Initial commit

This commit is contained in:
Ian Jauslin 2023-07-24 21:33:32 -05:00
commit dfaad7aaee
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Jauslin_2023c.tex Normal file

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53
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

44
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
color
etoolbox
graphics
hyperref
latex
marginnote
pgf
standalone
xcolor
gnuplot
GNU make
* Files:
Jauslin_2023c.tex:
main LaTeX file
libs:
custom LaTeX class file
figs:
source code for the figures

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\bibitem[AEe95]{AEe95}M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, E.A. Cornell - {\it Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor}, Science, volume\-~269, issue\-~5221, pages\-~198-201, 1995,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1126/science.269.5221.198}{10.1126/science.269.5221.198}}.\par\medskip
\bibitem[BCS21]{BCS21}G. Basti, S. Cenatiempo, B. Schlein - {\it A new second-order upper bound for the ground state energy of dilute Bose gases}, Forum of Mathematics, Sigma, volume\-~9, number e74, 2021,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1017/fms.2021.66}{10.1017/fms.2021.66}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/2101.06222}{2101.06222}}.\par\medskip
\bibitem[Bo47]{Bo47}N. Bogolubov - {\it On the theory of superfluidity}, Journal of Physics (USSR), volume\-~11, number\-~1, pages\-~23-32 (translated from the Russian Izv.Akad.Nauk Ser.Fiz, volume\-~11, pages\-~77-90), 1947.\par\medskip
\bibitem[Bo24]{Bo24}S.N. Bose - {\it Plancks Gesetz und Lichtquantenhypothese}, Weitschrift f\"ur Physik, volume\-~26, issue\-~1, pages\-~178-181, 1924,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/BF01327326}{10.1007/BF01327326}}.\par\medskip
\bibitem[CHe21]{CHe21}E.A. Carlen, M. Holzmann, I. Jauslin, E.H. Lieb - {\it Simplified approach to the repulsive Bose gas from low to high densities and its numerical accuracy}, Physical Review A, volume\-~103, issue\-~5, number\-~053309, 2021,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRevA.103.053309}{10.1103/PhysRevA.103.053309}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/2011.10869}{2011.10869}}.\par\medskip
\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[DMe95]{DMe95}K.B. Davis, M.O. Mewes, M.R. Andrews, N.J. van Druten, D.S. Durfee, D.M. Kurn, W. Ketterle - {\it Bose-Einstein Condensation in a Gas of Sodium Atoms}, Physical Review Letters, volume\-~75, issue\-~22, pages\-~3969-3973, 1995,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRevLett.75.3969}{10.1103/PhysRevLett.75.3969}}.\par\medskip
\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[FS23]{FS23}S. Fournais, J.P. Solovej - {\it The energy of dilute Bose gases II: the general case}, Inventiones mathematicae, volume\-~232, issue\-~2, pages\-~863-994, 2023,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/s00222-022-01175-0}{10.1007/s00222-022-01175-0}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/2108.12022}{2108.12022}}.\par\medskip
\bibitem[Ga99]{Ga99}G. Gallavotti - {\it Statistical mechanics, a short treatise}, Springer, 1999.\par\medskip
\bibitem[Ja22]{Ja22}I. Jauslin - {\it Review of a Simplified Approach to study the Bose gas at all densities}, The Physics and Mathematics of Elliott Lieb, The\-~90th Anniversary Volume I, chapter\-~25, pages\-~609-635, ed. Rupert L. Frank, Ari Laptev, Mathieu Lewin, Robert Seiringer, EMS Press, 2022,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.4171/90-1/25}{10.4171/90-1/25}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/2202.07637}{2202.07637}}.\par\medskip
\bibitem[Ja23]{Ja23b}I.\-~Jauslin - {\it Evidence of a liquid phase in interacting Bosons at intermediate densities}, 2023,\par\penalty10000
arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/2302.13449}{2302.13449}}.\par\medskip
\bibitem[Ja23b]{Ja23}I.\-~Jauslin - {\it The Simplified approach to the Bose gas without translation invariance}, 2023,\par\penalty10000
arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/2302.13446}{2302.13446}}.\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[LL64]{LL64}E.H. Lieb, W. Liniger - {\it Simplified Approach to the Ground-State Energy of an Imperfect Bose Gas. III. Application to the One-Dimensional Model}, Physical Review, volume\-~134, issue\-~2A, pages A312-A315, 1964,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRev.134.A312}{10.1103/PhysRev.134.A312}}.\par\medskip
\bibitem[LS64]{LS64}E.H. Lieb, A.Y. Sakakura - {\it Simplified Approach to the Ground-State Energy of an Imperfect Bose Gas. II. Charged Bose Gas at High Density}, Physical Review, volume\-~133, issue\-~4A, pages A899-A906, 1964,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRev.133.A899}{10.1103/PhysRev.133.A899}}.\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[Op31]{Op31}J.R. Oppenheimer - {\it Note on Light Quanta and the Electromagnetic Field}, Physical Review, volume\-~38, issue\-~4, pages\-~725-746, 1931,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRev.38.725}{10.1103/PhysRev.38.725}}.\par\medskip
\bibitem[Ru99]{Ru99}D. Ruelle - {\it Statistical mechanics: rigorous results}, Imperial College Press, World Scientific, (first edition: Benjamin, 1969), 1999.\par\medskip
\bibitem[Sc22]{Sc22}B. Schlein - {\it Bose gases in the Gross-Pitaevskii limit: A survey of some rigorous results}, The Physics and Mathematics of Elliott Lieb, The\-~90th anniversary volume II, eds R.L. Frank, A. Laptev, M. Lewin, R. Seiringer, pages\-~277-305, 2022,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.4171/90-2/40}{10.4171/90-2/40}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/2203.10855}{2203.10855}}.\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[JaSS]{ss}I.\-~Jauslin - {\tt simplesolv} software package v0.4.1,\par\penalty10000
{\tt\color{blue}\href{http://ian.jauslin.org/software/simplesolv}{http://ian.jauslin.org/software/simplesolv}}.\par\medskip

