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1214
Jauslin_2022.tex Normal file
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Makefile Normal file
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PROJECTNAME=$(basename $(wildcard *.tex))
LIBS=$(notdir $(wildcard libs/*))
FIGS=$(notdir $(wildcard figs/*.fig))
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
SYNCTEXS=$(addsuffix .synctex.gz, $(PROJECTNAME))
all: $(PROJECTNAME)
$(PROJECTNAME): $(LIBS) $(FIGS)
pdflatex -file-line-error $@.tex
pdflatex -file-line-error $@.tex
pdflatex -synctex=1 $@.tex
$(PROJECTNAME).aux: $(LIBS) $(FIGS)
pdflatex -file-line-error -draftmode $(PROJECTNAME).tex
$(SYNCTEXS): $(LIBS) $(FIGS)
pdflatex -synctex=1 $(patsubst %.synctex.gz, %.tex, $@)
libs: $(LIBS)
$(LIBS):
ln -fs libs/$@ ./
figs: $(FIGS)
$(FIGS):
make -C figs/$@
for pdf in $$(find figs/$@/ -name '*.pdf'); do ln -fs "$$pdf" ./ ; done
clean-aux: clean-figs-aux
rm -f $(addsuffix .aux, $(PROJECTNAME))
rm -f $(addsuffix .log, $(PROJECTNAME))
rm -f $(addsuffix .out, $(PROJECTNAME))
rm -f $(addsuffix .toc, $(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

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README Normal file
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This directory contains the source files to typeset the article, and generate
the figures. This can be accomplished by running
make
The data pertaining to the Big, Medium and Simple equations in the figures were
generated using 'simplesolv' which is available from
http://ian.jauslin.org/software/simplesolv
This document uses a custom class file, located in the 'libs' directory, which
defines a number of commands. Most of these are drop-in replacements for those
defined in the 'article' class.
Some extra functionality is provided in custom style files, located in the
'libs' directory.
* Dependencies:
pdflatex
TeXlive packages:
amsfonts
array
xcolor
dsfont
graphicx
hyperref
latex
marginnote
pgf
standalone
GNU make
simplesolv
* Files:
Jauslin_2022.tex:
main LaTeX file
libs:
custom LaTeX class file
figs:
source code for the figures

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\bibitem[CJL20]{CJL20}E.A. Carlen, I. Jauslin, E.H. Lieb - {\it Analysis of a simple equation for the ground state energy of the Bose gas}, Pure and Applied Analysis, volume\-~2, issue\-~3, pages\-~659-684, 2020,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.2140/paa.2020.2.659}{10.2140/paa.2020.2.659}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/1912.04987}{1912.04987}}.\par\medskip
\bibitem[CJL21]{CJL21}E.A. Carlen, I. Jauslin, E.H. Lieb - {\it Analysis of a Simple Equation for the Ground State of the Bose Gas II: Monotonicity, Convexity, and Condensate Fraction}, SIAM Journal on Mathematical Analysis, volume\-~53, number\-~5, pages\-~5322-5360, 2021,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1137/20M1376820}{10.1137/20M1376820}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/2010.13882}{2010.13882}}.\par\medskip
\bibitem[CJe21]{CJe21}E.A. Carlen, I. Jauslin, E.H. Lieb, M.P. Loss - {\it On the Convolution Inequality $f\geqslant f\star f$}, International Mathematics Research Notices, volume\-~2021, number\-~24, pages\-~18604-18612, 2021,\par\penalty10000
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\bibitem[Di49]{Di49}R. Dingle - {\it The zero-point energy of a system of particles}, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, volume\-~40, number\-~304, pages\-~573-578, 1949,\par\penalty10000
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\bibitem[Ei24]{Ei24}A. Einstein - {\it Quantentheorie des einatomigen idealen Gases}, Sitzungsberichte der Preussischen Akademie der Wissenschaften, volume\-~1, issue\-~3, 1924.\par\medskip
\bibitem[FS20]{FS20}S. Fournais, J.P. Solovej - {\it The energy of dilute Bose gases}, Annals of Mathematics, volume\-~192, issue\-~3, pages\-~893-976, 2020,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.4007/annals.2020.192.3.5}{10.4007/annals.2020.192.3.5}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/1904.06164}{1904.06164}}.\par\medskip
\bibitem[FS21]{FS21}S.\-~Fournais, J.P.\-~Solovej - {\it The energy of dilute Bose gases II: The general case}, arXiv preprint, 2021\par\penalty10000
arxiv:{\tt\color{blue}\href{https://arxiv.org/abs/2108.12022}{2108.12022}}.\par\medskip
\bibitem[Ja55]{Ja55}R. Jastrow - {\it Many-Body Problem with Strong Forces}, Physical Review, volume\-~98, issue\-~5, pages\-~1479-1484, 1955,\par\penalty10000
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\bibitem[KLS88]{KLS88}T. Kennedy, E.H. Lieb, B.S. Shastry - {\it Existence of N\'eel order in some spin-1/2 Heisenberg antiferromagnets}, Journal of Statistical Physics, volume\-~53, issue\-~5, pages\-~1019-1030, 1988,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/BF01023854}{10.1007/BF01023854}}.\par\medskip
\bibitem[LHY57]{LHY57}T.D. Lee, K. Huang, C.N. Yang - {\it Eigenvalues and Eigenfunctions of a Bose System of Hard Spheres and Its Low-Temperature Properties}, Physical Review, volume\-~106, issue\-~6, pages\-~1135-1145, 1957,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRev.106.1135}{10.1103/PhysRev.106.1135}}.\par\medskip
\bibitem[Li63]{Li63}E.H. Lieb - {\it Simplified Approach to the Ground-State Energy of an Imperfect Bose Gas}, Physical Review, volume\-~130, issue\-~6, pages\-~2518-2528, 1963,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRev.130.2518}{10.1103/PhysRev.130.2518}}.\par\medskip
\bibitem[LS02]{LS02}E.H. Lieb, R. Seiringer - {\it Proof of Bose-Einstein Condensation for Dilute Trapped Gases}, Physical Review Letters, volume\-~88, issue\-~17, number\-~170409, 2002,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRevLett.88.170409}{10.1103/PhysRevLett.88.170409}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/math-ph/0112032}{math-ph/0112032}}.\par\medskip
\bibitem[LSe05]{LSe05}E.H. Lieb, R. Seiringer, J.P. Solovej, J. Yngvason - {\it The Mathematics of the Bose Gas and its Condensation}, Oberwolfach Seminars, volume\-~34, Birkha\"user, 2005, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/cond-mat/0610117}{cond-mat/0610117}}.\par\medskip
\bibitem[LY98]{LY98}E.H. Lieb, J. Yngvason - {\it Ground State Energy of the Low Density Bose Gas}, Physical Review Letters, volume\-~80, issue\-~12, pages\-~2504-2507, 1998,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRevLett.80.2504}{10.1103/PhysRevLett.80.2504}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/cond-mat/9712138}{cond-mat/9712138}}.\par\medskip
\bibitem[Se11]{Se11}R. Seiringer - {\it The Excitation Spectrum for Weakly Interacting Bosons}, Communications in Mathematical Physics, volume\-~306, issue\-~2, pages\-~565-578, 2011,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/s00220-011-1261-6}{10.1007/s00220-011-1261-6}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/1008.5349}{1008.5349}}.\par\medskip
\bibitem[YY09]{YY09}H. Yau, J. Yin - {\it The Second Order Upper Bound for the Ground Energy of a Bose Gas}, Journal of Statistical Physics, volume\-~136, issue\-~3, pages\-~453-503, 2009,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/s10955-009-9792-3}{10.1007/s10955-009-9792-3}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/0903.5347}{0903.5347}}.\par\medskip
\bibitem[ss]{ss}{\tt simplesolv} software package v0.3, I.\-~Jauslin,\par\penalty10000
{\tt\color{blue}\href{http://ian.jauslin.org/software/simplesolv}{http://ian.jauslin.org/software/simplesolv}}.\par\medskip

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figs/condensate.fig/2020-08-27+0.5.dat Normal file
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# potential: 0.5 e^{-|x|}
# rho E 1-eta Jastrow E
1e-3 0.005189 0.978 0.005193
5e-3 0.027389 0.961 0.027395
1e-2 0.056223 0.959 0.05624
2e-2 0.11530 0.954 0.11530
1e-1 0.6037 0.953 0.60377
1e+0 6.221 0.97 6.22

