diff options
author | Ian Jauslin <ian@jauslin.org> | 2019-10-23 00:46:12 -0400 |
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committer | Ian Jauslin <ian@jauslin.org> | 2019-10-23 00:46:12 -0400 |
commit | 62c3c2d5e4cde0a7cf264cc486d38fb35e3c209c (patch) | |
tree | 3aee19aa5b58d86222789eaf3ee8bcd88889e748 |
-rw-r--r-- | Jauslin_GLaMP_2019.tex | 187 | ||||
-rw-r--r-- | Makefile | 50 | ||||
-rw-r--r-- | README | 33 | ||||
-rw-r--r-- | figs/1d.png | bin | 0 -> 70742 bytes | |||
-rw-r--r-- | figs/BEC.png | bin | 0 -> 44985 bytes | |||
-rw-r--r-- | figs/plots.fig/Makefile | 28 | ||||
-rw-r--r-- | figs/plots.fig/erho.dat | 104 | ||||
-rw-r--r-- | figs/plots.fig/erho.gnuplot | 44 | ||||
-rw-r--r-- | figs/plots.fig/erho_bare.gnuplot | 38 | ||||
-rw-r--r-- | libs/ian-presentation.cls | 187 |
10 files changed, 671 insertions, 0 deletions
diff --git a/Jauslin_GLaMP_2019.tex b/Jauslin_GLaMP_2019.tex new file mode 100644 index 0000000..2354d06 --- /dev/null +++ b/Jauslin_GLaMP_2019.tex @@ -0,0 +1,187 @@ +\documentclass{ian-presentation} + +\usepackage[hidelinks]{hyperref} +\usepackage{graphicx} +\usepackage{array} + +\begin{document} +\pagestyle{empty} +\hbox{}\vfil +\bf\Large +\hfil Lieb's simplified approach to interacting Bose gases\par +\vfil +\large +\hfil Ian Jauslin +\normalsize +\vfil +\hfil\rm joint with {\bf Eric Carlen}, {\bf Elliott H. Lieb}\par +\vfil +\hfill{\tt \href{http://ian.jauslin.org}{http://ian.jauslin.org}} +\eject + +\setcounter{page}1 +\pagestyle{plain} + +\title{Bose gas} +\hfil\includegraphics[height=6cm]{BEC.png} +\vfill +\eject + +\title{Interacting Bose gas} +\begin{itemize} + \item State: symmetric wave functions in a finite box of volume $V$ with periodic boundary conditions: + $$ + \psi(x_1,\cdots,x_N) + ,\quad + x_i\in \Lambda_d:=V^{\frac1d}\mathbb T^d + $$ + \item $N$-particle Hamiltonian: + $$ + H_N:= + -\frac12\sum_{i=1}^N\Delta_i + +\sum_{1\leqslant i<j\leqslant N}v(|x_i-x_j|) + $$ + with a repulsive, integrable interaction: $v(|x-y|)\geqslant 0$, $\int dx\ v(x)<\infty$. + +\end{itemize} +\vfill +\eject + +\title{Interacting Bose gas} +\begin{itemize} + \item Ground state: + $$ + H_N\psi_0=E_0\psi_0 + ,\quad + E_0=\min\mathrm{spec}(H_N) + $$ + \item Compute the ground state-energy per particle in the thermodynamic limit: + $$ + e_0:=\lim_{\displaystyle\mathop{\scriptstyle V,N\to\infty}_{\frac NV=\rho}}\frac{E_0}N + $$ +\end{itemize} +\vfill +\eject + +\title{Energy} +\begin{itemize} + \item Integrate $H_N\psi_0=E_0\psi_0$: + $$ + \frac{E_0}N=\frac{N-1}{2V}\int dx\ v(|x-y|)g_2(x,y) + $$ + \item $g_n$: marginal of $\psi_0$ + $$ + g_n(x_1,\cdots,x_n):=\frac{V^n\int dx_{n+1}\cdots dx_N\ \psi_0(x_1,\cdots,x_N)}{\int dx_1\cdots dx_N\ \psi_0(x_1,\cdots,x_N)} + $$ + \item $\psi_0\geqslant 0$, so it can be thought of as a probability distribution +\end{itemize} +\vfill +\eject + +\title{Hierarchy} +\vskip-10pt +\begin{itemize} + \item Equation for $g_2$: integrate $H_N\psi_0=E_0\psi_0$ with respect to $x_3,\cdots,x_N$: + $$ + \begin{array}{>\displaystyle l} + -\frac12(\Delta_x+\Delta_y) g_2(x,y) + +\frac{N-2}V\int dz\ (v(|x-z|)+v(|y-z|))g_3(x,y,z) + \\[0.5cm]\hfill + +v(|x-y|)g_2(x,y) + +\frac{(N-2)(N-3)}{2V^2}\int dzdt\ v(|z-t|)g_4(x,y,z,t) + =E_0g_2(x,y) + \end{array} + $$ + \item Factorization assumption: + $$ + g_3(x_1,x_2,x_3)=g_2(x_1,x_2)g_2(x_1,x_3)g_2(x_2,x_3) + $$ + $$ + g_4(x_1,x_2,x_3,x_4)=\prod_{i<j}(g_2(x_i,x_j)+O(V^{-1})) + $$ +\end{itemize} +\vfill +\eject + +\title{Lieb's simple equation} +\begin{itemize} + \item In the thermodynamic limit, after making a few additional assumptions, \href{https://doi.org/10.1103/PhysRev.130.2518}{[Lieb, 1963]}: + $$ + (-\Delta+v(|x|)+4e_0)u(|x|)=v(|x|)+2e_0\rho\ u\ast u(|x|) + $$ + $$ + e_0=\frac\rho2\int dx\ (1-u(|x|))v(|x|) + $$ + \item with $\rho:=\frac NV$ + $$ + g_2(x,y)=1-u(|x-y|) + ,\quad + u\ast u(|x|):=\int dy\ u(|x-y|)u(|y|) + $$ +\end{itemize} +\vfill +\eject + +\title{One dimension} +\hfil\includegraphics[height=6cm,angle=0.4]{1d.png} +\vfill +\eject + +\title{Numerical solution for $v(x)=e^{-|x|}$ in 3 dimensions} +\hfil\includegraphics[height=6cm]{erho_bare.pdf} +\vfill +\eject + +\title{Numerical solution for $v(x)=e^{-|x|}$ in 3 dimensions} +\hfil\includegraphics[height=6cm]{erho.pdf} +\vfill +\eject + +\title{Asymptotics} +\vskip-10pt +\begin{itemize} + \item {\bf Theorem} \href{https://doi.org/10.1103/PhysRev.130.2518}{[Lieb, 1963]}: if $\hat v(k):=\int dx\ e^{ikx}v(x)\geqslant 0$, then + $$ + \frac{e_0}\rho\mathop{\longrightarrow}_{\rho\to\infty}\frac12\int dx\ v(x) + $$ + \item {\bf Theorem} \href{https://doi.org/10.1103/PhysRevLett.80.2504}{[Lieb, Yngvason, 1998]}: in 3 dimensions + $$ + \frac{e_0}\rho\mathop{\longrightarrow}_{\rho\to0}2\pi a + $$ + \item {\bf Theorem} \href{https://doi.org/10.1023/A:101033721}{[Lieb, Yngvason, 2001]}: in 2 dimensions + $$ + \frac{e_0}\rho\mathop{\longrightarrow}_{\rho\to0}\frac{2\pi}{|\log(\rho a^2)|} + $$ +\end{itemize} +\vfill +\eject + +\title{Lee-Huang-Yang formula} +\begin{itemize} + \item In 3 dimensions, \href{https://doi.org/10.1103/PhysRev.106.1135}{[Lee, Huang, Yang, 1957]} conjecture: + $$ + e_0=2\pi\rho a\left(1+\frac{128}{15\sqrt\pi}\sqrt{\rho a^3}+o(\sqrt\rho)\right) + $$ + \item This was recently proved by \href{https://arxiv.org/abs/1904.06164}{[Fournais, Solovej, 2019]}. +\end{itemize} +\vfill +\eject + +\title{Results} +\begin{itemize} + \item {\bf Theorem}: For Lieb's simplified equation, + $$ + \frac{e_0}\rho\mathop{\longrightarrow}_{\rho\to\infty}\frac12\int dx\ v(x) + $$ + and, in 3 dimensions, + $$ + e_0=2\pi\rho a\left(1+\frac{128}{15\sqrt\pi}\sqrt{\rho a^3}+O(\rho)\right) + $$ + in 2 dimensions + $$ + \frac{e_0}\rho\mathop{\longrightarrow}_{\rho\to\infty}\frac{2\pi}{|\log(\rho a)|} + . + $$ +\end{itemize} + +\end{document} diff --git a/Makefile b/Makefile new file mode 100644 index 0000000..74cd1ca --- /dev/null +++ b/Makefile @@ -0,0 +1,50 @@ +PROJECTNAME=$(basename $(wildcard *.tex)) +LIBS=$(notdir $(wildcard libs/*)) +FIGS=$(notdir $(wildcard figs/*.fig)) +PNGS=$(notdir $(wildcard figs/*.png)) + +PDFS=$(addsuffix .pdf, $(PROJECTNAME)) +SYNCTEXS=$(addsuffix .synctex.gz, $(PROJECTNAME)) + +all: $(PROJECTNAME) + +$(PROJECTNAME): $(LIBS) $(FIGS) $(PNGS) + pdflatex -file-line-error $@.tex + pdflatex -synctex=1 $@.tex + +$(SYNCTEXS): $(LIBS) $(FIGS) $(PNGS) + pdflatex -synctex=1 $(patsubst %.synctex.gz, %.tex, $@) + + +$(LIBS): + ln -fs libs/$@ ./ + + +$(FIGS): + make -C figs/$@ + for pdf in $$(find figs/$@/ -name '*.pdf'); do ln -fs "$$pdf" ./ ; done + +$(PNGS): + ln -fs figs/$@ ./ + + +clean-aux: clean-figs-aux + rm -f $(addsuffix .aux, $(PROJECTNAME)) + rm -f $(addsuffix .log, $(PROJECTNAME)) + rm -f $(addsuffix .out, $(PROJECTNAME)) + +clean-libs: + rm -f $(LIBS) + +clean-figs: + $(foreach fig,$(addprefix figs/, $(FIGS)), make -C $(fig) clean; ) + rm -f $(notdir $(wildcard figs/*.fig/*.pdf)) + +clean-figs-aux: + $(foreach fig,$(addprefix figs/, $(FIGS)), make -C $(fig) clean-aux; ) + + +clean-tex: + rm -f $(PDFS) $(SYNCTEXS) + +clean: clean-aux clean-tex clean-libs clean-figs @@ -0,0 +1,33 @@ +This directory contains the source files to typeset the presentation, and +generate the figures. This can be accomplished by running + make + +This document uses a custom class file, located in the 'libs' directory, which +defines a number of commands. + + +* Dependencies: + + pdflatex + TeXlive packages: + amsfonts + array + graphics + hyperref + latex + pgf + standalone + GNU make + gnuplot + +* Files: + + Jauslin_GLaMP_2019.tex: + main LaTeX file + + libs: + custom LaTeX class file + + figs: + source code for the figures + diff --git a/figs/1d.png b/figs/1d.png Binary files differnew file mode 100644 index 0000000..e64f960 --- /dev/null +++ b/figs/1d.png diff --git a/figs/BEC.png b/figs/BEC.png Binary files differnew file mode 100644 index 0000000..b64fda1 --- /dev/null +++ b/figs/BEC.png diff --git a/figs/plots.fig/Makefile b/figs/plots.fig/Makefile new file mode 100644 index 0000000..8d17272 --- /dev/null +++ b/figs/plots.fig/Makefile @@ -0,0 +1,28 @@ +PROJECTNAME=erho_bare erho + +PDFS=$(addsuffix .pdf, $(PROJECTNAME)) + +all: $(PDFS) + +$(PDFS): + gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tex, $@) + pdflatex -file-line-error $(patsubst %.pdf, %.tex, $@) + +install: $(PDFS) + cp $^ $(INSTALLDIR)/ + +$(LIBS): + ln -fs libs/$@ ./ + +clean-libs: + rm -f $(LIBS) + +clean-aux: + rm -f $(addsuffix .aux, $(PROJECTNAME)) + rm -f $(addsuffix .log, $(PROJECTNAME)) + rm -f $(addsuffix .tex, $(PROJECTNAME)) + +clean-tex: + rm -f $(PDFS) + +clean: clean-libs clean-aux clean-tex diff --git a/figs/plots.fig/erho.dat b/figs/plots.fig/erho.dat new file mode 100644 index 0000000..837439f --- /dev/null +++ b/figs/plots.fig/erho.dat @@ -0,0 +1,104 @@ + # v(x)=exp(-|x|), order=100, tolerance=1e-14 + # + # rho energy + # + 1.00000000e-06 7.93445832e-06 + 1.20226443e-06 9.54545091e-06 + 1.44543977e-06 1.14842358e-05 + 1.73780083e-06 1.38177301e-05 + 2.08929613e-06 1.66265809e-05 + 2.51188643e-06 2.00080034e-05 + 3.01995172e-06 2.40792133e-05 + 3.63078055e-06 2.89815779e-05 + 4.36515832e-06 3.48856405e-05 + 5.24807460e-06 4.19972045e-05 + 6.30957344e-06 5.05647046e-05 + 7.58577575e-06 6.08881446e-05 + 9.12010839e-06 7.33299394e-05 + 1.09647820e-05 8.83280780e-05 + 1.31825674e-05 1.06412115e-04 + 1.58489319e-05 1.28222614e-04 + 1.90546072e-05 1.54534805e-04 + 2.29086765e-05 1.86287394e-04 + 2.75422870e-05 2.24617677e-04 + 3.31131121e-05 2.70904370e-04 + 3.98107171e-05 