chain(Polynomial input, Polynomial* inout, Fields_Table fields){
+ polynomial_prod_chain_nosimplify(input, inout, fields);
+ polynomial_simplify(inout, fields);
+ return(0);
+}
+
+// exp(V)
+int polynomial_exponential(Polynomial input_polynomial, Polynomial* output, Fields_Table fields){
+ // a buffer for the result of a given power
+ Polynomial tmp_poly;
+ // a buffer for the previous power
+ Polynomial previous_power;
+ // power
+ int power=1;
+ Int_Array out_monomial;
+ Int_Array out_factor;
+
+ // allocate memory
+ init_Polynomial(output,POLY_SIZE);
+
+ // 1
+ init_Int_Array(&out_monomial, 1);
+ init_Int_Array(&out_factor, 1);
+ polynomial_append_noinit(out_monomial, out_factor, number_one(), output);
+
+ while(1){
+ if(power>1){
+ if(power>33){
+ fprintf(stderr,"error: trying to take a power of a polynomial that is too high (>33)\n");
+ exit(-1);
+ }
+ // next power
+ polynomial_prod(input_polynomial,previous_power,&tmp_poly, fields);
+
+ // free
+ free_Polynomial(previous_power);
+ }
+ else{
+ polynomial_cpy(input_polynomial,&tmp_poly);
+ }
+
+ // if the power is high enough that V^p=0, then stop
+ if(tmp_poly.length==0){
+ free_Polynomial(tmp_poly);
+ break;
+ }
+
+ // copy for next power
+ polynomial_cpy(tmp_poly,&previous_power);
+
+ // 1/p!
+ polynomial_multiply_Qscalar(tmp_poly,quot(1,factorial(power)));
+ // append tmp to the output
+ polynomial_concat_noinit(tmp_poly,output);
+
+ // increase power
+ power++;
+ }
+
+ return(0);
+}
+
+
+// log(1+W)
+int polynomial_logarithm(Polynomial input_polynomial,Polynomial* output, Fields_Table fields){
+ // a buffer for the result of a given power
+ Polynomial tmp_poly;
+ // a buffer for the previous power
+ Polynomial previous_power;
+ // power
+ int power=1;
+
+ // allocate memory
+ init_Polynomial(output,POLY_SIZE);
+
+ while(1){
+ if(power>1){
+ // next power
+ polynomial_prod(input_polynomial,previous_power,&tmp_poly, fields);
+
+ // free
+ free_Polynomial(previous_power);
+ }
+ else{
+ polynomial_cpy(input_polynomial,&tmp_poly);
+ }
+
+ // if the power is high enough that V^p=0, then stop
+ if(tmp_poly.length==0){
+ free_Polynomial(tmp_poly);
+ break;
+ }
+
+ // copy for next power
+ polynomial_cpy(tmp_poly,&previous_power);
+
+ // (-1)^{p-1}/p
+ polynomial_multiply_Qscalar(tmp_poly,quot(ipower(-1,power-1),power));
+ // append tmp to the output
+ polynomial_concat_noinit(tmp_poly,output);
+
+ // increase power
+ power++;
+ }
+
+ return(0);
+}
+
+// check whether a monomial vanishes
+int check_monomial(Int_Array monomial, Fields_Table fields){
+ int i,j;
+ for(i=0;i<monomial.length;i++){
+ // check for repetitions
+ if(is_fermion(monomial.values[i], fields)==1){
+ for(j=i+1;j<monomial.length;j++){
+ if(monomial.values[j]==monomial.values[i]){
+ return(0);
+ }
+ }
+ }
+ }
+ return(1);
+}
+// check whether the product of two monomials will vanish
+int check_monomial_willnot_vanish(Int_Array monomial1, Int_Array monomial2, Fields_Table fields){
+ int i,j;
+ for(i=0;i<monomial1.length;i++){
+ // check for repetitions
+ if(is_fermion(monomial1.values[i], fields)==1){
+ for(j=0;j<monomial2.length;j++){
+ if(monomial2.values[j]==monomial1.values[i]){
+ return(0);
+ }
+ }
+ }
+ }
+ return(1);
+}
+
+// check whether one can add a term to a monomial without creating repetitions
+int check_monomial_addterm(Int_Array monomial, Int_Array term, Fields_Table fields){
+ int i,j;
+ for(i=0;i<term.length;i++){
+ // check for repetitions
+ if(is_fermion(term.values[i], fields)==1){
+ for(j=0;j<monomial.length;j++){
+ if(monomial.values[j]==term.values[i]){
+ return(0);
+ }
+ }
+ }
+ }
+ return(1);
+}
+
+// check whether a monomial vanishes or has unmatched +/- fields
+int check_monomial_match(Int_Array monomial, Fields_Table fields){
+ int i,j;
+ int match=0;
+ for(i=0;i<monomial.length;i++){
+ // count match
+ if(field_type(monomial.values[i], fields)==FIELD_INTERNAL){
+ if(monomial.values[i]>0){
+ match++;
+ }
+ else if(monomial.values[i]<0){
+ match--;
+ }
+ }
+
+ // check for repetitions
+ if(is_fermion(monomial.values[i], fields)==1){
+ for(j=i+1;j<monomial.length;j++){
+ if(monomial.values[j]==monomial.values[i]){
+ return(0);
+ }
+ }
+ }
+ }
+ if(match==0){
+ return(1);
+ }
+ else{
+ // different return codes depending on why the monomial was rejected
+ return(-1);
+ }
+}
+
+// remove terms with more plus internal fields than minus ones
+int remove_unmatched_plusminus(Polynomial* polynomial, Fields_Table fields){
+ int i,j;
+ int match_internals;
+ int type;
+ Polynomial output;
+
+ init_Polynomial(&output, (*polynomial).length);
+
+ for(i=0;i<(*polynomial).length;i++){
+ match_internals=0;
+ for(j=0;j<(*polynomial).monomials[i].length;j++){
+ // check for unmatched internal fields
+ type=field_type((*polynomial).monomials[i].values[j],fields);
+ if(type==FIELD_INTERNAL){
+ if((*polynomial).monomials[i].values[j]>0){
+ match_internals++;
+ }
+ else if((*polynomial).monomials[i].values[j]<0){
+ match_internals--;
+ }
+ }
+ // don't remove a term containing symbols
+ else if(type==FIELD_SYMBOL){
+ match_internals=0;
+ break;
+ }
+ }
+ if(match_internals==0){
+ polynomial_append((*polynomial).monomials[i], (*polynomial).factors[i], (*polynomial).nums[i], &output);
+ }
+ }
+
+ free_Polynomial(*polynomial);
+ *polynomial=output;
+ return(0);
+}
+
+
+// denominator of a multinomal factor: m1!m2!...