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figs/condensate.fig/Makefile Normal file
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PROJECTNAME=condensate
SIMPLESOLV=~/Work/Research/2018+bose_gas/cmp/simplesolv/source/src
DATS=simpleq.dat medeq.dat bigeq.dat
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME))
all: $(PDFS)
$(PDFS): $(DATS)
gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@)
pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
simpleq.dat:
julia $(SIMPLESOLV)/main.jl -p "eq=simpleq;tolerance=1e-11;order=100;maxiter=100;v_a=0.5;minlrho=-6;nlrho=100;maxlrho=2" -M easyeq -U exp condensate_fraction_rho > $@
medeq.dat:
julia $(SIMPLESOLV)/main.jl -p "eq=medeq;tolerance=1e-11;order=100;maxiter=100;v_a=0.5;minlrho=-6;nlrho=100;maxlrho=2" -M easyeq -U exp condensate_fraction_rho > $@
bigeq.dat:
julia -p 8 $(SIMPLESOLV)/main.jl -p "eq=bigeq;N=12;P=8;J=10;tolerance=1e-11;maxiter=21;v_a=0.5;minlrho=-6;nlrho=100;maxlrho=2" -M anyeq -U exp condensate_fraction_rho > $@
install: $(PDFS)
cp $^ $(INSTALLDIR)/
clean-aux:
rm -f $(addsuffix .tikz.tex, $(PROJECTNAME))
rm -f $(addsuffix .aux, $(PROJECTNAME))
rm -f $(addsuffix .log, $(PROJECTNAME))
clean-dat:
rm -f $(DATS)
clean-tex:
rm -f $(PDFS)
clean: clean-aux clean-tex

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1.000000000000000e-06 9.359600849904642e-04 4.769492271009877e-12
1.204503540258781e-06 1.026263695589573e-03 3.419474268720360e-12
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1.747528400007683e-06 1.243211901088135e-03 6.036870814265909e-14
2.104904144512022e-06 1.371540352505089e-03 1.465826916259999e-12
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4.430621457583877e-06 2.037906626012430e-03 6.922442639580641e-13
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1.123324032978027e-05 3.263387610365739e-03 5.798705939542849e-14
1.353047774579808e-05 3.577021358160436e-03 1.007850792994357e-13
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2.364489412645407e-05 4.697030635602372e-03 9.993404840576712e-14
2.848035868435805e-05 5.138553215636342e-03 7.889857713883516e-14
3.430469286314919e-05 5.618698153738680e-03 5.544933866100784e-14
4.132012400115334e-05 6.140366567754929e-03 3.505040625564625e-14
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7.220809018385471e-05 7.985017865199253e-03 2.911321693643152e-14
8.697490026177834e-05 8.703608059981844e-03 1.665264019357716e-14
1.047615752789665e-04 9.479343964932427e-03 1.735486882457866e-14
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1.519911082952935e-04 1.121458911634652e-02 1.063694582767876e-14
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3.199267137797384e-04 1.549505586477500e-02 3.187650388653336e-14
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5.590810182512228e-04 1.946333993043477e-02 3.849130191836202e-14
6.734150657750828e-04 2.092863160214499e-02 5.858344140792253e-14
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1.176811952434999e-03 2.570125163577371e-02 1.510104805632382e-13
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2.477076355991711e-03 3.264110309962052e-02 4.285413087823841e-13
2.983647240283340e-03 3.439816133650226e-02 5.302517700005698e-13
3.593813663804629e-03 3.613233114795761e-02 6.403992903217449e-13
4.328761281083062e-03 3.782558079607085e-02 7.571924192093096e-13
5.214008287999690e-03 3.945923077971335e-02 8.735665611670509e-13
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7.564633275546291e-03 4.247268081094784e-02 1.086591967833584e-12
9.111627561154896e-03 4.381637597402372e-02 1.171028110980761e-12
1.097498765493057e-02 4.502933773539811e-02 1.235182529056386e-12
1.321941148466031e-02 4.609730735888347e-02 1.273413495244793e-12
1.592282793341094e-02 4.700836649313180e-02 1.288870490747045e-12
1.917910261672489e-02 4.775326110412755e-02 1.277774794460160e-12
2.310129700083163e-02 4.832561126937697e-02 1.245436832753992e-12
2.782559402207126e-02 4.872199901018250e-02 1.194094596784815e-12
3.351602650938848e-02 4.894193587141005e-02 1.129149381775895e-12
4.037017258596558e-02 4.898772053354203e-02 1.056418952921306e-12
4.862601580065354e-02 4.886420356210291e-02 9.797825696635614e-13
5.857020818056673e-02 4.857848093382484e-02 9.036039641219436e-13
7.054802310718646e-02 4.813954002928141e-02 8.309184154224132e-13
8.497534359086456e-02 4.755788150120432e-02 7.632736986718884e-13
1.023531021899027e-01 4.684513825031006e-02 7.009835850851132e-13
1.232846739442068e-01 4.601370925687214e-02 6.445926849679039e-13
1.484968262254467e-01 4.507642184667945e-02 5.938594915648704e-13
1.788649529057435e-01 4.404623166683212e-02 5.471692016966516e-13
2.154434690031887e-01 4.293596563723694e-02 5.037037371246892e-13
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3.125715849688241e-01 4.052464054410850e-02 4.243706234593440e-13
3.764935806792471e-01 3.924689825998715e-02 3.870128277902043e-13
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1.149756995397738e+00 3.118893716272646e-02 1.896018293540065e-13
1.384886371393875e+00 2.985342837493234e-02 1.627002158331657e-13
1.668100537200059e+00 2.853613755533530e-02 1.381782671776070e-13
2.009233002565050e+00 2.724147654488262e-02 1.162433870344956e-13
2.420128264794383e+00 2.597322464354741e-02 9.667411489592391e-14
2.915053062825182e+00 2.473457624087447e-02 7.921718375131266e-14
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4.229242874389508e+00 2.235622749416585e-02 5.197716963886527e-14
5.094138014816386e+00 2.122041434752589e-02 4.164284351060715e-14
6.135907273413176e+00 2.012206730828386e-02 3.267501010541636e-14
7.390722033525790e+00 1.906214310748888e-02 2.631758984864249e-14
8.902150854450392e+00 1.804127525584338e-02 1.984138301410465e-14
1.072267222010325e+01 1.705980992860735e-02 1.572328524590868e-14
1.291549665014885e+01 1.611783932288287e-02 1.184638961517491e-14
1.555676143930475e+01 1.521523252238974e-02 9.222802498318025e-15
1.873817422860387e+01 1.435166393772974e-02 7.775425060459825e-15
2.257019719633922e+01 1.352663941296484e-02 5.807567740486978e-15
2.718588242732946e+01 1.273952010501215e-02 5.266597955329656e-15
3.274549162877732e+01 1.198954425222880e-02 4.772515936081468e-15
3.944206059437664e+01 1.127584695317193e-02 4.990759746751970e-15
4.750810162102803e+01 1.059747807695462e-02 4.465420870908758e-15
5.722367659350220e+01 9.953418424741895e-03 5.050460646392378e-15
6.892612104349709e+01 9.342594259386548e-03 4.878151124718388e-15
8.302175681319753e+01 8.763890317430715e-03 6.408523490975994e-15
1.000000000000000e+02 8.216161414267099e-03 7.308726309426102e-15

41
figs/condensate.fig/condensate.gnuplot Normal file
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@ -0,0 +1,41 @@
set ylabel "$\\tilde\\eta$" norotate offset -1,0
set xlabel "$\\rho$"
set xtics 1e-6, 100, 100
set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0, "$10^2$" 100)
unset mxtics
#set ytics 0.6, 0.1
set mytics 2
set xrange [4e-8:100]
set yrange [:0.06]
# default output canvas size: 12.5cm x 8.75cm
set term lua tikz size 8,6 standalone
set key top left box linetype rgbcolor"#999999" width 0.3 height 0.3 spacing 1.3
# set linestyle
set style line 1 linetype rgbcolor "#4169E1" linewidth 2 dashtype "."
set style line 2 linetype rgbcolor "#DC143C" linewidth 2
set style line 3 linetype rgbcolor "#32CD32" linewidth 2 dashtype "-"
set style line 4 linetype rgbcolor "#4B0082" linewidth 2
set style line 5 linetype rgbcolor "#DAA520" linewidth 2
set style line 6 linetype rgbcolor "#999999" linewidth 1.5 dashtype (1,5)
set pointsize 1
set logscale x
a=0.7666858699084325
plot \
"simpleq.dat" using 1:($3<1e-5 ? $2 : 1/0) with lines ls 1 title "simple",\
"medeq.dat" using 1:($3<1e-5 ? $2 : 1/0) with lines ls 3 title "med",\
"bigeq.dat" using 1:($3<1e-5 ? $2 : 1/0) with lines ls 5 title "big",\
"2020-08-27+0.5.dat" using 1:(1-$3) with points ls 2 title "QMC" ,\
8./(3*sqrt(pi))*sqrt(x*a**3) ls 6 title "Bog"

