path: root/src/grouped_polynomial.c

/*
Copyright 2015-2022 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<remainder.monomials[i].length;j++){
	fprintf(stderr,"%d", remainder.monomials[i].values[j]);
	if(j<remainder.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);
}


// differentiate 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);
}


/*
// differentiate 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",char_array_to_str_noinit(&buffer));
    }
    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 out, RCC in, Grouped_Polynomial poly){
  int i;
  long double* res=calloc(out.length,sizeof(long double));

  if(in.length!=poly.length){
    fprintf(stderr, "error: trying to evaluate a flow equation with %d components on an rcc with %d\n",poly.length,in.length);
    exit(-1);
  }
  if(out.length!=poly.length){
    fprintf(stderr, "error: trying to write the output of a flow equation with %d components on an rcc with %d\n",poly.length,out.length);
    exit(-1);
  }

  // initialize vectors to 0 in an auxiliary vector (to allow for out=in without interference)
  for(i=0;i<in.length;i++){
    res[i]=0.;
  }

  // for each equation
  for(i=0;i<poly.length;i++){
    evalcoef(in, poly.coefs[i], res+i);
  }

  // copy res to rccs
  for(i=0;i<out.length;i++){
    out.values[i]=res[i];
  }

  // free memory
  free(res);
  return(0);

}
// evaluate an equation on a vector (using mpfr floats)
int evaleq_mpfr(RCC_mpfr out, RCC_mpfr in, Grouped_Polynomial poly){
  int i;
  mpfr_t* res;

  if(in.length!=poly.length){
    fprintf(stderr, "error: trying to evaluate a flow equation with %d components on an rcc with %d\n",poly.length,in.length);
    exit(-1);
  }
  if(out.length!=poly.length){
    fprintf(stderr, "error: trying to write the output of a flow equation with %d components on an rcc with %d\n",poly.length,out.length);
    exit(-1);
  }

  res=calloc(out.length,sizeof(mpfr_t));

  // for each equation
  for(i=0;i<poly.length;i++){
    evalcoef_mpfr(in, poly.coefs[i], res[i]);
  }

  // copy res to rccs
  for(i=0;i<out.length;i++){
    mpfr_set(out.values[i], res[i], MPFR_RNDN);
    mpfr_clear(res[i]);
  }

  // free memory
  free(res);
  return(0);
}


// compose two flow equations (replace the rcc's of flow1 by the right hand side of flow2)
int compose_flow_equations(Grouped_Polynomial flow1, Grouped_Polynomial flow2, Grouped_Polynomial* out){
  if(flow1.length!=flow2.length){
    fprintf(stderr, "error: trying to compose two flow equations of different size\n");
    exit(-1);
  }
  int i,j,k;
  Coefficient constant;

  // init
  init_Grouped_Polynomial(out, flow1.length);
  (*out).length=flow1.length;

  // init constant (so we can tell when the constant was not found)
  constant.length=0;

  // loop over rcc's
  for(i=0;i<flow1.length;i++){
    // set indices
    (*out).indices[i]=flow1.indices[i];

    // passthrough constant terms
    if((*out).indices[i]<0){
      int index=intlist_find_err(flow2.indices,flow2.length,(*out).indices[i]);
      coefficient_cpy(flow2.coefs[index], (*out).coefs+i);
      constant=flow2.coefs[index];
      continue;
    }

    // init
    init_Coefficient((*out).coefs+i, COEF_SIZE);

    // loop over terms
    for(j=0;j<flow1.coefs[i].length;j++){
      Coefficient tmp_coef;

      // init
      init_Coefficient(&tmp_coef, COEF_SIZE);
      // init factor
      Int_Array tmp_factor;
      init_Int_Array(&tmp_factor, MONOMIAL_SIZE);
      // init denom
      coef_denom denom;
      // index should be that appearing in flow2
      if(flow2.coefs[i].length<1){
	fprintf(stderr,"error: composing two flow equations: the %d-th term in the flow equation is empty\n",flow1.indices[i]);
	exit(-1);
      }
      denom.index=flow2.coefs[i].denoms[0].index;
      denom.power=0;
      // init num
      Number tmp_num;
      number_cpy(flow1.coefs[i].nums[j], &tmp_num);

      // init coefficient with numerical prefactor
      coefficient_append_noinit(tmp_factor, tmp_num, denom, &tmp_coef);

      // loop over factors
      for(k=0;k<flow1.coefs[i].factors[j].length;k++){
	// multiply factors together
	coefficient_prod_chain(flow2.coefs[intlist_find_err(flow2.indices,flow2.length,flow1.coefs[i].factors[j].values[k])], &tmp_coef);
      }

      // add to out
      coefficient_concat_noinit(tmp_coef, (*out).coefs+i);
    }

  }

  // simplify fractions
  if(constant.length!=0){
    for(i=0;i<(*out).length;i++){
      if((*out).indices[i]>=0){
	// reduce them to a common denominator (not much is gained from trying to simplify them)
	coefficient_common_denominator(constant, (*out).coefs+i);
	//coefficient_simplify_rational(constant, (*out).coefs+i);
      }
    }
  }

  return(0);
}