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PROJECT=$(basename $(wildcard *.gnuplot))
all: $(addsuffix .pdf, $(PROJECT))
define gnuplot2pdf
gnuplot $(1).gnuplot > $(1).tikz.tex
pdflatex -jobname $(1) -file-line-error $(1).tikz.tex
endef
bec_phase.pdf:
$(call gnuplot2pdf, $(basename $@))
clean-aux:
rm -f $(addsuffix .tikz.tex, $(PROJECT))
rm -f *.aux *.log
clean-dat:
rm -f phase_boundary.dat
clean-pdf:
rm -f $(addsuffix .pdf, $(PROJECT))
clean: clean-aux clean-pdf

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set ylabel "$\\rho_m\\ (\\mathrm{g}/\\mathrm{cm}^3)$"
set xlabel "$T\\ (\\mathrm{K})$"
set xrange[0:300]
set yrange [0:20]
# default output canvas size: 12.5cm x 8.75cm
set term lua tikz size 12.5,8.75 standalone
set key off
# 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 style line 6 linetype rgbcolor "#000000" linewidth 3
set pointsize 0.6
set label "\\bf BEC" at 10,10 front textcolor "white"
set label "\\bf Gas" at 150,10 front textcolor "white"
kb=1.380649e-23
hbar=1.054571817e-34
cst=0.05864362134764442
m=1.66053906660e-27*4
plot (2*m/hbar/hbar*kb*x)**1.5*cst*m/1000 with filledcurves x2 linestyle 1 ,\
(2*m/hbar/hbar*kb*x)**1.5*cst*m/1000 with filledcurves x1 linestyle 2, \
(2*m/hbar/hbar*kb*x)**1.5*cst*m/1000 with lines linestyle 6

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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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PROJECTNAME=condensate
SIMPLESOLV= # path/to/simplesolv
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
1.450828778495940e-06 1.128447423932415e-03 1.284844855728227e-12
1.747528400007683e-06 1.243211901088135e-03 6.036870814265909e-14
2.104904144512022e-06 1.371540352505089e-03 1.465826916259999e-12
2.535364493970111e-06 1.514563172953764e-03 5.278911635708756e-12
3.053855508833412e-06 1.673162936456016e-03 6.438854837197395e-12
3.678379771828634e-06 1.847621600906275e-03 3.277884092656937e-12
4.430621457583877e-06 2.037906626012430e-03 6.922442639580641e-13
5.336699231206313e-06 2.244403765508714e-03 4.301594724689213e-14
6.428073117284319e-06 2.468275249347463e-03 3.149478739794029e-14
7.742636826811277e-06 2.711300000206942e-03 1.692972150200860e-14
9.326033468832200e-06 2.975586773983234e-03 2.485257044540253e-14
1.123324032978027e-05 3.263387610365739e-03 5.798705939542849e-14
1.353047774579808e-05 3.577021358160436e-03 1.007850792994357e-13
1.629750834620643e-05 3.918861287982854e-03 1.180879418675055e-13
1.963040650040272e-05 4.291351386383927e-03 1.164548699163096e-13
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
4.977023564332114e-05 6.706568098963386e-03 2.719353007326749e-14
5.994842503189409e-05 7.320399534465997e-03 2.419046911428554e-14
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
1.261856883066021e-04 1.031533974401874e-02 1.231730471561613e-14
1.519911082952935e-04 1.121458911634652e-02 1.063694582767876e-14
1.830738280295370e-04 1.217988982497501e-02 2.605952558828706e-14
2.205130739903046e-04 1.321375095073367e-02 1.948459628184608e-14
2.656087782946686e-04 1.431828101890961e-02 2.204861946752505e-14
3.199267137797384e-04 1.549505586477500e-02 3.187650388653336e-14
3.853528593710532e-04 1.674496732600098e-02 3.041558319770699e-14
4.641588833612782e-04 1.806805674261242e-02 3.132688775353608e-14
5.590810182512228e-04 1.946333993043477e-02 3.849130191836202e-14
6.734150657750828e-04 2.092863160214499e-02 5.858344140792253e-14
8.111308307896872e-04 2.246037686139622e-02 8.179691054969686e-14
9.770099572992256e-04 2.405349636533224e-02 1.097457892783796e-13
1.176811952434999e-03 2.570125163577371e-02 1.510104805632382e-13
1.417474162926806e-03 2.739513888148153e-02 2.017323906157568e-13
1.707352647470692e-03 2.912482328833103e-02 2.635554179184661e-13
2.056512308348653e-03 3.087812926296352e-02 3.398621654197443e-13
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
6.280291441834260e-03 4.101443056577509e-02 9.852419079005244e-13
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
2.595024211399737e-01 4.175810970901533e-02 4.628803528432183e-13
3.125715849688241e-01 4.052464054410850e-02 4.243706234593440e-13
3.764935806792471e-01 3.924689825998715e-02 3.870128277902043e-13
4.534878508128591e-01 3.793549610670589e-02 3.506993848968064e-13
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View File