100
figs/condensate.fig/medeq.dat Normal file
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@ -0,0 +1,100 @@
1.000000000000000e-06 9.996791129944504e-04 2.557931963013874e-14
1.204503540258781e-06 1.096049436651035e-03 1.355586210122227e-14
1.450828778495940e-06 1.201592925494163e-03 1.225664725981035e-14
1.747528400007683e-06 1.317158886205431e-03 1.598257741770033e-14
2.104904144512022e-06 1.443670377419786e-03 1.553247893694121e-14
2.535364493970111e-06 1.582129599439783e-03 2.230882620498033e-14
3.053855508833412e-06 1.733623466010337e-03 1.130567634193424e-14
3.678379771828634e-06 1.899329292079710e-03 9.168136807150408e-15
4.430621457583877e-06 2.080520546462278e-03 8.941527845815565e-15
5.336699231206313e-06 2.278572579850316e-03 1.057140657470087e-14
6.428073117284319e-06 2.494968213624501e-03 1.682809007854741e-14
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9.111627561154896e-03 4.231020439338591e-02 9.583441188473053e-14
1.097498765493057e-02 4.358967353465550e-02 9.098040840969979e-14
1.321941148466031e-02 4.475427741179566e-02 9.678591042746094e-14
1.592282793341094e-02 4.579226915716316e-02 9.326011061107550e-14
1.917910261672489e-02 4.669358156904567e-02 7.331622846406362e-14
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1.000000000000000e+02 9.203798259569440e-03 1.635211949437703e-14

100
figs/condensate.fig/simpleq.dat Normal file
View File

@ -0,0 +1,100 @@
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1.873817422860387e+01 1.292225141205694e-04 9.319604832811551e-16
2.257019719633922e+01 1.073551496286977e-04 5.244863713602307e-14
2.718588242732946e+01 8.917813671942175e-05 4.169604052705751e-16
3.274549162877732e+01 7.407180357771646e-05 5.251294860012204e-14
3.944206059437664e+01 6.151957225656779e-05 5.364972970438718e-14
4.750810162102803e+01 5.109110263615562e-05 2.702282606280617e-16
5.722367659350220e+01 4.242810110983234e-05 2.445655240740449e-15
6.892612104349709e+01 3.523240116597968e-05 3.302696900260679e-16
8.302175681319753e+01 2.925597188965025e-05 9.050712276340781e-12
1.000000000000000e+02 2.429255623845345e-05 6.242595970465304e-12

102
figs/correlation.fig/2020-08-27+correlation.dat Normal file
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@ -0,0 +1,102 @@
# Potential: 16 e^{-|x|}, rho=0.02
# |x| 2-pt correlation
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3.48119163 1.00058535 0.00016426 1.00058535 0.00016426 0.00000000 0.00000000 0.00000000 0.00000000
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3.94535051 1.06104242 0.00015316 1.06104242 0.00015316 0.00000000 0.00000000 0.00000000 0.00000000
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4.40950939 1.05993711 0.00014682 1.05993711 0.00014682 0.00000000 0.00000000 0.00000000 0.00000000
4.50234117 1.05561851 0.00014625 1.05561851 0.00014625 0.00000000 0.00000000 0.00000000 0.00000000
4.59517295 1.05060642 0.00013572 1.05060642 0.00013572 0.00000000 0.00000000 0.00000000 0.00000000
4.68800472 1.04534502 0.00013193 1.04534502 0.00013193 0.00000000 0.00000000 0.00000000 0.00000000
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6.45180848 0.98948384 0.00009719 0.98948384 0.00009719 0.00000000 0.00000000 0.00000000 0.00000000
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6.91596736 0.99305844 0.00008686 0.99305844 0.00008686 0.00000000 0.00000000 0.00000000 0.00000000
7.00879914 0.99402451 0.00008778 0.99402451 0.00008778 0.00000000 0.00000000 0.00000000 0.00000000
7.10163092 0.99501487 0.00008386 0.99501487 0.00008386 0.00000000 0.00000000 0.00000000 0.00000000
7.19446269 0.99598405 0.00007919 0.99598405 0.00007919 0.00000000 0.00000000 0.00000000 0.00000000
7.28729447 0.99683782 0.00008214 0.99683782 0.00008214 0.00000000 0.00000000 0.00000000 0.00000000
7.38012625 0.99779938 0.00007994 0.99779938 0.00007994 0.00000000 0.00000000 0.00000000 0.00000000
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7.56578980 0.99930080 0.00008203 0.99930080 0.00008203 0.00000000 0.00000000 0.00000000 0.00000000
7.65862158 1.00001485 0.00008598 1.00001485 0.00008598 0.00000000 0.00000000 0.00000000 0.00000000
7.75145335 1.00049762 0.00008693 1.00049762 0.00008693 0.00000000 0.00000000 0.00000000 0.00000000
7.84428513 1.00095153 0.00008531 1.00095153 0.00008531 0.00000000 0.00000000 0.00000000 0.00000000
7.93711691 1.00133388 0.00008126 1.00133388 0.00008126 0.00000000 0.00000000 0.00000000 0.00000000
8.02994868 1.00152882 0.00007855 1.00152882 0.00007855 0.00000000 0.00000000 0.00000000 0.00000000
8.12278046 1.00163599 0.00007736 1.00163599 0.00007736 0.00000000 0.00000000 0.00000000 0.00000000
8.21561224 1.00175148 0.00007549 1.00175148 0.00007549 0.00000000 0.00000000 0.00000000 0.00000000
8.30844401 1.00172584 0.00007298 1.00172584 0.00007298 0.00000000 0.00000000 0.00000000 0.00000000
8.40127579 1.00175558 0.00007456 1.00175558 0.00007456 0.00000000 0.00000000 0.00000000 0.00000000
8.49410757 1.00175353 0.00007550 1.00175353 0.00007550 0.00000000 0.00000000 0.00000000 0.00000000
8.58693934 1.00167392 0.00007070 1.00167392 0.00007070 0.00000000 0.00000000 0.00000000 0.00000000
8.67977112 1.00158009 0.00006882 1.00158009 0.00006882 0.00000000 0.00000000 0.00000000 0.00000000
8.77260290 1.00144512 0.00006669 1.00144512 0.00006669 0.00000000 0.00000000 0.00000000 0.00000000
8.86543467 1.00130747 0.00006420 1.00130747 0.00006420 0.00000000 0.00000000 0.00000000 0.00000000
8.95826645 1.00117137 0.00006419 1.00117137 0.00006419 0.00000000 0.00000000 0.00000000 0.00000000
9.05109823 1.00109365 0.00006530 1.00109365 0.00006530 0.00000000 0.00000000 0.00000000 0.00000000
9.14393000 1.00094515 0.00006273 1.00094515 0.00006273 0.00000000 0.00000000 0.00000000 0.00000000
9.23676178 1.00076430 0.00006358 1.00076430 0.00006358 0.00000000 0.00000000 0.00000000 0.00000000

36
figs/correlation.fig/Makefile Normal file
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@ -0,0 +1,36 @@
PROJECTNAME=correlation
SIMPLESOLV=~/Work/Research/2018+bose_gas/cmp/simplesolv/source/src
DATS=bigeq.dat medeq.dat simpleq.dat
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME))
all: $(PDFS)
$(PDFS): $(DATS)
gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@)
pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
simpleq.dat:
julia $(SIMPLESOLV)/main.jl -p "rho=2e-2;minlrho_init=-6;nlrho_init=60;v_a=16;N=12;P=8;J=10;tolerance=1e-11;maxiter=21;xmin=0;nx=100;xmax=10" -M simpleq-Kv -U exp 2pt > $@
medeq.dat:
julia $(SIMPLESOLV)/main.jl -p "rho=2e-2;minlrho_init=-6;nlrho_init=60;v_a=16;eq=medeq;N=12;P=8;J=10;tolerance=1e-11;maxiter=21;xmin=0;nx=100;xmax=10" -M anyeq -U exp 2pt > $@
bigeq.dat:
julia $(SIMPLESOLV)/main.jl -p "rho=2e-2;minlrho_init=-6;nlrho_init=60;v_a=16;eq=bigeq;N=12;P=8;J=10;tolerance=1e-11;maxiter=21;xmin=0;nx=100;xmax=10" -M anyeq -U exp 2pt > $@
install: $(PDFS)
cp $^ $(INSTALLDIR)/
clean-aux:
rm -f $(addsuffix .tikz.tex, $(PROJECTNAME))
rm -f $(addsuffix .aux, $(PROJECTNAME))
rm -f $(addsuffix .log, $(PROJECTNAME))
clean-dat:
rm -f $(DATS)
clean-tex:
rm -f $(PDFS)
clean: clean-aux clean-tex