+// requires terms to be sorted
+int multinomial(int power,int* terms){
+ int multiple=1;
+ int ret=1;
+ int i;
+ // the number of numbers to be multiplied in the multinomial is
+ // equal to power-1 (the first is 1)
+ for(i=1;i<power;i++){
+ // if there is a degeneracy, then increment the multiple by
+ // which the multinomial is multiplied
+ if(terms[i-1]==terms[i]){
+ multiple++;
+ }
+ // if there is no degeneracy, reset it to 1
+ else{
+ multiple=1;
+ }
+ // multiply the result by the multiple
+ ret*=multiple;
+ }
+ return(ret);
+}
+
+
+// simplify a Polynomial
+// the fields table is there to compute the sign coming from re-arranging monomials
+int polynomial_simplify(Polynomial* polynomial, Fields_Table fields){
+ int i;
+ int monomial_cmp;
+ int factor_cmp;
+ int sign;
+ Polynomial output;
+ init_Polynomial(&output,(*polynomial).length);
+ // the combination of numerical factors
+ Number new_num;
+ init_Number(&new_num,NUMBER_SIZE);
+
+ // sort monomials and factors
+ for(i=0;i<(*polynomial).length;i++){
+ sign=1;
+ monomial_sort((*polynomial).monomials[i],0,(*polynomial).monomials[i].length-1,fields,&sign);
+ number_Qprod_chain(quot(sign,1),(*polynomial).nums+i);
+ int_array_sort((*polynomial).factors[i],0,(*polynomial).factors[i].length-1);
+ }
+
+ // resolve the identities specified in the fields table
+ resolve_ids(polynomial, fields);
+
+ // in order to perform a simplification, the list of terms must be
+ // sorted (so that terms that are proportional are next to each other)
+ polynomial_sort(polynomial,0,(*polynomial).length-1);
+
+ for(i=0;i<(*polynomial).length;i++){
+ // if the term actually exists
+ if(number_is_zero((*polynomial).nums[i])!=1){
+ // combine numerical factors
+ number_add_chain((*polynomial).nums[i], &new_num);
+ }
+ // if the numerator is 0, the previous terms that may have the same factors should still be added, hence the 'if' ends here
+
+ // if either the monomial or the factor is different from the next then add term
+ if(i<(*polynomial).length-1){
+ monomial_cmp=int_array_cmp((*polynomial).monomials[i],(*polynomial).monomials[i+1]);
+ factor_cmp=int_array_cmp((*polynomial).factors[i],(*polynomial).factors[i+1]);
+ }
+ if(i>=(*polynomial).length-1 || monomial_cmp!=0 || factor_cmp!=0 ){
+ // check that the polynomial is not trivial
+ if(number_is_zero(new_num)!=1){
+ polynomial_append((*polynomial).monomials[i],(*polynomial).factors[i],new_num,&output);
+ }
+
+ // reset new numerical factor
+ free_Number(new_num);
+ init_Number(&new_num,NUMBER_SIZE);
+ }
+ }
+
+ free_Number(new_num);
+ free_Polynomial(*polynomial);
+ *polynomial=output;
+ return(0);
+}
+
+// sort a polynomial
+// requires the monomials and factors to be sorted
+int polynomial_sort(Polynomial* polynomial, int begin, int end){
+ int i;
+ int index;
+ int monomial_cmp;
+ int factor_cmp;
+
+ // the pivot: middle of the array
+ int pivot=(begin+end)/2;
+ // if the array is non trivial
+ if(begin<end){
+ // send pivot to the end
+ exchange_polynomial_terms(pivot,end,polynomial);
+ // loop over the others
+ for(i=begin, index=begin;i<end;i++){
+ // compare with pivot
+ monomial_cmp=int_array_cmp((*polynomial).monomials[i],(*polynomial).monomials[end]);
+ factor_cmp=int_array_cmp((*polynomial).factors[i],(*polynomial).factors[end]);
+ if(monomial_cmp<0 || (monomial_cmp==0 && factor_cmp<0)){
+ // if smaller, exchange with reference index
+ exchange_polynomial_terms(i,index,polynomial);
+ // move reference index
+ index++;
+ }
+ }
+ // put pivot (which we had sent to the end) in the right place
+ exchange_polynomial_terms(index,end,polynomial);
+ // recurse
+ polynomial_sort(polynomial, begin, index-1);
+ polynomial_sort(polynomial, index+1, end);
+ }
+ return(0);
+}
+
+// exchange two terms (for the sorting algorithm)
+int exchange_polynomial_terms(int i, int j, Polynomial* polynomial){
+ Int_Array ptmp;
+ Number tmp;
+
+ ptmp=(*polynomial).monomials[j];
+ (*polynomial).monomials[j]=(*polynomial).monomials[i];
+ (*polynomial).monomials[i]=ptmp;
+
+ ptmp=(*polynomial).factors[j];
+ (*polynomial).factors[j]=(*polynomial).factors[i];
+ (*polynomial).factors[i]=ptmp;
+
+ tmp=(*polynomial).nums[j];
+ (*polynomial).nums[j]=(*polynomial).nums[i];
+ (*polynomial).nums[i]=tmp;
+
+ return(0);
+}
+
+// sort a monomial (with sign coming from exchanging two Fermions)
+int monomial_sort(Int_Array monomial, int begin, int end, Fields_Table fields, int* sign){
+ int i;
+ int index;
+ // the pivot: middle of the monomial
+ int pivot=(begin+end)/2;
+
+ // if the monomial is non trivial
+ if(begin<end){
+ // send pivot to the end
+ exchange_monomial_terms(monomial, pivot, end, fields, sign);
+
+ // loop over the others
+ for(i=begin, index=begin;i<end;i++){
+ // compare with pivot
+ if(compare_monomial_terms(monomial, i, end, fields)<0){
+ // if smaller, exchange with reference index
+ exchange_monomial_terms(monomial, index, i, fields, sign);
+ // move reference index
+ index++;
+ }
+ }
+ // put pivot (which we had sent to the end) in the right place
+ exchange_monomial_terms(monomial, index, end, fields, sign);
+
+ // recurse
+ monomial_sort(monomial, begin, index-1, fields, sign);
+ monomial_sort(monomial, index+1, end, fields, sign);
+ }
+ return(0);
+}
+
+// order fields: parameter, external, internal
+int compare_monomial_terms(Int_Array monomial, int pos1, int pos2, Fields_Table fields){
+ int type1=field_type(monomial.values[pos1], fields);
+ int type2=field_type(monomial.values[pos2],fields);
+
+ if(type1 < type2){
+ return(-1);
+ }
+ else if(type1 > type2){
+ return(1);
+ }
+
+ if(monomial.values[pos1] < monomial.values[pos2]){
+ return(-1);
+ }
+ else if (monomial.values[pos1] > monomial.values[pos2]){
+ return(1);
+ }
+
+ return(0);
+}
+
+// exchange two fields (with sign)
+int exchange_monomial_terms(Int_Array monomial, int pos1, int pos2, Fields_Table fields, int* sign){
+ int tmp=monomial.values[pos1];
+ int f1,f2;
+ int i;
+
+ monomial.values[pos1]=monomial.values[pos2];
+ monomial.values[pos2]=tmp;
+
+ // sign change
+ // only if the exchange is not trivial
+ if(pos1!=pos2){
+ f1=is_fermion(monomial.values[pos1],fields);
+ f2=is_fermion(monomial.values[pos2],fields);
+ // if both Fermions then sign
+ if(f1==1 && f2==1){
+ *sign*=-1;
+ }
+ // if only one of them is a Fermion, then count the number of Fermions between them
+ else if(f1==1 || f2==1){