@ -0,0 +1,41 @@
set ylabel "$\\eta$" 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"

View File

@ -0,0 +1,100 @@
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1.668100537200059e+00 1.396852592590819e-03 1.077505663391400e-13
2.009233002565050e+00 1.167708942604489e-03 9.617247230343784e-15
2.420128264794383e+00 9.750960054767535e-04 1.332892817532053e-14
2.915053062825182e+00 8.135033134750610e-04 7.070633698527270e-15
3.511191734215135e+00 6.781586746197346e-04 8.192151573803895e-15
4.229242874389508e+00 5.649574306198204e-04 2.173395402515360e-14
5.094138014816386e+00 4.703892580579609e-04 3.221397384087175e-15
6.135907273413176e+00 3.914665137901705e-04 2.465093210577484e-15
7.390722033525790e+00 3.256566560554041e-04 1.054195282267954e-13
8.902150854450392e+00 2.708201876121645e-04 1.763579120526998e-15
1.072267222010325e+01 2.251547953209304e-04 1.048264548971050e-13
1.291549665014885e+01 1.871458338265689e-04 9.947599265439233e-15
1.555676143930475e+01 1.555229594282470e-04 1.158199515173392e-15
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

View File

@ -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
View File

@ -0,0 +1,37 @@
PROJECTNAME=energy
SIMPLESOLV= # path/to/simplesolv
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
View File

@ -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
5.336699231206313e-06 4.268711577772934e-05 8.111082866158586e-13
6.428073117284319e-06 5.148770312835425e-05 1.258065696556162e-12
7.742636826811277e-06 6.211034042585299e-05 1.460046719339352e-12
9.326033468832200e-06 7.493461690987080e-05 1.403493327361502e-12
1.123324032978027e-05 9.041991424013260e-05 1.190931394710978e-12
1.353047774579808e-05 1.091223876997595e-04 9.122943906836504e-13
1.629750834620643e-05 1.317156211714737e-04 6.270289167996145e-13
1.963040650040272e-05 1.590157675195849e-04 3.932273380946167e-13
2.364489412645407e-05 1.920121690316943e-04 2.176631964805619e-13
2.848035868435805e-05 2.319046775947738e-04 1.026358506480137e-13
3.430469286314919e-05 2.801491713026256e-04 4.446534105626415e-14
4.132012400115334e-05 3.385131054920545e-04 4.144974620326791e-14
4.977023564332114e-05 4.091433566527190e-04 2.207980896760987e-14
5.994842503189409e-05 4.946491352779899e-04 4.572485754229845e-14
7.220809018385471e-05 5.982033804561970e-04 6.770202411898077e-14
8.697490026177834e-05 7.236668315738020e-04 8.932369095090413e-14
1.047615752789665e-04 8.757399333684964e-04 1.182248084569074e-13
1.261856883066021e-04 1.060148908761868e-03 1.344231243816312e-13
1.519911082952935e-04 1.283873775901215e-03 1.493216888971958e-13
1.830738280295370e-04 1.555427846566146e-03 1.699458131695914e-13
2.205130739903046e-04 1.885200386765900e-03 2.059019619099669e-13
2.656087782946686e-04 2.285876721564974e-03 2.649891700928507e-13
3.199267137797384e-04 2.772953210497389e-03 3.620701665273268e-13
3.853528593710532e-04 3.365368304619666e-03 4.982472417338292e-13
4.641588833612782e-04 4.086275430706575e-03 6.801465168364811e-13
5.590810182512228e-04 4.963988854528130e-03 9.137218648090623e-13
6.734150657750828e-04 6.033140090007556e-03 1.205112818608528e-12
8.111308307896872e-04 7.336089997726976e-03 1.568949512234829e-12
9.770099572992256e-04 8.924650630547374e-03 2.015537944839303e-12
1.176811952434999e-03 1.086218134368278e-02 2.551669271262342e-12
1.417474162926806e-03 1.322613594632949e-02 3.175541504984204e-12
1.707352647470692e-03 1.611115205690737e-02 3.882570582394582e-12
2.056512308348653e-03 1.963279076107542e-02 4.659084950581694e-12
2.477076355991711e-03 2.393205473004278e-02 5.480860359934871e-12
2.983647240283340e-03 2.918083689398976e-02 6.316773798635380e-12
3.593813663804629e-03 3.558848057549190e-02 7.128689280361588e-12
4.328761281083062e-03 4.340966694307487e-02 7.877742721930180e-12
5.214008287999690e-03 5.295388832723841e-02 8.538097040660639e-12
6.280291441834260e-03 6.459681825795255e-02 9.099882246799092e-12
7.564633275546291e-03 7.879395326961169e-02 9.571289375001028e-12
9.111627561154896e-03 9.609698014020246e-02 9.973223641678962e-12
1.097498765493057e-02 1.171734181893564e-01 5.721422548997492e-15
1.321941148466031e-02 1.428302028457424e-01 2.220152020103125e-15
1.592282793341094e-02 1.740420176882147e-01 3.826728826701929e-15
1.917910261672489e-02 2.119853520055517e-01 2.868300139436348e-15
2.310129700083163e-02 2.580794649360160e-01 7.610004429207492e-15
2.782559402207126e-02 3.140356819487004e-01 6.059675090044115e-15
3.351602650938848e-02 3.819167428256006e-01 3.079883529777644e-15
4.037017258596558e-02 4.642082722623484e-01 5.845027410285226e-15
4.862601580065354e-02 5.639048668198076e-01 3.816993895235883e-15
5.857020818056673e-02 6.846137999573778e-01 3.474232903786021e-15
7.054802310718646e-02 8.306799580954581e-01 4.088512836639771e-15
8.497534359086456e-02 1.007336356586333e+00 3.416440773537374e-15
1.023531021899027e-01 1.220885470968219e+00 3.150210853153027e-15
1.232846739442068e-01 1.478917686986172e+00 2.371648956613387e-15
1.484968262254467e-01 1.790574459885084e+00 2.131970502004566e-15
1.788649529057435e-01 2.166865324247355e+00 1.071205796436568e-15
2.154434690031887e-01 2.621049764085537e+00 9.990417291453287e-12
2.595024211399737e-01 3.169097203910113e+00 9.249109275328039e-12
3.125715849688241e-01 3.830241093220283e+00 8.462348103996382e-12
3.764935806792471e-01 4.627646323429371e+00 7.654951972758785e-12
4.534878508128591e-01 5.589213151008605e+00 6.847954951876310e-12
5.462277217684348e-01 6.748545540181854e+00 6.060205450067071e-12
6.579332246575682e-01 8.146117547346687e+00 5.306471340562747e-12
7.924828983539185e-01 9.830678245708585e+00 4.598704413056710e-12
9.545484566618347e-01 1.186094397111715e+01 3.945605710986110e-12
1.149756995397738e+00 1.430763664633719e+01 3.351869307817862e-12
1.384886371393875e+00 1.725593895734062e+01 2.820957127030768e-12
1.668100537200059e+00 2.080845162887957e+01 2.352147114974057e-12
2.009233002565050e+00 2.508875548012610e+01 1.943437328683651e-12
2.420128264794383e+00 3.024570193985361e+01 1.592153241178217e-12
2.915053062825182e+00 3.645858099358198e+01 1.293588310581549e-12
3.511191734215135e+00 4.394334600051280e+01 1.042306124720846e-12
4.229242874389508e+00 5.296011151374482e+01 8.333799477286008e-13
5.094138014816386e+00 6.382218443728761e+01 6.605722153418092e-13
6.135907273413176e+00 7.690694209247896e+01 5.199590335170479e-13
7.390722033525790e+00 9.266893489306236e+01 4.063068137082775e-13
8.902150854450392e+00 1.116556685689670e+02 3.149814651697356e-13
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