100
figs/correlation.fig/bigeq.dat Normal file
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@ -0,0 +1,100 @@
1.000000000000000e-01 2.815645668703404e-07
2.000000000000000e-01 3.771201995017570e-07
3.000000000000000e-01 5.573083439994964e-07
4.000000000000000e-01 8.556251627958034e-07
5.000000000000000e-01 1.320674217324758e-06
6.000000000000000e-01 2.018694725059689e-06
7.000000000000000e-01 3.035072077005863e-06
8.000000000000000e-01 4.474473100824739e-06
9.000000000000000e-01 6.463169864770135e-06
1.000000000000000e+00 9.145824377893419e-06
1.100000000000000e+00 1.268065874031561e-05
1.200000000000000e+00 1.723697883125914e-05
1.300000000000000e+00 2.298641995034885e-05
1.400000000000000e+00 3.009340795508391e-05
1.500000000000000e+00 3.870378505052217e-05
1.600000000000000e+00 4.893439939736397e-05
1.700000000000000e+00 6.086815836828259e-05
1.800000000000000e+00 7.454040323990952e-05
1.900000000000000e+00 8.992947608336822e-05
2.000000000000000e+00 1.069578478121016e-04
2.100000000000000e+00 1.254917813401447e-04
2.200000000000000e+00 1.453456861558196e-04
2.300000000000000e+00 1.662829558495016e-04
2.400000000000000e+00 1.880235498245581e-04
2.500000000000000e+00 2.102631019307806e-04
2.600000000000000e+00 2.326800099021663e-04
2.700000000000000e+00 2.549475411844160e-04
2.800000000000000e+00 2.767498310631324e-04
2.900000000000000e+00 2.977891460952948e-04
3.000000000000000e+00 3.177970059564316e-04
3.100000000000000e+00 3.365398251332887e-04
3.200000000000000e+00 3.538276894692456e-04
3.300000000000000e+00 3.695227606507144e-04
3.400000000000000e+00 3.835298625242662e-04
3.500000000000000e+00 3.957945216412487e-04
3.600000000000000e+00 4.063058424765387e-04
3.700000000000000e+00 4.150938073101305e-04
3.800000000000000e+00 4.222258495380544e-04
3.900000000000000e+00 4.277930177177151e-04
4.000000000000000e+00 4.319051405003001e-04
4.100000000000000e+00 4.346916273515270e-04
4.200000000000000e+00 4.362910698562371e-04
4.300000000000000e+00 4.368483889522392e-04
4.400000000000000e+00 4.365117022300800e-04
4.500000000000000e+00 4.354257230678466e-04
4.600000000000000e+00 4.337293215931519e-04
4.700000000000000e+00 4.315499980775908e-04
4.800000000000000e+00 4.290065333365035e-04
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5.000000000000000e+00 4.232612058969635e-04
5.100000000000000e+00 4.202417151371156e-04
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5.300000000000000e+00 4.142752266215253e-04
5.400000000000000e+00 4.114454301530826e-04
5.500000000000000e+00 4.087764640179003e-04
5.600000000000000e+00 4.062986163033597e-04
5.700000000000000e+00 4.040357632119026e-04
5.800000000000000e+00 4.020023512522621e-04
5.900000000000000e+00 4.002058609762183e-04
6.000000000000000e+00 3.986479410743549e-04
6.100000000000000e+00 3.973258486571445e-04
6.200000000000000e+00 3.962343351128094e-04
6.300000000000000e+00 3.953634402182200e-04
6.400000000000000e+00 3.947016475514070e-04
6.500000000000000e+00 3.942361349633637e-04
6.600000000000000e+00 3.939489438152859e-04
6.700000000000000e+00 3.938195472796021e-04
6.800000000000000e+00 3.938271252610278e-04
6.900000000000000e+00 3.939535337225030e-04
7.000000000000000e+00 3.941830350799711e-04
7.100000000000000e+00 3.944975316993734e-04
7.200000000000000e+00 3.948795394336185e-04
7.300000000000000e+00 3.953138211780876e-04
7.400000000000000e+00 3.957855128554423e-04
7.500000000000000e+00 3.962812697100951e-04
7.600000000000000e+00 3.967881536726375e-04
7.700000000000000e+00 3.972944903641516e-04
7.800000000000000e+00 3.977901679291229e-04
7.900000000000000e+00 3.982652029650100e-04
8.000000000000000e+00 3.987132916951087e-04
8.100000000000000e+00 3.991310569263629e-04
8.199999999999999e+00 3.995148186075982e-04
8.300000000000001e+00 3.998610349357616e-04
8.400000000000000e+00 4.001663085173719e-04
8.500000000000000e+00 4.004299880400858e-04
8.600000000000000e+00 4.006532574836569e-04
8.699999999999999e+00 4.008360199803870e-04
8.800000000000001e+00 4.009797694514636e-04
8.900000000000000e+00 4.010873950339037e-04
9.000000000000000e+00 4.011614782779821e-04
9.100000000000000e+00 4.012045847492319e-04
9.199999999999999e+00 4.012185293630343e-04
9.300000000000001e+00 4.012064074730058e-04
9.400000000000000e+00 4.011720950022673e-04
9.500000000000000e+00 4.011186205709775e-04
9.600000000000000e+00 4.010502350510486e-04
9.699999999999999e+00 4.009708050953865e-04
9.800000000000001e+00 4.008825998897835e-04
9.900000000000000e+00 4.007873038383584e-04
1.000000000000000e+01 4.006865033429884e-04

28
figs/correlation.fig/correlation.gnuplot Normal file
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@ -0,0 +1,28 @@
set title ""
set ylabel "$\\frac{\\tilde C_2}{\\rho^2}$" norotate offset -1,0
set xlabel "$|\\mathbf x|$"
# default output canvas size: 12.5cm x 8.75cm
set term lua tikz size 8,6 standalone
set key bottom right box linetype rgbcolor"#999999" width 0.3 height 0.3 spacing 1.3
# set linestyle
set style line 1 linetype rgbcolor "#4169E1" linewidth 2 dashtype "."
set style line 2 linetype rgbcolor "#DC143C" linewidth 1
set style line 3 linetype rgbcolor "#32CD32" linewidth 2 dashtype "-"
set style line 4 linetype rgbcolor "#4B0082" linewidth 2
set style line 5 linetype rgbcolor "#DAA520" linewidth 2
set style line 6 linetype rgbcolor "#555500" linewidth 2
set pointsize 0.5
rho=2e-2
plot \
"simpleq.dat" using 1:($2/rho**2) with lines ls 1 title "simple",\
"medeq.dat" using 1:($2/rho**2) with lines ls 3 title "med",\
"bigeq.dat" using 1:($2/rho**2) with lines ls 5 title "big",\
"2020-08-27+correlation.dat" using 1:2 ls 2 title "QMC"

100
figs/correlation.fig/medeq.dat Normal file
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@ -0,0 +1,100 @@
1.000000000000000e-01 2.409497558083658e-05
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3.000000000000000e-01 2.803118585850437e-05
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1.200000000000000e+00 8.719953260639284e-05
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1.400000000000000e+00 1.102770859953400e-04
1.500000000000000e+00 1.230991240794582e-04
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1.700000000000000e+00 1.509169722024169e-04
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9.900000000000000e+00 4.002407173561036e-04
1.000000000000000e+01 4.002468273509336e-04