3.26819905e-04 + 4.78630092e-05 3.94394317e-04 + 5.75439937e-05 4.76093386e-04 + 6.91830971e-05 5.74914264e-04 + 8.31763771e-05 6.94502595e-04 + 1.00000000e-04 8.39296065e-04 + 1.20226443e-04 1.01470042e-03 + 1.44543977e-04 1.22730542e-03 + 1.73780083e-04 1.48514988e-03 + 2.08929613e-04 1.79804690e-03 + 2.51188643e-04 2.17798310e-03 + 3.01995172e-04 2.63960836e-03 + 3.63078055e-04 3.20083623e-03 + 4.36515832e-04 3.88357954e-03 + 5.24807460e-04 4.71465030e-03 + 6.30957344e-04 5.72685888e-03 + 7.58577575e-04 6.96035420e-03 + 9.12010839e-04 8.46425370e-03 + 1.09647820e-03 1.02986208e-02 + 1.31825674e-03 1.25368572e-02 + 1.58489319e-03 1.52685874e-02 + 1.90546072e-03 1.86031268e-02 + 2.29086765e-03 2.26736380e-02 + 2.75422870e-03 2.76420977e-02 + 3.31131121e-03 3.37052167e-02 + 3.98107171e-03 4.11014850e-02 + 4.78630092e-03 5.01195435e-02 + 5.75439937e-03 6.11081308e-02 + 6.91830971e-03 7.44879092e-02 + 8.31763771e-03 9.07655413e-02 + 1.00000000e-02 1.10550483e-01 + 1.20226443e-02 1.34575061e-01 + 1.44543977e-02 1.63718539e-01 + 1.73780083e-02 1.99036030e-01 + 2.08929613e-02 2.41793284e-01 + 2.51188643e-02 2.93508614e-01 + 3.01995172e-02 3.56003446e-01 + 3.63078055e-02 4.31463277e-01 + 4.36515832e-02 5.22511186e-01 + 5.24807460e-02 6.32296416e-01 + 6.30957344e-02 7.64601077e-01 + 7.58577575e-02 9.23968602e-01 + 9.12010839e-02 1.11585830e+00 + 1.09647820e-01 1.34683126e+00 + 1.31825674e-01 1.62477387e+00 + 1.58489319e-01 1.95916654e+00 + 1.90546072e-01 2.36140673e+00 + 2.29086765e-01 2.84519724e+00 + 2.75422870e-01 3.42701297e+00 + 3.31131121e-01 4.12666196e+00 + 3.98107171e-01 4.96795983e+00 + 4.78630092e-01 5.97954056e+00 + 5.75439937e-01 7.19583118e+00 + 6.91830971e-01 8.65822353e+00 + 8.31763771e-01 1.04164830e+01 + 1.00000000e+00 1.25304420e+01 + 1.20226443e+00 1.50720365e+01 + 1.44543977e+00 1.81277534e+01 + 1.73780083e+00 2.18015742e+01 + 2.08929613e+00 2.62185132e+01 + 2.51188643e+00 3.15288712e+01 + 3.01995172e+00 3.79133506e+01 + 3.63078055e+00 4.55892039e+01 + 4.36515832e+00 5.48176270e+01 + 5.24807460e+00 6.59126465e+01 + 6.30957344e+00 7.92518063e+01 + 7.58577575e+00 9.52890139e+01 + 9.12010839e+00 1.14569987e+02 + 1.09647820e+01 1.37750822e+02 + 1.31825674e+01 1.65620322e+02 + 1.58489319e+01 1.99126836e+02 + 1.90546072e+01 2.39410530e+02 + 2.29086765e+01 2.87842186e+02 + 2.75422870e+01 3.46069846e+02 + 3.31131121e+01 4.16074894e+02 + 3.98107171e+01 5.00239474e+02 + 4.78630092e+01 6.01427558e+02 + 5.75439937e+01 7.23082394e+02 + 6.91830971e+01 8.69343678e+02 + 8.31763771e+01 1.04518842e+03 diff --git a/figs/plots.fig/erho.gnuplot b/figs/plots.fig/erho.gnuplot new file mode 100644 index 0000000..f91dc28 --- /dev/null +++ b/figs/plots.fig/erho.gnuplot @@ -0,0 +1,44 @@ +datafile="erho.dat" + +## can also set the following options +#set title "" +set ylabel "$\\displaystyle\\frac{e_0}{\\rho}$" norotate +set xlabel "$\\log_{10}(\\rho)$" +# +#set xrange[:] +#set yrange [7:] +# +## start ticks at 0, then every x +#set xtics -6,2 +#set ytics 8,2 +## puts 4 minor tics between tics (5 intervals, i.e. every 0.01) +set mxtics 5 +set mytics 5 + +# default output canvas size: 12.5cm x 8.75cm +set term lua