View File

@ -0,0 +1,41 @@
set title ""
set ylabel "$\\displaystyle\\frac{e}{\\rho}$" 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
2.104904144512022e-06 1.675062919238505e-05 1.653650872454784e-14
2.535364493970111e-06 2.019490280396468e-05 2.336983658291679e-14
3.053855508833412e-06 2.434951404943966e-05 2.214775068136617e-14
3.678379771828634e-06 2.936162846930739e-05 3.805584891901638e-14
4.430621457583877e-06 3.540910828910534e-05 1.427802345533630e-14
5.336699231206313e-06 4.270697869633961e-05 2.003273138190368e-14
6.428073117284319e-06 5.151527512777095e-05 2.551774430173645e-14
7.742636826811277e-06 6.214857192276333e-05 3.705994224138530e-14
9.326033468832200e-06 7.498755947811933e-05 7.265095211681475e-14
1.123324032978027e-05 9.049311901844221e-05 1.264190454286157e-14
1.353047774579808e-05 1.092234447947087e-04 1.053352694614131e-14
1.629750834620643e-05 1.318548872942263e-04 2.368465480922291e-14
1.963040650040272e-05 1.592073432336066e-04 1.660337987885090e-14
2.364489412645407e-05 1.922752053054458e-04 8.646141141307886e-15
2.848035868435805e-05 2.322651149462809e-04 2.442896517713713e-14
3.430469286314919e-05 2.806420446977329e-04 9.776919033399443e-15
4.132012400115334e-05 3.391855851696971e-04 1.271987985520055e-14
4.977023564332114e-05 4.100587399374810e-04 2.239769985922260e-14
5.994842503189409e-05 4.958920578361200e-04 2.600603141419754e-14
7.220809018385471e-05 5.998865777048775e-04 3.305695605996821e-14
8.697490026177834e-05 7.259398517100161e-04 1.348707825208008e-14
1.047615752789665e-04 8.788002810614415e-04 2.107644168610072e-14
1.261856883066021e-04 1.064256179216188e-03 3.010939452255121e-14
1.519911082952935e-04 1.289367416181562e-03 4.528098249733624e-14
1.830738280295370e-04 1.562749244492149e-03 7.011583917825588e-14
2.205130739903046e-04 1.894920022439264e-03 1.127696093174950e-13
2.656087782946686e-04 2.298727102221577e-03 1.467479187573012e-13
3.199267137797384e-04 2.789868219377111e-03 2.329360329563977e-13
3.853528593710532e-04 3.387529396559262e-03 2.906251121896537e-13
4.641588833612782e-04 4.115164764506077e-03 3.999178759473060e-13
5.590810182512228e-04 5.001448927349123e-03 5.543444903233915e-13
6.734150657750828e-04 6.081438699757301e-03 7.247686124008659e-13
8.111308307896872e-04 7.397988387264389e-03 9.394231632434480e-13
9.770099572992256e-04 9.003471469917696e-03 1.188210506033121e-12
1.176811952434999e-03 1.096187182983169e-02 1.453939404386284e-12
1.417474162926806e-03 1.335131984243035e-02 1.748927540773990e-12
1.707352647470692e-03 1.626716311543043e-02 2.048075825913765e-12
2.056512308348653e-03 1.982567889735244e-02 2.340515412122970e-12
2.477076355991711e-03 2.416855580506204e-02 2.605854351607331e-12
2.983647240283340e-03 2.946829731035233e-02 2.824445163694187e-12
3.593813663804629e-03 3.593472933729397e-02 2.981866401807997e-12
4.328761281083062e-03 4.382283052883180e-02 3.067362472205469e-12
5.214008287999690e-03 5.344214766200744e-02 3.073513956716823e-12
6.280291441834260e-03 6.516811202317233e-02 3.006095534695811e-12
7.564633275546291e-03 7.945563730982247e-02 2.868424849163193e-12
9.111627561154896e-03 9.685545817966755e-02 2.674678867537749e-12
1.097498765493057e-02 1.180337637230369e-01 2.440734483972164e-12