+ for(i=min(pos1,pos2)+1;i<max(pos1,pos2);i++){
+ if(is_fermion(monomial.values[i],fields)==1){
+ *sign*=-1;
+ }
+ }
+ }
+ }
+ return(0);
+}
+
+
+// sort a monomial by putting each group together
+int monomial_sort_groups(Int_Array monomial, int begin, int end, Fields_Table fields, Groups groups, int* sign){
+ int i;
+ int index;
+ // the pivot: middle of the monomial
+ int pivot=(begin+end)/2;
+
+ // if the monomial is non trivial
+ if(begin<end){
+ // send pivot to the end
+ exchange_monomial_terms(monomial, pivot, end, fields, sign);
+
+ // loop over the others
+ for(i=begin, index=begin;i<end;i++){
+ // compare with pivot
+ if(compare_monomial_terms_groups(monomial, i, end, fields, groups)<0){
+ // if smaller, exchange with reference index
+ exchange_monomial_terms(monomial, index, i, fields, sign);
+ // move reference index
+ index++;
+ }
+ }
+ // put pivot (which we had sent to the end) in the right place
+ exchange_monomial_terms(monomial, index, end, fields, sign);
+
+ // recurse
+ monomial_sort(monomial, begin, index-1, fields, sign);
+ monomial_sort(monomial, index+1, end, fields, sign);
+ }
+ return(0);
+}
+
+// order fields: group, then parameter, external, internal
+int compare_monomial_terms_groups(Int_Array monomial, int pos1, int pos2, Fields_Table fields, Groups groups){
+ int group1=find_group(monomial.values[pos1], groups);
+ int group2=find_group(monomial.values[pos2], groups);
+
+ if(group1 < group2){
+ return(-1);
+ }
+ else if(group1 > group2){
+ return(1);
+ }
+
+ int type1=field_type(monomial.values[pos1], fields);
+ int type2=field_type(monomial.values[pos2],fields);
+
+ if(type1 < type2){
+ return(-1);
+ }
+ else if(type1 > type2){
+ return(1);
+ }
+
+ if(monomial.values[pos1] < monomial.values[pos2]){
+ return(-1);
+ }
+ else if (monomial.values[pos1] > monomial.values[pos2]){
+ return(1);
+ }
+
+ return(0);
+}
+
+
+// convert and idtable to a polynomial
+int idtable_to_polynomial(Id_Table idtable, Polynomial* polynomial){
+ int i,j;
+ int start=0;
+
+ // allocate memory
+ init_Polynomial(polynomial,POLY_SIZE);
+
+ for(i=0;i<idtable.length;i++){
+ polynomial_concat(idtable.polynomials[i],polynomial);
+ // set factors
+ for(j=start;j<(*polynomial).length;j++){
+ int_array_append(idtable.indices[i],(*polynomial).factors+j);
+ }
+ // shift start point
+ start+=idtable.polynomials[i].length;
+ }
+
+ return(0);
+}
+
+
+// replace the factors in a polynomial as prescribed by an equation in the form of a Grouped_Polynomial
+int replace_factors(Grouped_Polynomial equations, Polynomial* polynomial){
+ int i,j;
+ int index;
+ Polynomial output;
+ Coefficient coef;
+
+ init_Polynomial(&output, POLY_SIZE);
+
+ // loop over monomials
+ for(i=0;i<(*polynomial).length;i++){
+ if((*polynomial).factors[i].length>0){
+ // initialize coef to store the product of factors
+ init_Coefficient(&coef, POLY_SIZE);
+
+ // first term
+ index=intlist_find_err(equations.indices, equations.length, (*polynomial).factors[i].values[0]);
+ if(index>=0){
+ coefficient_cpy_noinit(equations.coefs[index],&coef);
+ }
+
+ // other terms
+ for(j=1;j<(*polynomial).factors[i].length;j++){
+ index=intlist_find_err(equations.indices, equations.length, (*polynomial).factors[i].values[j]);
+ if(index>=0){
+ coefficient_prod_chain(equations.coefs[index],&coef);
+ }
+ }
+
+ // new polynomial terms
+ for(j=0;j<coef.length;j++){
+ // add to output
+ polynomial_append((*polynomial).monomials[i], coef.factors[j], number_prod_ret((*polynomial).nums[i],coef.nums[j]), &output);
+ }
+
+ // free memory
+ free_Coefficient(coef);
+ }
+ // if no factors
+ else{
+ polynomial_append((*polynomial).monomials[i], (*polynomial).factors[i], (*polynomial).nums[i], &output);
+ }
+ }
+
+ // replace output
+ free_Polynomial(*polynomial);
+ *polynomial=output;
+
+ return(0);
+}
+
+
+// print a polynomial to a string
+int polynomial_sprint(Polynomial polynomial, Char_Array* output){
+ int i,j;
+
+ // for each monomial
+ for(i=0;i<polynomial.length;i++){
+ if(i==0){
+ char_array_snprintf(output, " ");
+ }
+ else{
+ char_array_snprintf(output, "+ ",i);
+ }
+
+ // print num
+ char_array_append('(',output);
+ number_sprint(polynomial.nums[i],output);
+ char_array_append(')',output);
+
+ // print factors
+ for(j=0;j<polynomial.factors[i].length;j++){
+ char_array_snprintf(output,"[l%d]",polynomial.factors[i].values[j]);
+ }
+
+ // print monomials
+ for(j=0;j<polynomial.monomials[i].length;j++){
+ char_array_snprintf(output,"[f%d]",polynomial.monomials[i].values[j]);
+ }
+
+ char_array_append('\n',output);
+ }
+ return(0);
+}
+// print
+int polynomial_print(Polynomial polynomial){
+ Char_Array buffer;
+ init_Char_Array(&buffer, STR_SIZE);
+ polynomial_sprint(polynomial, &buffer);
+ printf("%s",buffer.str);
+ free_Char_Array(buffer);
+ return(0);
+}
+
+// read a polynomial from a Char_Array
+#define PP_NULL_MODE 0
+#define PP_BRACKET_MODE 1
+#define PP_MONOMIAL_MODE 2
+#define PP_FACTOR_MODE 3
+#define PP_NUMBER_MODE 4
+int Char_Array_to_Polynomial(Char_Array str_polynomial,Polynomial* output){
+ // buffer
+ char* buffer=calloc(str_polynomial.length+1,sizeof(char));
+ char* buffer_ptr=buffer;
+ Int_Array monomial;
+ Int_Array factor;
+ Number num, tmp1_num;
+ int mode;
+ int comment=0;
+ int i,j;
+ int parenthesis_count=0;
+
+ // allocate memory
+ init_Polynomial(output,POLY_SIZE);
+
+ // init
+ init_Int_Array(&monomial, MONOMIAL_SIZE);
+ init_Int_Array(&factor, MONOMIAL_SIZE);
+ num=number_one();
+
+ // if the string contains no '[', then read a number
+ for(j=0;j<str_polynomial.length;j++){
+ // ignore comments
+ if(comment==1){
+ if(str_polynomial.str[j]=='\n'){
+ comment=0;
+ }
+ }
+ else{
+ if(str_polynomial.str[j]=='['){
+ break;
+ }
+ if(str_polynomial.str[j]=='#'){
+ comment=1;
+ }
+ }
+ }
+ // no '[': read a number
+ if(j==str_polynomial.length){
+ free_Number(num);
+ char_array_to_Number(str_polynomial,&num);
+ polynomial_append_noinit(monomial, factor, num, output);
+ free(buffer);
+ return(0);
+ }
+
+ // reset comment flag
+ comment=0;
+
+ *buffer_ptr='\0';
+ // loop over the input polynomial
+ // start in null mode
+ mode=PP_NULL_MODE;
+ for(j=0;j<str_polynomial.length;j++){
+ if(comment==1){
+ if(str_polynomial.str[j]=='\n'){
+ comment=0;
+ }
+ }
+ else{
+ switch(str_polynomial.str[j]){
+ // new monomial
+ case '+':
+ if(mode==PP_NULL_MODE){
+ polynomial_append_noinit(monomial, factor, num, output);