tikz size 12.5,8.75 standalone + +set key off + +# 3=1+2 draw bottom and left sides of the box +#set border 3 +# don't show tics on opposite sides +#set xtics nomirror +#set ytics nomirror + +# set linestyle +set style line 1 linetype rgbcolor "#4169E1" linewidth 3 +set style line 2 linetype rgbcolor "#DC143C" linewidth 3 +set style line 3 linetype rgbcolor "#32CD32" linewidth 3 +set style line 4 linetype rgbcolor "#4B0082" linewidth 3 +set style line 5 linetype rgbcolor "#DAA520" linewidth 3 + +a=1.2544 +set arrow from -2,4*pi to 2,4*pi linewidth 2 dashtype "." linecolor "#DC143C" nohead +set label at -4,4*pi "$\\displaystyle\\frac12\\int dx\\ v(x)$" textcolor "#DC143C" +set arrow from -6,2*pi*a to -2,2*pi*a linewidth 2 dashtype "." linecolor "#DC143C" nohead +set label at -2,2*pi*a "$2\\pi a$" textcolor "#DC143C" + +set pointsize 0.6 + +plot datafile using (log10($1)):($2/$1) with lines linestyle 1 diff --git a/figs/plots.fig/erho_bare.gnuplot b/figs/plots.fig/erho_bare.gnuplot new file mode 100644 index 0000000..9509abf --- /dev/null +++ b/figs/plots.fig/erho_bare.gnuplot @@ -0,0 +1,38 @@ +datafile="erho.dat" + +## can also set the following options +#set title "" +set ylabel "$\\displaystyle\\frac{e_0}{\\rho}$" norotate +set xlabel "$\\log_{10}(\\rho)$" +# +#set xrange[:] +#set yrange [7:] +# +## start ticks at 0, then every x +#set xtics -6,2 +#set ytics 8,2 +## puts 4 minor tics between tics (5 intervals, i.e. every 0.01) +set mxtics 5 +set mytics 5 + +# default output canvas size: 12.5cm x 8.75cm +set term lua tikz size 12.5,8.75 standalone + +set key off + +# 3=1+2 draw bottom and left sides of the box +#set border 3 +# don't show tics on opposite sides +#set xtics nomirror +#set ytics nomirror + +# set linestyle +set style line 1 linetype rgbcolor "#4169E1" linewidth 3 +set style line 2 linetype rgbcolor "#DC143C" linewidth 3 +set style line 3 linetype rgbcolor "#32CD32" linewidth 3 +set style line 4 linetype rgbcolor "#4B0082" linewidth 3 +set style line 5 linetype rgbcolor "#DAA520" linewidth 3 + +set pointsize 0.6 + +plot datafile using (log10($1)):($2/$1) with lines linestyle 1 diff --git a/libs/ian-presentation.cls b/libs/ian-presentation.cls new file mode 100644 index 0000000..91bd487 --- /dev/null +++ b/libs/ian-presentation.cls @@ -0,0 +1,187 @@ +%% +%% Ian's presentation class +%% + +%% TeX format +\NeedsTeXFormat{LaTeX2e}[1995/12/01] + +%% class name +\ProvidesClass{ian-presentation}[2017/09/29] + +\def\ian@defaultoptions{ + \pagestyle{plain} + \RequirePackage{color} + \RequirePackage{amssymb} +} + +%% paper dimensions +\setlength\paperheight{240pt} +\setlength\paperwidth{427pt} + +%% fonts +\input{size11.clo} +\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm} +\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf} +\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt} +\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf} +\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit} + +%% text dimensions +\textheight=208pt +\textwidth=370pt +\hoffset=-1in +\voffset=-1in +\oddsidemargin=24pt +\evensidemargin=24pt +\topmargin=8pt +\headheight=0pt +\headsep=0pt +\marginparsep=0pt +\marginparwidth=0pt +\footskip=16pt + + +%% remove default skips +\parindent=0pt +\parskip=0pt +\baselineskip=0pt + +%% something is wrong with \thepage, redefine it +\gdef\thepage{\the\c@page} + +%% correct vertical alignment at the end of a document +\AtEndDocument{ + % save total slide count + \immediate\write\@auxout{\noexpand\gdef\noexpand\slidecount{\thepage}} + \vfill + \eject +} + + +%% footer +\def\ps@plain{ + \def\@oddhead{} + \def\@evenhead{\@oddhead} + \def\@oddfoot{\tiny\hfill\thepage/\safe\slidecount\hfill} + \def\@evenfoot{\@oddfoot} +} +\def\ps@empty{ + \def\@oddhead{} + \def\@evenhead{\@oddhead} + \def\@oddfoot{} + \def\@evenfoot{\@oddfoot} +} + + +%% title of slide +\def\title#1{ + \hfil{\bf\large #1}\par + \hfil\vrule width0.75\textwidth height0.3pt\par + \vskip5pt +} + + +%% hyperlinks +% hyperlinkcounter +\newcounter{lncount} +% hyperref anchor +\def\hrefanchor{% +\stepcounter{lncount}% +\hypertarget{ln.\thelncount}{}% +} + +%% define a command and write it to aux file +\def\outdef#1#2{% + % define command% + \expandafter\xdef\csname #1\endcsname{#2}% + % hyperlink number% + \expandafter\xdef\csname #1@hl\endcsname{\thelncount}% + % write command to aux% + \immediate\write\@auxout{\noexpand\expandafter\noexpand\gdef\noexpand\csname #1\endcsname{\csname #1\endcsname}}% + \immediate\write\@auxout{\noexpand\expandafter\noexpand\gdef\noexpand\csname #1@hl\endcsname{\thelncount}}% +} + +%% can call commands even when they are not defined +\def\safe#1{% + \ifdefined#1% + #1% + \else% + {\color{red}\bf?}% + \fi% +} + + +%% itemize +\newlength\itemizeskip +% left margin for items +\setlength\itemizeskip{20pt} +\newlength\itemizeseparator +% space between the item symbol and the text +\setlength\itemizeseparator{5pt} +% penalty preceding an itemize +\def\itemizepenalty{0} +% counter counting the itemize level +\newcounter{itemizecount} + +% item symbol +\def\itemizept#1{ + \ifnum#1=1 + \textbullet + \else + $\scriptstyle\blacktriangleright$ + \fi +} + +\newlength\current@itemizeskip +\setlength\current@itemizeskip{0pt} +\def\itemize{ + \par\penalty\itemizepenalty\medskip\penalty\itemizepenalty + \addtocounter{itemizecount}{1} + \addtolength\current@itemizeskip{\itemizeskip} + \leftskip\current@itemizeskip +} +\def\enditemize{ + \addtocounter{itemizecount}{-1} + \addtolength\current@itemizeskip{-\itemizeskip} + \par\leftskip\current@itemizeskip + \medskip +} +\newlength\itempt@total +\def\item{ + \settowidth\itempt@total{\itemizept\theitemizecount} + \addtolength\itempt@total{\itemizeseparator} + \par + \medskip + \hskip-\itempt@total\itemizept\theitemizecount\hskip\itemizeseparator +} + +%% enumerate +\newcounter{enumerate@count} +\def\enumerate{ + \setcounter{enumerate@count}0 + \let\olditem\item + \let\olditemizept\itemizept + \def\item{ + % counter + \stepcounter{enumerate@count} + % set header + \def\itemizept{\theenumerate@count.} + % hyperref anchor + \hrefanchor + % define tag (for \label) + \xdef\tag{\theenumerate@count} + \olditem + } + \itemize +} +\def\endenumerate{ + \enditemize + \let\item\olditem + \let\itemizept\olditemizept +} + + +%% end +\ian@defaultoptions + +\endinput |