1.321941148466031e-02 1.437957952077961e-01 2.184363028675561e-12
1.592282793341094e-02 1.751142163796972e-01 1.917824774341397e-12
1.917910261672489e-02 2.131632321105708e-01 1.656059900213277e-12
2.310129700083163e-02 2.593596329389756e-01 1.410306668963206e-12
2.782559402207126e-02 3.154121858791141e-01 1.195131021990613e-12
3.351602650938848e-02 3.833810840481612e-01 9.871852649538251e-13
4.037017258596558e-02 4.657495191763944e-01 8.136332883253271e-13
4.862601580065354e-02 5.655098640080871e-01 6.823741984126656e-13
5.857020818056673e-02 6.862674605812320e-01 5.705185315457055e-13
7.054802310718646e-02 8.323656230237174e-01 4.590853816780889e-13
8.497534359086456e-02 1.009036201088274e+00 3.723504950962481e-13
1.023531021899027e-01 1.222580938798058e+00 3.740344313966540e-13
1.232846739442068e-01 1.480589932164776e+00 2.590030624091089e-13
1.484968262254467e-01 1.792204778156467e+00 4.308044222824868e-13
1.788649529057435e-01 2.168435558712142e+00 1.711857922602610e-13
2.154434690031887e-01 2.622542672548128e+00 2.630630812010949e-13
2.595024211399737e-01 3.170496778713019e+00 4.862348792954930e-13
3.125715849688241e-01 3.831532827526695e+00 3.222631437243052e-13
3.764935806792471e-01 4.628817420866958e+00 9.063217628519465e-14
4.534878508128591e-01 5.590252678180098e+00 3.126299632971088e-13
5.462277217684348e-01 6.749444523712865e+00 5.271767714437587e-13
6.579332246575682e-01 8.146869018854765e+00 7.067258691723872e-13
7.924828983539185e-01 9.831277239349690e+00 1.976481716430481e-13
9.545484566618347e-01 1.186138747922958e+01 1.213984608946686e-13
1.149756995397738e+00 1.430792353920593e+01 1.001843165310050e-13
1.384886371393875e+00 1.725606987330165e+01 7.356460075303617e-14
1.668100537200059e+00 2.080842884092954e+01 1.207511033175393e-13
2.009233002565050e+00 2.508858274495347e+01 1.420167716375784e-13
2.420128264794383e+00 3.024538433481086e+01 2.404214126545545e-13
2.915053062825182e+00 3.645812474662149e+01 8.020433476813964e-14
3.511191734215135e+00 4.394275831754763e+01 7.725490959360697e-14
4.229242874389508e+00 5.295940040730246e+01 9.193832425125519e-14
5.094138014816386e+00 6.382135855972534e+01 5.965887874370161e-14
6.135907273413176e+00 7.690601057644308e+01 7.369357116862908e-14
7.390722033525790e+00 9.266790720131583e+01 6.733622484011242e-14
8.902150854450392e+00 1.116545543551900e+02 7.236758339264480e-14
1.072267222010325e+01 1.345254228973254e+02 7.214733858698264e-14
1.291549665014885e+01 1.620748459530638e+02 4.566762659089573e-14
1.555676143930475e+01 1.952595988278435e+02 4.016462557967500e-14
1.873817422860387e+01 2.352321191121707e+02 4.222275907971552e-14
2.257019719633922e+01 2.833805204158014e+02 4.452644207417061e-14
2.718588242732946e+01 3.413767890516622e+02 9.381962021977345e-14
3.274549162877732e+01 4.112348371110992e+02 2.985855401371043e-14
3.944206059437664e+01 4.953804275968574e+02 4.510651797992799e-14
4.750810162102803e+01 5.967353994911545e+02 2.755681866935816e-14
5.722367659350220e+01 7.188191171458401e+02 2.159989114361577e-14
6.892612104349709e+01 8.658706664291410e+02 2.997352502706469e-14
8.302175681319753e+01 1.042996040413900e+03 4.590753851046225e-14
1.000000000000000e+02 1.256345425056825e+03 2.310603796838004e-14