+ // reset monomial, factor, num
+ init_Int_Array(&monomial, MONOMIAL_SIZE);
+ init_Int_Array(&factor, MONOMIAL_SIZE);
+ num=number_one();
+ }
+ break;
+
+ // enter monomial or factor mode
+ case '[':
+ if(mode==PP_NULL_MODE){
+ mode=PP_BRACKET_MODE;
+ }
+ break;
+ // factor mode
+ case 'l':
+ if(mode==PP_BRACKET_MODE){
+ mode=PP_FACTOR_MODE;
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ break;
+ // monomial mode
+ case 'f':
+ if(mode==PP_BRACKET_MODE){
+ mode=PP_MONOMIAL_MODE;
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ break;
+ // read monomial or factor
+ case ']':
+ sscanf(buffer,"%d",&i);
+ if(mode==PP_FACTOR_MODE){
+ int_array_append(i,&factor);
+ }
+ else if(mode==PP_MONOMIAL_MODE){
+ int_array_append(i,&monomial);
+ }
+ // switch back to null mode
+ mode=PP_NULL_MODE;
+ break;
+
+ // numerical pre-factor
+ case '(':
+ if(mode==PP_NULL_MODE){
+ mode=PP_NUMBER_MODE;
+ parenthesis_count=0;
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ }
+ else if(mode==PP_NUMBER_MODE){
+ // match parentheses
+ parenthesis_count++;
+ buffer_ptr=str_addchar(buffer_ptr,str_polynomial.str[j]);
+ }
+ break;
+ case ')':
+ if(mode==PP_NUMBER_MODE){
+ if(parenthesis_count==0){
+ // write num
+ str_to_Number(buffer,&tmp1_num);
+ number_prod_chain(tmp1_num,&num);
+ free_Number(tmp1_num);
+ // back to null mode
+ mode=PP_NULL_MODE;
+ }
+ else{
+ parenthesis_count--;
+ buffer_ptr=str_addchar(buffer_ptr,str_polynomial.str[j]);
+ }
+ }
+ break;
+
+ // characters to ignore
+ case ' ':break;
+ case '&':break;
+ case '\n':break;
+
+ // comments
+ case '#':
+ comment=1;
+ break;
+
+ default:
+ if(mode!=PP_NULL_MODE){
+ // write to buffer
+ buffer_ptr=str_addchar(buffer_ptr,str_polynomial.str[j]);
+ }
+ break;
+ }
+ }
+ }
+
+ // last term
+ polynomial_append_noinit(monomial, factor, num, output);
+
+ free(buffer);
+ return(0);
+}
+
+// with str input
+int str_to_Polynomial(char* str_polynomial,Polynomial* output){
+ Char_Array buffer;
+ str_to_char_array(str_polynomial, &buffer);
+ Char_Array_to_Polynomial(buffer, output);
+ free_Char_Array(buffer);
+ return(0);
+}
+
+
+// -------------------- Polynomial_Matrix ---------------------
+
+// init
+int init_Polynomial_Matrix(Polynomial_Matrix* matrix, int length){
+ int i,j;
+ (*matrix).matrix=calloc(length,sizeof(Polynomial*));
+ (*matrix).indices=calloc(length,sizeof(int));
+ for(i=0;i<length;i++){
+ (*matrix).matrix[i]=calloc(length,sizeof(Polynomial));
+ for(j=0;j<length;j++){
+ (*matrix).matrix[i][j]=polynomial_zero();
+ }
+ }
+ (*matrix).length=length;
+ return(0);
+}
+int free_Polynomial_Matrix(Polynomial_Matrix matrix){
+ int i,j;
+ for(i=0;i<matrix.length;i++){
+ for(j=0;j<matrix.length;j++){
+ free_Polynomial(matrix.matrix[i][j]);
+ }
+ free(matrix.matrix[i]);
+ }
+ free(matrix.matrix);
+ free(matrix.indices);
+ return(0);
+}
diff --git a/src/polynomial.h b/src/polynomial.h
new file mode 100644
index 0000000..ec50227
--- /dev/null
+++ b/src/polynomial.h
@@ -0,0 +1,131 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+Represent a polynomial as a list of monomials with factors
+*/
+
+#ifndef POLYNOMIAL_H
+#define POLYNOMIAL_H
+
+#include "types.h"
+
+// allocate memory
+int init_Polynomial(Polynomial* polynomial,int size);
+// free memory
+int free_Polynomial(Polynomial polynomial);
+
+// resize the memory allocated to a polynomial
+int resize_polynomial(Polynomial* polynomial,int new_size);
+
+// copy a polynomial
+int polynomial_cpy(Polynomial input, Polynomial* output);
+int polynomial_cpy_noinit(Polynomial input, Polynomial* output);
+
+// append an element to a polynomial
+int polynomial_append(Int_Array monomial, Int_Array factor, Number num, Polynomial* output);
+int polynomial_append_noinit(Int_Array monomial, Int_Array factor, Number num, Polynomial* output);
+// noinit, and if there already exists an element with the same monomial and factor, then just add numbers
+int polynomial_append_noinit_inplace(Int_Array monomial, Int_Array factor, Number num, Polynomial* output);
+
+// concatenate two polynomials
+int polynomial_concat(Polynomial input, Polynomial* output);
+int polynomial_concat_noinit(Polynomial input, Polynomial* output);
+int polynomial_concat_noinit_inplace(Polynomial input, Polynomial* output);
+
+// add polynomials
+int polynomial_add_chain(Polynomial input, Polynomial* inout, Fields_Table fields);
+// add polynomials (noinit)
+int polynomial_add_chain_noinit(Polynomial input, Polynomial* inout, Fields_Table fields);
+
+// multiply a polynomial by a scalar
+int polynomial_multiply_scalar(Polynomial polynomial, Number num);
+int polynomial_multiply_Qscalar(Polynomial polynomial, Q q);
+
+// change the sign of the monomials in a polynomial
+int polynomial_conjugate(Polynomial polynomial);
+
+// returns an initialized polynomial, equal to 1
+Polynomial polynomial_one();
+// returns an initialized polynomial, equal to 0
+Polynomial polynomial_zero();
+
+// check whether a polynomial is 0
+int polynomial_is_zero(Polynomial poly);
+
+// compute V^p
+int polynomial_power(Polynomial input_polynomial, Polynomial* output, int power, Fields_Table fields);
+// compute V*W
+int polynomial_prod(Polynomial input1, Polynomial input2, Polynomial* output, Fields_Table fields);
+int polynomial_prod_chain_nosimplify(Polynomial input, Polynomial* inout, Fields_Table fields);
+int polynomial_prod_chain(Polynomial input, Polynomial* inout, Fields_Table fields);
+// exp(V)
+int polynomial_exponential(Polynomial input_polynomial,Polynomial* output, Fields_Table fields);
+// log(1+W)
+int polynomial_logarithm(Polynomial input_polynomial, Polynomial* output, Fields_Table fields);
+
+// check whether a monomial vanishes
+int check_monomial(Int_Array monomial, Fields_Table fields);
+// check whether the product of two monomials will vanish
+int check_monomial_willnot_vanish(Int_Array monomial1, Int_Array monomial2, Fields_Table fields);
+// check whether one can add a term to a monomial without creating repetitions
+int check_monomial_addterm(Int_Array monomial, Int_Array term, Fields_Table fields);
+// check whether a monomial vanishes or has unmatched +/- fields
+int check_monomial_match(Int_Array monomial, Fields_Table fields);
+// remove terms with more plus internal fields than minus ones
+int remove_unmatched_plusminus(Polynomial* polynomial, Fields_Table fields);
+
+// denominator of a multinomal factor: m1!m2!...