100
figs/correlation.fig/simpleq.dat Normal file
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@ -0,0 +1,100 @@
1.000000000000000e-01 1.605737780249551e-04
2.000000000000000e-01 1.646572439544047e-04
3.000000000000000e-01 1.704080757058912e-04
4.000000000000000e-01 1.773557851093461e-04
5.000000000000000e-01 1.851044224101348e-04
6.000000000000000e-01 1.934631179487515e-04
7.000000000000000e-01 2.022815783256444e-04
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1.000000000000000e+00 2.299100922022419e-04
1.100000000000000e+00 2.392010687597398e-04
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1.300000000000000e+00 2.574627216447642e-04
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1.600000000000000e+00 2.833194447156991e-04
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15
figs/energy.fig/2020-10-15+energy.dat Normal file
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@ -0,0 +1,15 @@
# Potential: e^{-|x|}
# rho E E+dE eta eta+deta Jastrow E Jastrow E+dE Jastrow eta Jastrow eta+deta
1e-6 7.90e-6 7.91e-6
1e-4 8.344e-4 8.345e-4 0.017 0.018 8.355e-4 8.356e-4 0.015 0.016
1e-3 9.1338e-3 9.1339e-3 0.048 0.049 9.142e-3 9.143e-3 0.045 0.046
5e-3 5.0613e-2 5.0614e-2 0.080 0.081 5.0648e-2 5.0649e-2 0.070 0.071
1e-2 1.06107e-1 1.06108e-1 0.087 0.088 1.0627e-1 1.0628e-1 0.073 0.074
1.5e-2 1.6337e-1 1.6338e-1 0.090 0.091 1.6342e-1 1.6343e-1 0.088 0.089
2e-2 2.2162e-1 2.2163e-1 0.093 0.094 2.2169e-1 2.2170e-1 0.090 0.091
5e-2 5.8044e-1 5.8045e-1 0.091 0.092 5.8046e-1 5.8047e-1 0.091 0.092
1e-1 1.1918e+0 1.1919e+0 0.088 0.089 1.1919e+0 1.1920e+0 0.085 0.086
1e-0 1.2430e+1 1.2431e+1 0.058 0.059 1.245e+1 1.246e+1 0.05 0.06
1e+1 1.2544e+2 1.2545e+2 0.031 0.032
5e+1 6.2803e+2 6.2804e+2 0.02 0.03

37
figs/energy.fig/Makefile Normal file
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@ -0,0 +1,37 @@
PROJECTNAME=energy
SIMPLESOLV=~/Work/Research/2018+bose_gas/cmp/simplesolv/source/src
DATS=simpleq.dat medeq.dat bigeq.dat
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME))
all: $(PDFS)
$(PDFS): $(DATS)
gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@)
pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
simpleq.dat:
julia $(SIMPLESOLV)/main.jl -p "eq=simpleq;tolerance=1e-11;order=100;maxiter=100;v_a=1;minlrho=-6;nlrho=100;maxlrho=2" -M easyeq -U exp energy_rho > $@
medeq.dat:
julia $(SIMPLESOLV)/main.jl -p "eq=medeq;tolerance=1e-11;order=100;maxiter=100;v_a=1;minlrho=-6;nlrho=100;maxlrho=2" -M easyeq -U exp energy_rho > $@
bigeq.dat:
julia -p 8 $(SIMPLESOLV)/main.jl -p "eq=bigeq;N=12;P=8;J=10;tolerance=1e-11;maxiter=21;v_a=1;minlrho=-6;nlrho=100;maxlrho=2" -M anyeq -U exp energy_rho > $@
install: $(PDFS)
cp $^ $(INSTALLDIR)/
clean-aux:
rm -f $(addsuffix .tikz.tex, $(PROJECTNAME))
rm -f $(addsuffix .aux, $(PROJECTNAME))
rm -f $(addsuffix .log, $(PROJECTNAME))
clean-dat:
rm -f $(DATS)
clean-tex:
rm -f $(PDFS)
clean: clean-aux clean-tex

100
figs/energy.fig/bigeq.dat Normal file
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@ -0,0 +1,100 @@
1.000000000000000e-06 7.933345669932108e-06 1.704968357654747e-12
1.204503540258781e-06 9.561695772478549e-06 3.479042916950106e-13
1.450828778495940e-06 1.152494614052415e-05 1.105615828881523e-13
1.747528400007683e-06 1.389218915189634e-05 6.516057629638973e-13
2.104904144512022e-06 1.674683575161553e-05 2.538927058524327e-13
2.535364493970111e-06 2.018960215367572e-05 1.880964786680250e-14
3.053855508833412e-06 2.434212593011697e-05 2.973660811899432e-14
3.678379771828634e-06 2.935134616878758e-05 2.601027107910687e-14
4.430621457583877e-06 3.539481155461295e-05 2.963343053481389e-13
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1.072267222010325e+01 1.345266139156320e+02 2.426172104464820e-13
1.291549665014885e+01 1.620761041088648e+02 1.855737958789898e-13
1.555676143930475e+01 1.952609146057077e+02 1.407488425834523e-13
1.873817422860387e+01 2.352334832362353e+02 1.059912258811251e-13
2.257019719633922e+01 2.833819239247995e+02 7.975496994680734e-14
2.718588242732946e+01 3.413782233614627e+02 5.927022309304956e-14
3.274549162877732e+01 4.112362940653811e+02 4.383487153196387e-14
3.944206059437664e+01 4.953818995066683e+02 3.264119493319829e-14
4.750810162102803e+01 5.967368791641958e+02 2.438476380986774e-14
5.722367659350220e+01 7.188205979063790e+02 1.780368664039960e-14
6.892612104349709e+01 8.658721421294766e+02 1.399123723605710e-14
8.302175681319753e+01 1.042997505438325e+03 1.067384124266308e-14
1.000000000000000e+02 1.256346874319010e+03 8.538692087201394e-15

41
figs/energy.fig/energy.gnuplot Normal file
View File

@ -0,0 +1,41 @@
set title ""
set ylabel "$\\displaystyle\\frac{\\tilde e}{\\rho}$" norotate offset -1,0
set xlabel "$\\rho$"
set xtics 1e-6, 100, 100
set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0, "$10^2$" 100)
unset mxtics
set xrange [0.000001:100]
set ytics 8, 1, 13
set mytics 2
set yrange [7.5:13]
# default output canvas size: 12.5cm x 8.75cm
set term lua tikz size 8,6 standalone
set key bottom right box linetype rgbcolor"#999999" width 0.3 height 0.3 spacing 1.3
# set linestyle
set style line 1 linetype rgbcolor "#4169E1" linewidth 2 dashtype "."
set style line 2 linetype rgbcolor "#DC143C" linewidth 2
set style line 3 linetype rgbcolor "#32CD32" linewidth 2 dashtype "-"
set style line 4 linetype rgbcolor "#4B0082" linewidth 2
set style line 5 linetype rgbcolor "#DAA520" linewidth 2
set style line 6 linetype rgbcolor "#999999" linewidth 1.5 dashtype (1,5)
set pointsize 1
set logscale x
a=1.2543564105910647
plot \
"simpleq.dat" using 1:($3<1e-5 ? ($2/$1) : 1/0) with lines ls 1 title "simple" ,\
"medeq.dat" using 1:($3<1e-5 ? ($2/$1) : 1/0) with lines ls 3 title "med",\
"bigeq.dat" using 1:($3<1e-5 ? ($2/$1) : 1/0) with lines ls 5 title "big",\
"2020-10-15+energy.dat" using 1:($2/$1) with points ls 2 title "QMC" ,\
2*pi*a*(1+128./(15*sqrt(pi))*sqrt(x*a**3)) ls 6 title "LHY"

100
figs/energy.fig/medeq.dat Normal file
View File

@ -0,0 +1,100 @@
1.000000000000000e-06 7.934286257047021e-06 3.350843411796514e-14
1.204503540258781e-06 9.563044082528665e-06 2.273624432538743e-14
1.450828778495940e-06 1.152686262633478e-05 1.298430519766377e-14
1.747528400007683e-06 1.389489317614862e-05 1.894777566363843e-14
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1.000000000000000e+02 1.256345425056825e+03 2.310603796838004e-14

100
figs/energy.fig/simpleq.dat Normal file
View File

@ -0,0 +1,100 @@
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3.274549162877732e+01 4.114552381359539e+02 1.315017988355486e-14
3.944206059437664e+01 4.956068009543682e+02 1.004394652722235e-14
4.750810162102803e+01 5.969676580241880e+02 5.364915392605858e-14
5.722367659350220e+01 7.190571706518009e+02 5.378285825138610e-14
6.892612104349709e+01 8.661144220395618e+02 5.426311368936924e-14
8.302175681319753e+01 1.043245402953268e+03 9.067219514460403e-12
1.000000000000000e+02 1.256600297381089e+03 6.252162647544124e-12