100
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@ -0,0 +1,100 @@
1.000000000000000e-06 7.934458317554770e-06 1.253408725811047e-14
1.204503540258781e-06 9.563293402409969e-06 1.640998151881320e-14
1.450828778495940e-06 1.152722385213290e-05 3.251262837839683e-14
1.747528400007683e-06 1.389541646472593e-05 3.019030546809478e-14
2.104904144512022e-06 1.675138713852244e-05 2.275714260526642e-14
2.535364493970111e-06 2.019600045252957e-05 3.271639597766372e-14
3.053855508833412e-06 2.435110335988150e-05 2.142094245826877e-14
3.678379771828634e-06 2.936392920320935e-05 1.339250507659264e-14
4.430621457583877e-06 3.541243815820425e-05 3.893851454934391e-14
5.336699231206313e-06 4.271179685321251e-05 3.095940660023124e-14
6.428073117284319e-06 5.152224486652221e-05 5.125396859042871e-14
7.742636826811277e-06 6.215865101443218e-05 2.890206750836624e-14
9.326033468832200e-06 7.500213022394945e-05 2.241466297924041e-14
1.123324032978027e-05 9.051417532865902e-05 2.370776274109386e-14
1.353047774579808e-05 1.092538610497785e-04 4.796262972662893e-14
1.629750834620643e-05 1.318988043420983e-04 4.229814231373338e-14
1.963040650040272e-05 1.592707219208866e-04 3.808954617986591e-14
2.364489412645407e-05 1.923666192393963e-04 2.141860559824167e-14
2.848035868435805e-05 2.323968842530530e-04 4.584119591708702e-14
3.430469286314919e-05 2.808318548521666e-04 2.138418227061501e-14
4.132012400115334e-05 3.394587942820992e-04 1.918556578598127e-14
4.977023564332114e-05 4.104516606676139e-04 1.694104962972332e-14
5.994842503189409e-05 4.964566151029166e-04 3.002291274309623e-14
7.220809018385471e-05 6.006969022092982e-04 4.294873137027481e-14
8.697490026177834e-05 7.271015873319120e-04 2.062540444418305e-14
1.047615752789665e-04 8.804636812878449e-04 3.334031557301778e-14
1.261856883066021e-04 1.066634469195621e-03 7.194072311053829e-14
1.519911082952935e-04 1.292762434131901e-03 8.278169514315650e-14
1.830738280295370e-04 1.567587086789660e-03 1.161190654702787e-13
2.205130739903046e-04 1.901800344392313e-03 1.797096379984733e-13
2.656087782946686e-04 2.308490918746631e-03 2.637598652434219e-13
3.199267137797384e-04 2.803690553578959e-03 3.722231676096834e-13
3.853528593710532e-04 3.407044978502708e-03 5.427762733833543e-13
4.641588833612782e-04 4.142637205871173e-03 7.734027562664818e-13
5.590810182512228e-04 5.039996370506877e-03 1.084741759773931e-12
6.734150657750828e-04 6.135331779936552e-03 1.475538242058165e-12
8.111308307896872e-04 7.473039279209971e-03 1.968813103343645e-12
9.770099572992256e-04 9.107535515599206e-03 2.559305054777023e-12
1.176811952434999e-03 1.110548530561432e-02 3.246800230285997e-12
1.417474162926806e-03 1.354849819420097e-02 3.999740063734383e-12
1.707352647470692e-03 1.653638267729146e-02 4.785597934980074e-12
2.056512308348653e-03 2.019106081393928e-02 5.541961698394948e-12
2.477076355991711e-03 2.466126270506543e-02 6.209989300668736e-12
2.983647240283340e-03 3.012814052292188e-02 6.719913925774575e-12
3.593813663804629e-03 3.681196682685592e-02 7.010516326080206e-12
4.328761281083062e-03 4.498011366911493e-02 7.042737419751455e-12
5.214008287999690e-03 5.495654983134250e-02 6.803473563255481e-12
6.280291441834260e-03 6.713314618359296e-02 6.316173694015080e-12
7.564633275546291e-03 8.198314659254460e-02 5.630438859203436e-12
9.111627561154896e-03 1.000772469953260e-01 4.814460500479356e-12
1.097498765493057e-02 1.221028309649795e-01 3.948371699573414e-12
1.321941148466031e-02 1.488870387812890e-01 3.104931054226393e-12
1.592282793341094e-02 1.814245009403908e-01 2.339516913805968e-12
1.917910261672489e-02 2.209107486051246e-01 1.688210571908239e-12
2.310129700083163e-02 2.687825259198435e-01 1.167659413279469e-12
2.782559402207126e-02 3.267664771683836e-01 7.775556337126751e-13
3.351602650938848e-02 3.969379725867567e-01 4.949300609691499e-13
4.037017258596558e-02 4.817921803787671e-01 3.047835972157860e-13
4.862601580065354e-02 5.843299025667947e-01 1.744034034347572e-13
5.857020818056673e-02 7.081611855740870e-01 2.145108372619088e-13
7.054802310718646e-02 8.576303130499369e-01 1.004811457230378e-13
8.497534359086456e-02 1.037966511958588e+00 4.718419633908083e-14
1.023531021899027e-01 1.255465580586508e+00 2.639823583877913e-14
1.232846739442068e-01 1.517708710502109e+00 1.889177952517916e-13
1.484968262254467e-01 1.833826060755470e+00 1.262402568827356e-13
1.788649529057435e-01 2.214814195859386e+00 2.307786324072868e-13
2.154434690031887e-01 2.673918372281924e+00 3.831494558709393e-14
2.595024211399737e-01 3.227092915163674e+00 6.546666422710970e-14
3.125715849688241e-01 3.893555644968086e+00 8.786410093299553e-14
3.764935806792471e-01 4.696455586182800e+00 3.094041097523017e-14
4.534878508128591e-01 5.663677129915349e+00 1.346721396138190e-14
5.462277217684348e-01 6.828808565598630e+00 2.348290345391161e-14
6.579332246575682e-01 8.232308608511897e+00 6.075413859670748e-14
7.924828983539185e-01 9.922911427699711e+00 3.551771518542288e-14
9.545484566618347e-01 1.195931896203401e+01 8.585404990085891e-14
1.149756995397738e+00 1.441223928837902e+01 4.176255867225544e-14
1.384886371393875e+00 1.736684182166722e+01 1.114486677072019e-13
1.668100537200059e+00 2.092571459958015e+01 5.653897977104765e-14
2.009233002565050e+00 2.521242633713612e+01 1.048273767790111e-14
2.420128264794383e+00 3.037581693424489e+01 8.488597666410238e-15
2.915053062825182e+00 3.659516541136894e+01 5.400259352206385e-14
3.511191734215135e+00 4.408641471307532e+01 5.485916680303097e-14
4.229242874389508e+00 5.310966951429405e+01 5.278885434248808e-14
5.094138014816386e+00 6.397822736362556e+01 2.945680129079298e-15
6.135907273413176e+00 7.706945673674652e+01 1.960764876087084e-15
7.390722033525790e+00 9.283789969933954e+01 3.647567907334253e-15
8.902150854450392e+00 1.118310541195708e+02 1.199399938192319e-15
1.072267222010325e+01 1.347083834068206e+02 5.355510579254647e-14
1.291549665014885e+01 1.622642138164582e+02 9.997141006638315e-15
1.555676143930475e+01 1.954553143409147e+02 1.109395412861689e-14
1.873817422860387e+01 2.354341167917606e+02 1.106759345282809e-15
2.257019719633922e+01 2.835887295111127e+02 2.010906753044690e-14
2.718588242732946e+01 3.415911340329474e+02 1.043218765631230e-14
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