+int multinomial(int power,int* terms);
+
+// simplify a Polynomial
+int polynomial_simplify(Polynomial* polynomial, Fields_Table fields);
+// sort a polynomial
+int polynomial_sort(Polynomial* polynomial, int begin, int end);
+// exchange two terms (for the sorting algorithm)
+int exchange_polynomial_terms(int i, int j, Polynomial* polynomial);
+
+// sort a monomial (with sign coming from exchanging two Fermions)
+int monomial_sort(Int_Array monomial, int begin, int end, Fields_Table fields, int* sign);
+// order fields: parameter, external, internal
+int compare_monomial_terms(Int_Array monomial, int pos1, int pos2, Fields_Table fields);
+// exchange two fields (with sign)
+int exchange_monomial_terms(Int_Array monomial, int pos1, int pos2, Fields_Table fields, int* sign);
+
+// sort a monomial by putting each group together
+int monomial_sort_groups(Int_Array monomial, int begin, int end, Fields_Table fields, Groups groups, int* sign);
+// order fields: group, then parameter, external, internal
+int compare_monomial_terms_groups(Int_Array monomial, int pos1, int pos2, Fields_Table fields, Groups groups);
+
+// convert and idtable to a polynomial
+int idtable_to_polynomial(Id_Table idtable, Polynomial* polynomial);
+
+// replace the factors in a polynomial as prescribed by an equation in the form of a Grouped_Polynomial
+int replace_factors(Grouped_Polynomial equations, Polynomial* polynomial);
+
+// print a polynomial
+int polynomial_sprint(Polynomial polynomial, Char_Array* output);
+int polynomial_print(Polynomial polynomial);
+// read a polynomial
+int Char_Array_to_Polynomial(Char_Array str_polynomial,Polynomial* output);
+int str_to_Polynomial(char* str_polynomial,Polynomial* output);
+
+//------------------------ Polynomial_Matrix --------------------------
+// init
+int init_Polynomial_Matrix(Polynomial_Matrix* matrix, int length);
+int free_Polynomial_Matrix(Polynomial_Matrix matrix);
+
+#endif
diff --git a/src/rational.h b/src/rational.h
new file mode 100644
index 0000000..5beab8d
--- /dev/null
+++ b/src/rational.h
@@ -0,0 +1,23 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+ represent rational numbers either as a quotient of 64-bit integers, or a quotient of 80-bit floats (with 64-bit precision)
+*/
+
+// include both, only one is non empty
+#include "rational_float.h"
+#include "rational_int.h"
diff --git a/src/rational_float.c b/src/rational_float.c
new file mode 100644
index 0000000..eebc4f4
--- /dev/null
+++ b/src/rational_float.c
@@ -0,0 +1,196 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#ifdef RATIONAL_AS_FLOAT
+
+#include "rational_float.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include "istring.h"
+#include "array.h"
+#include "math.h"
+
+Q quot(long double p, long double q){
+ Q ret;
+ if(q==0){
+ fprintf(stderr,"error: %Lf/%Lf is ill defined\n",p,q);
+ exit(-1);
+ }
+ ret.numerator=p;
+ ret.denominator=q;
+ return(ret);
+}
+
+// add
+Q Q_add(Q x1,Q x2){
+ Q ret;
+ ret.denominator=lcm(x1.denominator,x2.denominator);
+ ret.numerator=x1.numerator*(ret.denominator/x1.denominator)+x2.numerator*(ret.denominator/x2.denominator);
+ return(Q_simplify(ret));
+}
+//multiply
+Q Q_prod(Q x1,Q x2){
+ return(Q_simplify(quot(x1.numerator*x2.numerator,x1.denominator*x2.denominator)));
+}
+// inverse
+Q Q_inverse(Q x1){
+ if(x1.numerator>0){
+ return(quot(x1.denominator,x1.numerator));
+ }
+ else if(x1.numerator<0){
+ return(quot(-x1.denominator,-x1.numerator));
+ }
+ else{
+ fprintf(stderr,"error: attempting to invert %Lf/%Lf\n",x1.numerator, x1.denominator);
+ exit(-1);
+ }
+
+}
+// quotient
+Q Q_quot(Q x1, Q x2){
+ if(x2.numerator>0){
+ return(Q_simplify(quot(x1.numerator*x2.denominator,x1.denominator*x2.numerator)));
+ }
+ else if(x2.numerator<0){
+ return(Q_simplify(quot(-x1.numerator*x2.denominator,-x1.denominator*x2.numerator)));
+ }
+ else{
+ fprintf(stderr,"error: attempting to invert %Lf/%Lf\n",x2.numerator, x2.denominator);
+ exit(-1);
+ }
+}
+
+// compare
+int Q_cmp(Q x1, Q x2){
+ Q quo=Q_quot(x1,x2);
+ if(quo.numerator > quo.denominator){
+ return(1);
+ }
+ else if(quo.numerator < quo.denominator){
+ return(-1);
+ }
+ else{
+ return(0);
+ }
+}
+
+// simplify
+Q Q_simplify(Q x){
+ return(quot(x.numerator/gcd(x.numerator,x.denominator),x.denominator/gcd(x.numerator,x.denominator)));
+}
+//simplify in place
+int Q_simplify_inplace(Q* x){
+ Q ret=Q_simplify(*x);
+ *x=ret;
+ return(0);
+}
+
+// greatest common divisor
+long double gcd(long double x, long double y){
+ long double ax=fabsl(x);
+ long double ay=fabsl(y);
+ int security=0;
+ while(ax!=0 && ay!=0){
+ if(ax>ay){ax=modld(ax,ay);}
+ else{ay=modld(ay,ax);}
+
+ security++;
+ if(security>1000000){
+ fprintf(stderr,"error: could not compute gcd( %Lf , %Lf ) after %d tries\n",x,y,security);
+ exit(-1);
+ }
+ }
+ // if both are negative, gcd should be negative (useful for simplification of fractions and product of square roots)
+ if(x<0 && y<0){
+ ax*=-1;
+ ay*=-1;
+ }
+ if(fabsl(ay)>fabsl(ax)){return(ay);}
+ else{return(ax);}
+}
+
+long double modld(long double x, long double m){
+ long double q=floorl(x/m);
+ return(x-q*m);
+}
+
+// least common multiple
+long double lcm(long double x,long double y){
+ if(x!=0 || y!=0){
+ return((x*y)/gcd(x,y));
+ }
+ else{
+ return(0);
+ }
+}
+
+// approximate value as double
+double Q_double_value(Q q){
+ return(1.0*q.numerator/q.denominator);
+}
+
+
+// print to string
+int Q_sprint(Q num, Char_Array* out){