673
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%%
%% Ian's class file
%%
%% TeX format
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
%% class name
\ProvidesClass{ian}[2017/09/29]
%% boolean to signal that this class is being used
\newif\ifianclass
%% options
% no section numbering in equations
\DeclareOption{section_in_eq}{\sectionsineqtrue}
\DeclareOption{section_in_fig}{\sectionsinfigtrue}
\DeclareOption{section_in_theo}{\PassOptionsToPackage{\CurrentOption}{iantheo}}
\DeclareOption{section_in_all}{\sectionsineqtrue\sectionsinfigtrue\PassOptionsToPackage{section_in_theo}{iantheo}}
\DeclareOption{subsection_in_eq}{\subsectionsineqtrue}
\DeclareOption{subsection_in_fig}{\subsectionsinfigtrue}
\DeclareOption{subsection_in_theo}{\PassOptionsToPackage{\CurrentOption}{iantheo}}
\DeclareOption{subsection_in_all}{\subsectionsineqtrue\subsectionsinfigtrue\PassOptionsToPackage{subsection_in_theo}{iantheo}}
\DeclareOption{no_section_in_eq}{\sectionsineqfalse}
\DeclareOption{no_section_in_fig}{\sectionsinfigfalse}
\DeclareOption{no_section_in_theo}{\PassOptionsToPackage{\CurrentOption}{iantheo}}
\DeclareOption{no_section_in_all}{\sectionsineqfalse\sectionsinfigfalse\PassOptionsToPackage{no_section_in_theo}{iantheo}}
\DeclareOption{no_subsection_in_eq}{\subsectionsineqfalse}
\DeclareOption{no_subsection_in_fig}{\subsectionsinfigfalse}
\DeclareOption{no_subsection_in_theo}{\PassOptionsToPackage{\CurrentOption}{iantheo}}
\DeclareOption{no_subsection_in_all}{\subsectionsineqfalse\subsectionsinfigfalse\PassOptionsToPackage{no_subsection_in_theo}{iantheo}}
% reset point
\DeclareOption{point_reset_at_section}{\PassOptionsToPackage{reset_at_section}{point}}
\DeclareOption{point_no_reset_at_section}{\PassOptionsToPackage{no_reset_at_section}{point}}
\DeclareOption{point_reset_at_theo}{\PassOptionsToPackage{reset_at_theo}{point}}
\DeclareOption{point_no_reset_at_theo}{\PassOptionsToPackage{no_reset_at_theo}{point}}
\def\ian@defaultoptions{
\ExecuteOptions{section_in_all, no_subsection_in_all}
\ProcessOptions
%% required packages
\RequirePackage{iantheo}
\RequirePackage{point}
\RequirePackage{color}
\RequirePackage{marginnote}
\RequirePackage{amssymb}
\PassOptionsToPackage{hidelinks}{hyperref}
\RequirePackage{hyperref}
\pagestyle{plain}
}
%% paper dimensions
\setlength\paperheight{297mm}
\setlength\paperwidth{210mm}
%% 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
\hoffset=-50pt
\voffset=-72pt
\textwidth=460pt
\textheight=704pt
%% remove default indentation
\parindent=0pt
%% indent command
\def\indent{\hskip20pt}
%% something is wrong with \thepage, redefine it
\gdef\thepage{\the\c@page}
%% array lines (to use the array environment)
\setlength\arraycolsep{5\p@}
\setlength\arrayrulewidth{.4\p@}
%% correct vertical alignment at the end of a document
\AtEndDocument{
\vfill
\eject
}
%% 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%
}
%% define a label for the latest tag
%% label defines a command containing the string stored in \tag
\def\deflabel{
\def\label##1{\expandafter\outdef{label@##1}{\safe\tag}}
\def\ref##1{%
% check whether the label is defined (hyperlink runs into errors if this check is omitted)
\ifcsname label@##1@hl\endcsname%
\hyperlink{ln.\csname label@##1@hl\endcsname}{{\color{blue}\safe\csname label@##1\endcsname}}%
\else%
\ifcsname label@##1\endcsname%
{\color{blue}\csname ##1\endcsname}%
\else%
{\bf ??}%
\fi%
\fi%
}
}
%% make a custom link at any given location in the document
\def\makelink#1#2{%
\hrefanchor%
\outdef{label@#1}{#2}%
}
%% section command
% counter
\newcounter{sectioncount}
% space before section
\newlength\secskip
\setlength\secskip{40pt}
% a prefix to put before the section number, e.g. A for appendices
\def\sectionprefix{}
% define some lengths
\newlength\secnumwidth
\newlength\sectitlewidth
\def\section#1{
% reset counters
\stepcounter{sectioncount}
\setcounter{subsectioncount}{0}
\ifsectionsineq
\setcounter{seqcount}0
\fi
\ifsectionsinfig
\setcounter{figcount}0
\fi
% space before section (if not first)
\ifnum\thesectioncount>1
\vskip\secskip
\penalty-1000
\fi
% hyperref anchor
\hrefanchor
% define tag (for \label)
\xdef\tag{\sectionprefix\thesectioncount}
% get widths
\def\@secnum{{\bf\Large\sectionprefix\thesectioncount.\hskip10pt}}
\settowidth\secnumwidth{\@secnum}
\setlength\sectitlewidth\textwidth
\addtolength\sectitlewidth{-\secnumwidth}
% print name
\parbox{\textwidth}{
\@secnum
\parbox[t]{\sectitlewidth}{\Large\bf #1}}
% write to table of contents
\iftoc
% save lncount in aux variable which is written to toc
\immediate\write\tocoutput{\noexpand\expandafter\noexpand\edef\noexpand\csname toc@sec.\thesectioncount\endcsname{\thelncount}}
\write\tocoutput{\noexpand\tocsection{#1}{\thepage}}
\fi
%space
\par\penalty10000
\bigskip\penalty10000
}
%% subsection
% counter
\newcounter{subsectioncount}
% space before subsection
\newlength\subsecskip
\setlength\subsecskip{30pt}
\def\subsection#1{
% counters
\stepcounter{subsectioncount}
\setcounter{subsubsectioncount}{0}
\ifsubsectionsineq
\setcounter{seqcount}0
\fi
\ifsubsectionsinfig
\setcounter{figcount}0
\fi
% space before subsection (if not first)
\ifnum\thesubsectioncount>1
\vskip\subsecskip
\penalty-500
\fi
% hyperref anchor
\hrefanchor
% define tag (for \label)
\xdef\tag{\sectionprefix\thesectioncount.\thesubsectioncount}
% get widths
\def\@secnum{{\bf\large\hskip.5cm\sectionprefix\thesectioncount.\thesubsectioncount.\hskip5pt}}
\settowidth\secnumwidth{\@secnum}
\setlength\sectitlewidth\textwidth
\addtolength\sectitlewidth{-\secnumwidth}
% print name
\parbox{\textwidth}{
\@secnum
\parbox[t]{\sectitlewidth}{\large\bf #1}}
% write to table of contents
\iftoc
% save lncount in aux variable which is written to toc
\immediate\write\tocoutput{\noexpand\expandafter\noexpand\edef\noexpand\csname toc@subsec.\thesectioncount.\thesubsectioncount\endcsname{\thelncount}}
\write\tocoutput{\noexpand\tocsubsection{#1}{\thepage}}
\fi
% space
\par\penalty10000
\medskip\penalty10000
}
%% subsubsection
% counter
\newcounter{subsubsectioncount}
% space before subsubsection
\newlength\subsubsecskip
\setlength\subsubsecskip{20pt}
\def\subsubsection#1{
% counters
\stepcounter{subsubsectioncount}
% space before subsubsection (if not first)
\ifnum\thesubsubsectioncount>1
\vskip\subsubsecskip
\penalty-500
\fi
% hyperref anchor
\hrefanchor
% define tag (for \label)
\xdef\tag{\sectionprefix\thesectioncount.\thesubsectioncount.\thesubsubsectioncount}
% get widths
\def\@secnum{{\bf\hskip1.cm\sectionprefix\thesectioncount.\thesubsectioncount.\thesubsubsectioncount.\hskip5pt}}
\settowidth\secnumwidth{\@secnum}
\setlength\sectitlewidth\textwidth
\addtolength\sectitlewidth{-\secnumwidth}
% print name
\parbox{\textwidth}{
\@secnum
\parbox[t]{\sectitlewidth}{\large\bf #1}}
% write to table of contents
\iftoc
% save lncount in aux variable which is written to toc
\immediate\write\tocoutput{\noexpand\expandafter\noexpand\edef\noexpand\csname toc@subsubsec.\thesectioncount.\thesubsectioncount.\thesubsubsectioncount\endcsname{\thelncount}}
\write\tocoutput{\noexpand\tocsubsubsection{#1}{\thepage}}
\fi
% space
\par\penalty10000
\medskip\penalty10000
}
%% 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
\newcount\itemizepenalty
\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\expandafter\penalty\the\itemizepenalty\medskip\expandafter\penalty\the\itemizepenalty%
\addtocounter{itemizecount}{1}%
\addtolength\current@itemizeskip{\itemizeskip}%
\leftskip\current@itemizeskip%
}
\def\enditemize{%
\addtocounter{itemizecount}{-1}%
\addtolength\current@itemizeskip{-\itemizeskip}%
\par\expandafter\penalty\the\itemizepenalty\leftskip\current@itemizeskip%
\medskip\expandafter\penalty\the\itemizepenalty%
}
% item, with optional argument to specify the item point
% @itemarg is set to true when there is an optional argument
\newif\if@itemarg
\def\item{%
% check whether there is an optional argument (if there is none, add on empty '[]')
\@ifnextchar [{\@itemargtrue\@itemx}{\@itemargfalse\@itemx[]}%
}
\newlength\itempt@total
\def\@itemx[#1]{
\if@itemarg
\settowidth\itempt@total{#1}
\else
\settowidth\itempt@total{\itemizept\theitemizecount}
\fi
\addtolength\itempt@total{\itemizeseparator}
\par
\medskip
\if@itemarg
\hskip-\itempt@total#1\hskip\itemizeseparator
\else
\hskip-\itempt@total\itemizept\theitemizecount\hskip\itemizeseparator
\fi
}
%% prevent page breaks after itemize
\newcount\previtemizepenalty
\def\nopagebreakafteritemize{
\previtemizepenalty=\itemizepenalty
\itemizepenalty=10000
}
%% back to previous value
\def\restorepagebreakafteritemize{
\itemizepenalty=\previtemizepenalty
}
%% 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
}
%% equation numbering
% counter
\newcounter{seqcount}
% booleans (write section or subsection in equation number)
\newif\ifsectionsineq
\newif\ifsubsectionsineq
\def\seqcount{
\stepcounter{seqcount}
% the output
\edef\seqformat{\theseqcount}
% add subsection number
\ifsubsectionsineq
\let\tmp\seqformat
\edef\seqformat{\thesubsectioncount.\tmp}
\fi
% add section number
\ifsectionsineq
\let\tmp\seqformat
\edef\seqformat{\sectionprefix\thesectioncount.\tmp}
\fi
% define tag (for \label)
\xdef\tag{\seqformat}
% write number
\marginnote{\hfill(\seqformat)}
}
%% equation environment compatibility
\def\equation{\hrefanchor$$\seqcount}
\def\endequation{$$\@ignoretrue}
%% figures
% counter
\newcounter{figcount}
% booleans (write section or subsection in equation number)
\newif\ifsectionsinfig
\newif\ifsubsectionsinfig
% width of figures
\newlength\figwidth
\setlength\figwidth\textwidth
\addtolength\figwidth{-2.5cm}
% caption
\def\defcaption{
\long\def\caption##1{
\stepcounter{figcount}
% hyperref anchor
\hrefanchor
% the number of the figure
\edef\figformat{\thefigcount}
% add subsection number
\ifsubsectionsinfig
\let\tmp\figformat
\edef\figformat{\thesubsectioncount.\tmp}
\fi
% add section number
\ifsectionsinfig
\let\tmp\figformat
\edef\figformat{\sectionprefix\thesectioncount.\tmp}
\fi
% define tag (for \label)
\xdef\tag{\figformat}
% write
\hfil fig \figformat: \parbox[t]{\figwidth}{\leavevmode\small##1}
% space
\par\bigskip
}
}
%% short caption: centered
\def\captionshort#1{
\stepcounter{figcount}
% hyperref anchor
\hrefanchor
% the number of the figure
\edef\figformat{\thefigcount}
% add section number
\ifsectionsinfig
\let\tmp\figformat
\edef\figformat{\sectionprefix\thesectioncount.\tmp}
\fi
% define tag (for \label)
\xdef\tag{\figformat}
% write
\hfil fig \figformat: {\small#1}
%space
\par\bigskip
}
%% environment
\def\figure{
\par
\vfil\penalty100\vfilneg
\bigskip
}
\def\endfigure{
\par
\bigskip
}
%% start appendices
\def\appendix{
\vfill
\pagebreak
% counter
\setcounter{sectioncount}0
% prefix
\def\sectionprefix{A}
% write
{\bf \LARGE Appendices}\par\penalty10000\bigskip\penalty10000
% add a mention in the table of contents
\iftoc
\immediate\write\tocoutput{\noexpand\tocappendices}\penalty10000
\fi
%% uncomment for new page for each appendix
%\def\seqskip{\vfill\pagebreak}
}
%% bibliography
% size of header
\newlength\bibheader
\def\thebibliography#1{
\hrefanchor
% add a mention in the table of contents
\iftoc
% save lncount in aux variable which is written to toc
\immediate\write\tocoutput{\noexpand\expandafter\noexpand\edef\noexpand\csname toc@references\endcsname{\thelncount}}
\write\tocoutput{\noexpand\tocreferences{\thepage}}\penalty10000
\fi
% write
{\bf \LARGE References}\par\penalty10000\bigskip\penalty10000
% width of header
\settowidth\bibheader{[#1]}
\leftskip\bibheader
}
% end environment
\def\endthebibliography{
\par\leftskip0pt
}
%% bibitem command
\def\bibitem[#1]#2{%
\hrefanchor%
\outdef{label@cite#2}{#1}%
\hskip-\bibheader%
\makebox[\bibheader]{\cite{#2}\hfill}%
}
%% cite command
% @tempswa is set to true when there is an optional argument
\newif\@tempswa
\def\cite{%
% check whether there is an optional argument (if there is none, add on empty '[]')
\@ifnextchar [{\@tempswatrue\@citex}{\@tempswafalse\@citex[]}%
}
% command with optional argument
\def\@citex[#1]#2{\leavevmode%
% initialize loop
\let\@cite@separator\@empty%
% format
\@cite{%
% loop over ',' separated list
\@for\@cite@:=#2\do{%
% text to add at each iteration of the loop (separator between citations)
\@cite@separator\def\@cite@separator{,\ }%
% add entry to citelist
\@writecitation{\@cite@}%
\ref{cite\@cite@}%
}%
}%
% add optional argument text (as an argument to '\@cite')
{#1}%
}
\def\@cite#1#2{%
[#1\if@tempswa , #2\fi]%
}
%% add entry to citelist after checking it has not already been added
\def\@writecitation#1{%
\ifcsname if#1cited\endcsname%
\else%
\expandafter\newif\csname if#1cited\endcsname%
\immediate\write\@auxout{\string\citation{#1}}%
\fi%
}
%% table of contents
% boolean
\newif\iftoc
\def\tableofcontents{
% copy content from file
\IfFileExists{\jobname.toc}{\input{\jobname.toc}}{{\tt error: table of contents missing}}
% open new toc
\newwrite\tocoutput
\immediate\openout\tocoutput=\jobname.toc
\toctrue
}
%% close file
\AtEndDocument{
% close toc
\iftoc
\immediate\closeout\tocoutput
\fi
}
%% fill line with dots
\def\leaderfill{\leaders\hbox to 1em {\hss. \hss}\hfill}
%% same as sectionprefix
\def\tocsectionprefix{}
%% toc formats
\newcounter{tocsectioncount}
\def\tocsection #1#2{
\stepcounter{tocsectioncount}
\setcounter{tocsubsectioncount}{0}
\setcounter{tocsubsubsectioncount}{0}
% write
\smallskip\hyperlink{ln.\csname toc@sec.\thetocsectioncount\endcsname}{{\bf \tocsectionprefix\thetocsectioncount}.\hskip5pt {\color{blue}#1}\leaderfill#2}\par
}
\newcounter{tocsubsectioncount}
\def\tocsubsection #1#2{
\stepcounter{tocsubsectioncount}
\setcounter{tocsubsubsectioncount}{0}
% write
{\hskip10pt\hyperlink{ln.\csname toc@subsec.\thetocsectioncount.\thetocsubsectioncount\endcsname}{{\bf \thetocsubsectioncount}.\hskip5pt {\color{blue}\small #1}\leaderfill#2}}\par
}
\newcounter{tocsubsubsectioncount}
\def\tocsubsubsection #1#2{
\stepcounter{tocsubsubsectioncount}
% write
{\hskip20pt\hyperlink{ln.\csname toc@subsubsec.\thetocsectioncount.\thetocsubsectioncount.\thetocsubsubsectioncount\endcsname}{{\bf \thetocsubsubsectioncount}.\hskip5pt {\color{blue}\small #1}\leaderfill#2}}\par
}
\def\tocappendices{
\medskip
\setcounter{tocsectioncount}0
{\bf Appendices}\par
\smallskip
\def\tocsectionprefix{A}
}
\def\tocreferences#1{
\medskip
{\hyperlink{ln.\csname toc@references\endcsname}{{\color{blue}\bf References}\leaderfill#1}}\par
\smallskip
}
%% definitions that must be loaded at begin document
\let\ian@olddocument\document
\def\document{
\ian@olddocument
\deflabel
\defcaption
}
%% end
\ian@defaultoptions
\endinput