715
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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
\ianclasstrue
%% options
% no section numbering in equations
\DeclareOption{section_in_eq}{\sectionsineqtrue}
\DeclareOption{section_in_fig}{\sectionsinfigtrue}
\DeclareOption{section_in_all}{\sectionsineqtrue\sectionsinfigtrue}
\DeclareOption{subsection_in_eq}{\subsectionsineqtrue}
\DeclareOption{subsection_in_fig}{\subsectionsinfigtrue}
\DeclareOption{subsection_in_all}{\subsectionsineqtrue\subsectionsinfigtrue}
\DeclareOption{no_section_in_eq}{\sectionsineqfalse}
\DeclareOption{no_section_in_fig}{\sectionsinfigfalse}
\DeclareOption{no_section_in_all}{\sectionsineqfalse\sectionsinfigfalse}
\DeclareOption{no_subsection_in_eq}{\subsectionsineqfalse}
\DeclareOption{no_subsection_in_fig}{\subsectionsinfigfalse}
\DeclareOption{no_subsection_in_all}{\subsectionsineqfalse\subsectionsinfigfalse}
\def\ian@defaultoptions{
\ExecuteOptions{section_in_all, no_subsection_in_all}
\ProcessOptions
%% required packages
\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%
}
% omit link
\def\textref##1{%
\ifcsname label@##1@hl\endcsname%
\safe\csname label@##1\endcsname%
\else%
\ifcsname label@##1\endcsname%
\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}
% define possible prefix to equation
\def\eqprefix{}
% booleans (write section or subsection in equation number)
\newif\ifsectionsineq
\newif\ifsubsectionsineq
\def\seqcount{
\stepcounter{seqcount}
% the output
\edef\seqformat{\eqprefix\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%
\par\penalty10000\hfil fig \figformat: \parbox[t]{\figwidth}{\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%
\par\penalty10000\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}
}
%% start exercises
\def\exercises{
\vfill
\pagebreak
% counter
\setcounter{sectioncount}0
\setcounter{seqcount}0
% prefix
\def\sectionprefix{E}
\hrefanchor
% write
{\bf \LARGE Exercises}\par\penalty10000\bigskip\penalty10000
% 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@exercises\endcsname{\thelncount}}
\write\tocoutput{\noexpand\tocexercises{\thepage}}\penalty10000
\fi
\def\eqprefix{E}
\sectionsineqfalse
}
%% 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{
{\bf \large Table of contents:}\par\penalty10000\smallskip\penalty10000
% 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 \tocsectionprefix\thetocsectioncount.\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 \tocsectionprefix\thetocsectioncount.\thetocsubsectioncount.\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
}
\def\tocexercises#1{
\medskip
\setcounter{tocsectioncount}0
{\hyperlink{ln.\csname toc@exercises\endcsname}{{\color{blue}\bf Exercises}\leaderfill#1}}\par
\smallskip
\def\tocsectionprefix{E}
}
%% 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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%%
%% largearray package:
%% Array spanning the entire line
%%
%% TeX format
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
%% package name
\ProvidesPackage{largearray}[2016/11/10]
\RequirePackage{array}
%% array spanning the entire line
\newlength\largearray@width
\setlength\largearray@width\textwidth
\addtolength\largearray@width{-10pt}
\def\largearray{\begin{array}{@{}>{\displaystyle}l@{}}\hphantom{\hspace{\largearray@width}}\\[-.5cm]}
\def\endlargearray{\end{array}}