+ if(num.denominator!=1){
+ char_array_snprintf(out,"%Lf/%Lf", num.numerator,num.denominator);
+ }
+ else{
+ char_array_snprintf(out,"%Lf",num.numerator);
+ }
+
+ return(0);
+}
+
+#define PP_NUMERATOR_MODE 1
+#define PP_DENOMINATOR_MODE 2
+// read from a string
+int str_to_Q(char* str, Q* num){
+ char* ptr;
+ int mode;
+ char* buffer=calloc(str_len(str)+1,sizeof(char));
+ char* buffer_ptr=buffer;
+
+ *num=quot(0,1);
+
+ mode=PP_NUMERATOR_MODE;
+ for(ptr=str;*ptr!='\0';ptr++){
+ if(*ptr=='/'){
+ sscanf(buffer,"%Lf",&((*num).numerator));
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ mode=PP_DENOMINATOR_MODE;
+ }
+ else{
+ buffer_ptr=str_addchar(buffer_ptr,*ptr);
+ }
+ }
+
+ // last step
+ if(mode==PP_NUMERATOR_MODE){
+ sscanf(buffer,"%Lf",&((*num).numerator));
+ }
+ else if(mode==PP_DENOMINATOR_MODE){
+ sscanf(buffer,"%Lf",&((*num).denominator));
+ }
+
+ free(buffer);
+ return(0);
+}
+
+#else
+int null_declaration_so_that_the_compiler_does_not_complain;
+#endif
diff --git a/src/rational_float.h b/src/rational_float.h
new file mode 100644
index 0000000..931b5ec
--- /dev/null
+++ b/src/rational_float.h
@@ -0,0 +1,64 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+ Rational numbers
+ uses long doubles to represent integers (to avoid overflow)
+*/
+
+#ifdef RATIONAL_AS_FLOAT
+
+#ifndef RATIONAL_H
+#define RATIONAL_H
+
+#include "types.h"
+
+// Q from int/int
+Q quot(long double p, long double q);
+
+// add
+Q Q_add(Q x1,Q x2);
+//multiply
+Q Q_prod(Q x1,Q x2);
+// inverse
+Q Q_inverse(Q x1);
+// quotient
+Q Q_quot(Q x1, Q x2);
+
+// compare
+int Q_cmp(Q x1, Q x2);
+
+// simplify
+Q Q_simplify(Q x);
+//simplify in place
+int Q_simplify_inplace(Q* x);
+
+// greatest common divisor
+long double gcd(long double x,long double y);
+long double modld(long double x, long double m);
+// least common multiple
+long double lcm(long double x,long double y);
+
+// approximate value as double
+double Q_double_value(Q q);
+
+// print to string
+int Q_sprint(Q num, Char_Array* out);
+// read from a string
+int str_to_Q(char* str, Q* num);
+
+#endif
+#endif
diff --git a/src/rational_int.c b/src/rational_int.c
new file mode 100644
index 0000000..ec601a8
--- /dev/null
+++ b/src/rational_int.c
@@ -0,0 +1,190 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#ifndef RATIONAL_AS_FLOAT
+
+#include "rational_int.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include "istring.h"
+#include "array.h"
+
+Q quot(long int p, long int q){
+ Q ret;
+ if(q==0){
+ fprintf(stderr,"error: %ld/%ld is ill defined\n",p,q);
+ exit(-1);
+ }
+ ret.numerator=p;
+ ret.denominator=q;
+ return(ret);
+}
+
+// add
+Q Q_add(Q x1,Q x2){
+ Q ret;
+ ret.denominator=lcm(x1.denominator,x2.denominator);
+ ret.numerator=x1.numerator*(ret.denominator/x1.denominator)+x2.numerator*(ret.denominator/x2.denominator);
+ return(Q_simplify(ret));
+}
+//multiply
+Q Q_prod(Q x1,Q x2){
+ return(Q_simplify(quot(x1.numerator*x2.numerator,x1.denominator*x2.denominator)));
+}
+// inverse
+Q Q_inverse(Q x1){
+ if(x1.numerator>0){
+ return(quot(x1.denominator,x1.numerator));
+ }
+ else if(x1.numerator<0){
+ return(quot(-x1.denominator,-x1.numerator));
+ }
+ else{
+ fprintf(stderr,"error: attempting to invert %ld/%ld\n",x1.numerator, x1.denominator);
+ exit(-1);
+ }
+
+}
+// quotient
+Q Q_quot(Q x1, Q x2){
+ if(x2.numerator>0){
+ return(Q_simplify(quot(x1.numerator*x2.denominator,x1.denominator*x2.numerator)));
+ }
+ else if(x2.numerator<0){
+ return(Q_simplify(quot(-x1.numerator*x2.denominator,-x1.denominator*x2.numerator)));
+ }
+ else{
+ fprintf(stderr,"error: attempting to invert %ld/%ld\n",x2.numerator, x2.denominator);
+ exit(-1);
+ }
+}
+
+// compare
+int Q_cmp(Q x1, Q x2){
+ Q quo=Q_quot(x1,x2);
+ if(quo.numerator > quo.denominator){
+ return(1);
+ }
+ else if(quo.numerator < quo.denominator){
+ return(-1);
+ }
+ else{
+ return(0);
+ }
+}
+
+// simplify
+Q Q_simplify(Q x){
+ return(quot(x.numerator/gcd(x.numerator,x.denominator),x.denominator/gcd(x.numerator,x.denominator)));
+}
+//simplify in place
+int Q_simplify_inplace(Q* x){
+ Q ret=Q_simplify(*x);
+ *x=ret;
+ return(0);
+}
+
+// greatest common divisor
+long int gcd(long int x, long int y){
+ long int ax=labs(x);
+ long int ay=labs(y);
+ int security=0;
+ while(ax!=0 && ay!=0){
+ if(ax>ay){ax=ax%ay;}
+ else{ay=ay%ax;}
+
+ security++;
+ if(security>1000000){
+ fprintf(stderr,"error: could not compute gcd( %ld , %ld ) after %d tries\n",x,y,security);
+ exit(-1);
+ }
+ }
+ // if both are negative, gcd should be negative (useful for simplification of fractions and product of square roots)
+ if(x<0 && y<0){
+ ax*=-1;
+ ay*=-1;
+ }
+ if(labs(ay)>labs(ax)){return(ay);}
+ else{return(ax);}
+}
+
+// least common multiple
+long int lcm(long int x,long int y){
+ if(x!=0 || y!=0){
+ return((x*y)/gcd(x,y));
+ }
+ else{
+ return(0);
+ }
+}
+
+// approximate value as double
+double Q_double_value(Q q){
+ return(1.0*q.numerator/q.denominator);
+}
+
+
+// print to string
+int Q_sprint(Q num, Char_Array* out){
+ if(num.denominator!=1){
+ char_array_snprintf(out,"%ld/%ld", num.numerator,num.denominator);
+ }
+ else{
+ char_array_snprintf(out,"%ld",num.numerator);
+ }
+
+ return(0);
+}
+
+#define PP_NUMERATOR_MODE 1
+#define PP_DENOMINATOR_MODE 2
+// read from a string
+int str_to_Q(char* str, Q* num){
+ char* ptr;
+ int mode;
+ char* buffer=calloc(str_len(str)+1,sizeof(char));
+ char* buffer_ptr=buffer;
+
+ *num=quot(0,1);
+
+ mode=PP_NUMERATOR_MODE;