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%%
%% iantheorem package:
%% Ian's customized theorem command
%%
%% boolean to signal that this package was loaded
\newif\ifiantheo
%% TeX format
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
%% package name
\ProvidesPackage{iantheo}[2016/11/10]
%% options
\newif\ifsectionintheo
\DeclareOption{section_in_theo}{\sectionintheotrue}
\DeclareOption{no_section_in_theo}{\sectionintheofalse}
\newif\ifsubsectionintheo
\DeclareOption{subsection_in_theo}{\subsectionintheotrue}
\DeclareOption{no_subsection_in_theo}{\subsectionintheofalse}
\def\iantheo@defaultoptions{
\ExecuteOptions{section_in_theo, no_subsection_in_theo}
\ProcessOptions
%%% reset at every new section
\ifsectionintheo
\let\iantheo@oldsection\section
\gdef\section{\setcounter{theocount}{0}\iantheo@oldsection}
\fi
%% reset at every new subsection
\ifsubsectionintheo
\let\iantheo@oldsubsection\subsection
\gdef\subsection{\setcounter{theocount}{0}\iantheo@oldsubsection}
\fi
}
%% delimiters
\def\delimtitle#1{
\par%
\leavevmode%
\raise.3em\hbox to\hsize{%
\lower0.3em\hbox{\vrule height0.3em}%
\hrulefill%
\ \lower.3em\hbox{#1}\ %
\hrulefill%
\lower0.3em\hbox{\vrule height0.3em}%
}%
\par\penalty10000%
}
%% callable by ref
\def\delimtitleref#1{
\par%
%
\ifdefined\ianclass%
% hyperref anchor%
\hrefanchor%
% define tag (for \label)%
\xdef\tag{#1}%
\fi%
%
\leavevmode%
\raise.3em\hbox to\hsize{%
\lower0.3em\hbox{\vrule height0.3em}%
\hrulefill%
\ \lower.3em\hbox{\bf #1}\ %
\hrulefill%
\lower0.3em\hbox{\vrule height0.3em}%
}%
\par\penalty10000%
}
%% no title
\def\delim{
\par%
\leavevmode\raise.3em\hbox to\hsize{%
\lower0.3em\hbox{\vrule height0.3em}%
\hrulefill%
\lower0.3em\hbox{\vrule height0.3em}%
}%
\par\penalty10000%
}
%% end delim
\def\enddelim{
\par\penalty10000%
\leavevmode%
\raise.3em\hbox to\hsize{%
\vrule height0.3em\hrulefill\vrule height0.3em%
}%
\par%
}
%% theorem
% counter
\newcounter{theocount}
% booleans (write section or subsection in equation number)
\def\theo#1{
\stepcounter{theocount}
\ifdefined\ianclass
% hyperref anchor
\hrefanchor
\fi
% the number
\def\formattheo{\thetheocount}
% add subsection number
\ifsubsectionintheo
\let\tmp\formattheo
\edef\formattheo{\thesubsectioncount.\tmp}
\fi
% add section number
\ifsectionintheo
\let\tmp\formattheo
\edef\formattheo{\sectionprefix\thesectioncount.\tmp}
\fi
% define tag (for \label)
\xdef\tag{\formattheo}
% write
\delimtitle{\bf #1 \formattheo}
}
\let\endtheo\enddelim
%% theorem headers with name
\def\theoname#1#2{
\theo{#1}\hfil({\it #2})\par\penalty10000\medskip%
}
%% qed symbol
\def\qedsymbol{$\square$}
\def\qed{\penalty10000\hfill\penalty10000\qedsymbol}
%% compatibility with article class
\ifdefined\ianclasstrue
\relax
\else
\def\thesectioncount{\thesection}
\def\thesubsectioncount{\thesubsection}
\def\sectionprefix{}
\fi
%% prevent page breaks after displayed equations
\newcount\prevpostdisplaypenalty
\def\nopagebreakaftereq{
\prevpostdisplaypenalty=\postdisplaypenalty
\postdisplaypenalty=10000
}
%% back to previous value
\def\restorepagebreakaftereq{
\postdisplaypenalty=\prevpostdisplaypenalty
}
%% end
\iantheo@defaultoptions
\endinput