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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

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%%
%% problemset package:
%% macros for problem sets
%%
%% TeX format
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
%% package name
\ProvidesPackage{problemset}[2022/01/25]
\newif\ifproblemineq
\newif\ifquestionineq
\DeclareOption{problem_in_eq}{\problemineqtrue}
\DeclareOption{no_problem_in_eq}{\problemineqfalse}
\DeclareOption{question_in_eq}{\questionineqtrue}
\DeclareOption{no_question_in_eq}{\questionineqfalse}
\def\problemset@defaultoptions{
\ExecuteOptions{problem_in_eq, no_question_in_eq}
\ProcessOptions
}
%% the problem command handles automatic problem numbering, as well as per-problem equation numbering
% problem counter
\newcounter{problemcount}
% problem@temp is set to true when there is an optional argument
\newif\ifproblem@temp
\def\problem{%
% check whether there is an optional argument (if there is none, add on empty '[]')
\@ifnextchar [{\problem@temptrue\@problemx}{\problem@tempfalse\@problemx[]}%
}
% command with optional argument
\def\@problemx[#1]{%
% reset question counter
\setcounter{questioncount}{0}
% if optional argument, set problem num to argument
\ifproblem@temp%
\edef\problemnum{#1}%
% otherwise, count
\else%
\stepcounter{problemcount}%
\edef\problemnum{\theproblemcount}%
\fi%
% if ian class
\ifianclass%
% define tag for label
\hrefanchor%
\xdef\tag{E\problemnum}%
%
% add header to equation numbers (for ian class)
\ifproblemineq%
\def\eqprefix{E\problemnum.}%
% reset equation number
\setcounter{seqcount}{0}%
\fi%
\fi%
% header
\problemformat{E\problemnum}%
}
% problem formatting (override to customize)
\def\problemformat#1{{\bf #1}. }
%% question is to problem as subsection is to section
% question counter
\newcounter{questioncount}
% question@temp is set to true when there is an optional argument
\newif\ifquestion@temp
\def\question{%
% check whether there is an optional argument (if there is none, add on empty '[]')
\@ifnextchar [{\question@temptrue\@questionx}{\question@tempfalse\@questionx[]}%
}
% command with optional argument
\def\@questionx[#1]{%
% if optional argument, set problem num to argument
\ifquestion@temp%
\edef\questionnum{#1}%
% otherwise, count
\else%
\stepcounter{questioncount}%
\edef\questionnum{\alph{questioncount}}%
\fi%
% header
\questionformat{\questionnum}%
% if ian class
\ifianclass%
% define tag for label
\hrefanchor%
\xdef\tag{\questionnum}%
%
% add header to equation numbers (for ian class)
\ifquestionineq%
\def\eqprefix{\questionnum.}%
% reset equation number
\setcounter{seqcount}{0}%
\fi%
\fi%
}
% question formatting (override to customize)
\def\questionformat#1{{\bf(#1)} }
\def\solution#1{
\makelink{sol:#1}{\thepage}
{\bf Solution\-~\ref{ex:#1}}\par\penalty10000\smallskip\penalty10000
\def\eqprefix{S\textref{ex:#1}.}
\resetpointcounter
\setcounter{seqcount}{0}
}
%\newif\ifsolution
%% display solutions
%\long\def\solution#1{
% \ifsolution
% \bigskip
% \leftskip20pt
% \rightskip20pt
% {\bf Solution}: #1
% \par
% \leftskip0pt
% \rightskip0pt
% \bigskip
% \fi
%}
% rubric
\newif\ifrubric
\long\def\rubric#1{
\ifrubric
({\it #1})
\fi
}
%% end
\problemset@defaultoptions
\endinput