+ for(ptr=str;*ptr!='\0';ptr++){
+ if(*ptr=='/'){
+ sscanf(buffer,"%ld",&((*num).numerator));
+ buffer_ptr=buffer;
+ *buffer_ptr='\0';
+ mode=PP_DENOMINATOR_MODE;
+ }
+ else{
+ buffer_ptr=str_addchar(buffer_ptr,*ptr);
+ }
+ }
+
+ // last step
+ if(mode==PP_NUMERATOR_MODE){
+ sscanf(buffer,"%ld",&((*num).numerator));
+ }
+ else if(mode==PP_DENOMINATOR_MODE){
+ sscanf(buffer,"%ld",&((*num).denominator));
+ }
+
+ free(buffer);
+ return(0);
+}
+
+#else
+int null_declaration_so_that_the_compiler_does_not_complain;
+#endif
diff --git a/src/rational_int.h b/src/rational_int.h
new file mode 100644
index 0000000..a9f164d
--- /dev/null
+++ b/src/rational_int.h
@@ -0,0 +1,59 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/* Rational numbers */
+
+#ifndef RATIONAL_AS_FLOAT
+#ifndef RATIONAL_H
+#define RATIONAL_H
+
+#include "types.h"
+
+// Q from int/int
+Q quot(long int p, long int q);
+
+// add
+Q Q_add(Q x1,Q x2);
+//multiply
+Q Q_prod(Q x1,Q x2);
+// inverse
+Q Q_inverse(Q x1);
+// quotient
+Q Q_quot(Q x1, Q x2);
+
+// compare
+int Q_cmp(Q x1, Q x2);
+
+// simplify
+Q Q_simplify(Q x);
+//simplify in place
+int Q_simplify_inplace(Q* x);
+
+// greatest common divisor
+long int gcd(long int x,long int y);
+// least common multiple
+long int lcm(long int x,long int y);
+
+// approximate value as double
+double Q_double_value(Q q);
+
+// print to string
+int Q_sprint(Q num, Char_Array* out);
+// read from a string
+int str_to_Q(char* str, Q* num);
+
+#endif
+#endif
diff --git a/src/rcc.c b/src/rcc.c
new file mode 100644
index 0000000..484e20a
--- /dev/null
+++ b/src/rcc.c
@@ -0,0 +1,95 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "rcc.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include "array.h"
+
+// init
+int init_RCC(RCC* rccs, int size){
+ (*rccs).values=calloc(size,sizeof(long double));
+ (*rccs).indices=calloc(size,sizeof(int));
+ (*rccs).length=size;
+ return(0);
+}
+
+int free_RCC(RCC rccs){
+ free(rccs.values);
+ free(rccs.indices);
+ return(0);
+}
+
+// set a given element of an rcc
+int RCC_set_elem(long double value, int index, RCC* rcc, int pos){
+ (*rcc).values[pos]=value;
+ (*rcc).indices[pos]=index;
+ return(0);
+}
+
+int RCC_cpy(RCC input,RCC* output){
+ int i;
+
+ init_RCC(output,input.length);
+ for(i=0;i<input.length;i++){
+ RCC_set_elem(input.values[i], input.indices[i], output, i);
+ }
+ return(0);
+}
+
+// concatenate rccs
+int RCC_concat(RCC rccs1, RCC rccs2, RCC* output){
+ int i;
+
+ init_RCC(output,rccs1.length+rccs2.length);
+
+ for(i=0;i<rccs1.length;i++){
+ RCC_set_elem(rccs1.values[i], rccs1.indices[i], output, i);
+ }
+
+ for(i=0;i<rccs2.length;i++){
+ RCC_set_elem(rccs2.values[i], rccs2.indices[i], output, i+rccs1.length);
+ }
+
+ return(0);
+}
+
+// append an rcc at the end of another
+int RCC_append(RCC input, RCC* output){
+ int i;
+ for(i=0;i<input.length;i++){
+ RCC_set_elem(input.values[i], input.indices[i], output, i+(*output).length);
+ }
+ (*output).length+=input.length;
+ return(0);
+}
+
+// print an rcc vector with maximal precision
+int RCC_print(RCC rccs){
+ int j;
+
+ for(j=0;j<rccs.length;j++){
+ printf("%d:%.19Le",rccs.indices[j],rccs.values[j]);
+ if(j<rccs.length-1){
+ printf(",\n");
+ }
+ else{
+ printf("\n");
+ }
+ }
+
+ return(0);
+}
diff --git a/src/rcc.h b/src/rcc.h
new file mode 100644
index 0000000..770309c
--- /dev/null
+++ b/src/rcc.h
@@ -0,0 +1,39 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/* RCC struct */
+
+#ifndef RCC_H
+#define RCC_H
+
+#include "types.h"
+
+// init
+int init_RCC(RCC* rccs, int size);
+int free_RCC(RCC rccs);
+// set an element of an rcc
+int RCC_set_elem(long double value, int index, RCC* rcc, int pos);
+// copy
+int RCC_cpy(RCC input,RCC* output);
+// concatenate 2 rccs
+int RCC_concat(RCC rccs1, RCC rccs2, RCC* output);
+// append an rcc to another
+int RCC_append(RCC input, RCC* output);
+
+// print an rcc vector with maximal precision
+int RCC_print(RCC rccs);
+
+#endif
diff --git a/src/tools.c b/src/tools.c
new file mode 100644
index 0000000..2b7e85d
--- /dev/null
+++ b/src/tools.c
@@ -0,0 +1,142 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "tools.h"
+#include <stdio.h>
+#include <stdlib.h>
+
+int factorial(int n){
+ int i;
+ int res=1;
+ for(i=2;i<=n;i++){
+ res*=i;
+ }
+ return(res);
+}
+
+int ipower(int n, int p){
+ int i;
+ int res=1;
+ for(i=1;i<=p;i++){
+ res*=n;
+ }
+ return(res);
+}
+
+// power of a double
+long double dpower(long double x, int p){
+ int i;
+ long double res=1.;
+ if(p>=0){
+ for(i=1;i<=p;i++){
+ res*=x;
+ }
+ }
+ else{
+ for(i=1;i<=-p;i++){
+ res/=x;
+ }
+ }
+
+ return(res);
+}
+
+
+// find an element in a list whose first element is its size
+int list_find(int* list, int x){
+ int i;
+ for(i=1;i<=*list;i++){
+ if(list[i]==x){return(i);}
+ }
+ return(0);
+}
+
+// find an element in a list whose first element is not its number of elements (skips first element)
+int unlist_find(int* list, int size, int x){
+ int i;
+ for(i=1;i<size;i++){
+ if(list[i]==x){return(i);}
+ }
+ fprintf(stderr,"error: element %d not found\n",x);
+ exit(-1);
+}
+// find an element in a list whose first element is not its number of elements (skips first element)
+// no error reporting
+int unlist_find_noerr(int* list, int size, int x){
+ int i;
+ for(i=1;i<size;i++){
+ if(list[i]==x){return(i);}
+ }
+ return(-1);
+}
+
+
+// find an element in a list (checks first element)
+int intlist_find(int* list, int size, int x){
+ int i;
+ for(i=0;i<size;i++){