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%%
%% Points package:
%% \point commands
%%
%% TeX format
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
%% package name
\ProvidesPackage{point}[2017/06/13]
%% options
\newif\ifresetatsection
\DeclareOption{reset_at_section}{\resetatsectiontrue}
\DeclareOption{no_reset_at_section}{\resetatsectionfalse}
\newif\ifresetatsubsection
\DeclareOption{reset_at_subsection}{\resetatsubsectiontrue}
\DeclareOption{no_reset_at_subsection}{\resetatsubsectionfalse}
\newif\ifresetatsubsubsection
\DeclareOption{reset_at_subsubsection}{\resetatsubsubsectiontrue}
\DeclareOption{no_reset_at_subsubsection}{\resetatsubsubsectionfalse}
\newif\ifresetattheo
\DeclareOption{reset_at_theo}{\resetattheotrue}
\DeclareOption{no_reset_at_theo}{\resetattheofalse}
\def\point@defaultoptions{
\ExecuteOptions{reset_at_section, reset_at_subsection, reset_at_subsubsection, no_reset_at_theo}
\ProcessOptions
%% reset at every new section
\ifresetatsection
\let\point@oldsection\section
\gdef\section{\resetpointcounter\point@oldsection}
\fi
%% reset at every new subsection
\ifresetatsubsection
\let\point@oldsubsection\subsection
\gdef\subsection{\resetpointcounter\point@oldsubsection}
\fi
%% reset at every new subsubsection
\ifresetatsubsubsection
\let\point@oldsubsubsection\subsubsection
\gdef\subsubsection{\resetpointcounter\point@oldsubsubsection}
\fi
%% reset at every new theorem
\ifresetattheo
\ifdefined\iantheotrue
\let\point@oldtheo\theo
\gdef\theo{\resetpointcounter\point@oldtheo}
\fi
\fi
}
%% point
% counter
\newcounter{pointcount}
\def\point{
\stepcounter{pointcount}
\setcounter{subpointcount}{0}
% hyperref anchor (only if the class is 'ian')
\ifdefined\ifianclass
\hrefanchor
% define tag (for \label)
\xdef\tag{\thepointcount}
\fi
% header
\indent{\bf \thepointcount\ - }
}
%% subpoint
% counter
\newcounter{subpointcount}
\def\subpoint{
\stepcounter{subpointcount}
\setcounter{subsubpointcount}0
% hyperref anchor (only if the class is 'ian')
\ifdefined\ifianclass
\hrefanchor
% define tag (for \label)
\xdef\tag{\thepointcount-\thesubpointcount}
\fi
% header
\indent\hskip.5cm{\bf \thepointcount-\thesubpointcount\ - }
}
%% subsubpoint
% counter
\newcounter{subsubpointcount}
\def\subsubpoint{
\stepcounter{subsubpointcount}
% hyperref anchor (only if the class is 'ian')
\ifdefined\ifianclass
\hrefanchor
% define tag (for \label)
\xdef\tag{\thepointcount-\thesubpointcount-\thesubsubpointcount}
\fi
\indent\hskip1cm{\bf \thepointcount-\thesubpointcount-\thesubsubpointcount\ - }
}
%% reset point counters
\def\resetpointcounter{
\setcounter{pointcount}{0}
\setcounter{subpointcount}{0}
\setcounter{subsubpointcount}{0}
}
%% end
\point@defaultoptions
\endinput