+ if(list[i]==x){return(i);}
+ }
+ return(-1);
+}
+// with error
+int intlist_find_err(int* list, int size, int x){
+ int i;
+ for(i=0;i<size;i++){
+ if(list[i]==x){return(i);}
+ }
+ fprintf(stderr,"error: element %d not found\n",x);
+ exit(-1);
+}
+
+
+
+// compare two lists
+int list_cmp(int* list1, int* list2){
+ if(*list1!=*list2){
+ return(0);
+ }
+ int* ptr1=list1+1;
+ int* ptr2=list2+1;
+ int i;
+ for(i=1;i<=*list1;i++){
+ if(*ptr1!=*ptr2){
+ return(0);
+ }
+ ptr1++;
+ ptr2++;
+ }
+ return(1);
+}
+
+
+// max and min
+int max(int x1, int x2){
+ if(x1>=x2){
+ return(x1);
+ }
+ else{
+ return(x2);
+ }
+}
+int min(int x1, int x2){
+ if(x1<=x2){
+ return(x1);
+ }
+ else{
+ return(x2);
+ }
+}
diff --git a/src/tools.h b/src/tools.h
new file mode 100644
index 0000000..e5f319f
--- /dev/null
+++ b/src/tools.h
@@ -0,0 +1,49 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+Various tools
+*/
+
+#ifndef TOOLS_H
+#define TOOLS_H
+
+#include "types.h"
+
+int factorial(int n);
+int ipower(int n, int p);
+long double dpower(long double x, int p);
+
+// find an element in a list whose first element is its size
+int list_find(int* list, int x);
+// compare two lists
+int list_cmp(int* list1, int* list2);
+
+// find an element in a list whose first element is not its number of elements (skips first element)
+int unlist_find(int* list, int size, int x);
+// no error
+int unlist_find_noerr(int* list, int size, int x);
+
+// find an element in a list (checks first element)
+int intlist_find(int* list, int size, int x);
+// with error
+int intlist_find_err(int* list, int size, int x);
+
+// max and min
+int max(int x1, int x2);
+int min(int x1, int x2);
+
+#endif
diff --git a/src/types.h b/src/types.h
new file mode 100644
index 0000000..0452ebc
--- /dev/null
+++ b/src/types.h
@@ -0,0 +1,219 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+ typedefs used by meankondo
+*/
+
+#ifndef TYPES_H
+#define TYPES_H
+
+
+// rational number
+typedef struct Q{
+#ifndef RATIONAL_AS_FLOAT
+ long int numerator;
+ long int denominator;
+#else
+ long double numerator;
+ long double denominator;
+#endif
+} Q;
+
+// numbers
+typedef struct Number{
+ Q* scalars;
+ int* base;
+ int length;
+ int memory;
+} Number;
+
+// matrix
+typedef struct Number_Matrix{
+ Number** matrix;
+ int* indices;
+ int length;
+} Number_Matrix;
+
+// list of integers
+typedef struct Int_Array{
+ int* values;
+ int length;
+ int memory;
+} Int_Array;
+
+// string
+typedef struct Char_Array{
+ char* str;
+ int length;
+ int memory;
+} Char_Array;
+
+// string array
+typedef struct Str_Array{
+ Char_Array* strs;
+ int length;
+ int memory;
+} Str_Array;
+
+// polynomial
+typedef struct Polynomial{
+ Int_Array* monomials;
+ Int_Array* factors;
+ Number* nums;
+ int length;
+ int memory;
+} Polynomial;
+
+// matrix of polynomial
+typedef struct Polynomial_Matrix{
+ Polynomial** matrix;
+ int* indices;
+ int length;
+} Polynomial_Matrix;
+
+// denominators in coefficients (index of the denominator and the power to which it is raised)
+typedef struct coef_denom{
+ int index;
+ int power;
+} coef_denom;
+
+// coefficient
+typedef struct Coefficient{
+ Int_Array* factors;
+ Number* nums;
+ coef_denom* denoms;
+ int length;
+ int memory;
+} Coefficient;
+
+// grouped polynomial
+typedef struct Grouped_Polynomial{
+ Coefficient* coefs;
+ int* indices;
+ int length;
+ int memory;
+} Grouped_Polynomial;
+
+// rcc
+typedef struct RCC{
+ long double* values;
+ int* indices;
+ int length;
+} RCC;
+
+// identities between fields
+typedef struct Identities{
+ // left hand sides
+ Int_Array* lhs;
+ // right hand sides
+ Polynomial* rhs;
+ int length;
+ int memory;
+} Identities;
+
+// symbolic expressions
+typedef struct Symbols{
+ int* indices;
+ Polynomial* expr;
+ int length;
+ int memory;
+} Symbols;
+
+// groups of independent fields
+typedef struct Groups{
+ Int_Array* indices;
+ int length;
+ int memory;
+} Groups;
+
+// collection of fields
+typedef struct Fields_Table{
+ // constant parameters
+ Int_Array parameter;
+ // anticommuting external fields
+ Int_Array external;
+ // anticommuting internal fields
+ Int_Array internal;
+ // identities between fields
+ Identities ids;
+ // symbolic expressions (commuting)
+ Symbols symbols;
+ // list of anti-commuting variables (fields or symbols)
+ Int_Array fermions;
+} Fields_Table;
+
+// index labels
+typedef struct Labels{
+ Char_Array* labels;
+ int* indices;
+ int length;
+ int memory;
+} Labels;
+
+// id table
+typedef struct Id_Table{
+ int* indices;
+ Polynomial* polynomials;
+ int length;
+ int memory;
+} Id_Table;
+
+/*
+// polynomial scalar and vectors
+typedef struct Polynomial_Scalar{
+ Coefficient coef;
+ int* indices;
+ int length;
+} Polynomial_Scalar;
+typedef struct Polynomial_Vector{
+ Coefficient* coefv;
+ int* indices;
+ int length;
+} Polynomial_Vector;
+typedef struct Polynomial_Matrix{
+ Coefficient** coefm;
+ int* indices;
+ int length;
+} Polynomial_Matrix;
+*/
+
+
+// command line options
+typedef struct Meankondo_Options{
+ int threads;
+ int chain;
+} Meankondo_Options;
+
+typedef struct Numkondo_Options{
+ int display_mode;
+ int niter;
+ long double tol;
+ Char_Array eval_rccstring;
+} Numkondo_Options;
+
+typedef struct Meantools_Options{
+ int command;
+ int deriv_derivs;
+ Int_Array deriv_vars;
+ Char_Array eval_rccstring;
+} Meantools_Options;
+
+typedef struct Kondopp_Options{
+ int dimension;
+} Kondopp_Options;
+
+#endif