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PROJECTNAME=Carlen_Jauslin_Lieb_2020
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SYNCTEXS=$(PROJECTNAME).synctex.gz
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all: $(PROJECTNAME).pdf
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$(PROJECTNAME).pdf: $(PROJECTNAME).bbl
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pdflatex -file-line-error $(PROJECTNAME).tex
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pdflatex -file-line-error $(PROJECTNAME).tex
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pdflatex -synctex=1 $(PROJECTNAME).tex
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$(PROJECTNAME).aux:
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pdflatex -file-line-error -draftmode $(PROJECTNAME).tex
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$(PROJECTNAME).bbl: $(PROJECTNAME).aux bibliography.bib
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bibtex $(PROJECTNAME).aux
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clean-aux:
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rm -f $(PROJECTNAME).aux
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rm -f $(PROJECTNAME).log
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rm -f $(PROJECTNAME).out
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rm -f $(PROJECTNAME).toc
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rm -f $(PROJECTNAME).blg
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clean-tex:
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rm -f $(PROJECTNAME).pdf $(PROJECTNAME).synctex.gz
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clean-bibliography:
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rm -f $(PROJECTNAME).bbl
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clean: clean-aux clean-tex clean-bibliography
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This directory contains the source files to typeset the article, and generate
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the figures. This can be accomplished by running
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make
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This document uses a custom class file, located in the 'libs' directory, which
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defines a number of commands. Most of these are drop-in replacements for those
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defined in the 'article' class.
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* Dependencies:
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pdflatex
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TeXlive packages:
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amsart
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amsfonts
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amsthm
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amssymb
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amsxtra
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array
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color
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hyperref
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latex
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bibtex
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GNU make
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* Files:
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Carlen_Jauslin_Lieb_2020.tex:
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main LaTeX file
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point.sty:
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custom LaTeX style file
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bibliography.bib:
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BibTeX database file
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@article{BBe18, doi = {10.1007/s00220-017-3016-5}, url = {https://doi.org/10.1007
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2Fs00220-017-3016-5}, year = 2017, month = {nov}, publisher = {Springer Nature}, volume = {359}, number = {3}, pages = {975--1026}, author = {Chiara Boccato and Christian Brennecke and Serena Cenatiempo and Benjamin Schlein}, title = {Complete Bose{\textendash}Einstein Condensation in the Gross{\textendash}Pitaevskii Regime}, journal = {Communications in Mathematical Physics} }
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@article{Bo47, title={On the theory of superfluidity}, author={Bogolyubov, Nikolay Nikolaevich}, journal={Izv. Akad. Nauk Ser. Fiz.}, volume={11}, pages={23--32}, year={1947} }
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@article{CHe, author = {Carlen, Eric A. and Holzmann, Markus and Jauslin, Ian and Lieb, Elliott H.},journal = {in preparation} }
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@article{CJL20, title={Analysis of a simple equation for the ground state energy of the Bose gas}, author = {Carlen, Eric A. and Jauslin, Ian and Lieb, Elliott H.},journal = {Pure and Applied Analysis, in press, arXiv preprint: 1912.04987}, year={2020} }
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@article{CAL09, doi = {10.1103/physreva.79.053640}, url = {https://doi.org/10.1103
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2Fphysreva.79.053640}, year = 2009, month = {may}, publisher = {American Physical Society ({APS})}, volume = {79}, number = {5}, author = {R. Combescot and F. Alzetto and X. Leyronas}, title = {Particle distribution tail and related energy formula}, journal = {Physical Review A} }
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@article{Dy57, doi = {10.1103/physrev.106.20}, url = {https://doi.org/10.1103
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2Fphysrev.106.20}, year = 1957, month = {apr}, publisher = {American Physical Society ({APS})}, volume = {106}, number = {1}, pages = {20--26}, author = {F. J. Dyson}, title = {Ground-State Energy of a Hard-Sphere Gas}, journal = {Physical Review} }
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@article{ESY08, doi = {10.1103/physreva.78.053627}, url = {https://doi.org/10.1103
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2Fphysreva.78.053627}, year = 2008, month = {nov}, publisher = {American Physical Society ({APS})}, volume = {78}, number = {5}, author = {L{\'{a}}szl{\'{o}} Erd{\H{o}}s and Benjamin Schlein and Horng-Tzer Yau}, title = {Ground-state energy of a low-density Bose gas: A second-order upper bound}, journal = {Physical Review A} , pages={053627}}
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@article{FS20, title={The energy of dilute Bose gases}, author={Fournais, S\o{}ren and Solovej, Jan Philip}, journal={The Annals of Mathematics, in press, arXiv preprint:1904.06164}, year={2020} }
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@article{GS09, doi = {10.1007/s10955-009-9718-0}, url = {https://doi.org/10.1007
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2Fs10955-009-9718-0}, year = 2009, month = {apr}, publisher = {Springer Science and Business Media {LLC}}, volume = {135}, number = {5-6}, pages = {915--934}, author = {Alessandro Giuliani and Robert Seiringer}, title = {The Ground State Energy of the Weakly Interacting Bose Gas at High Density}, journal = {Journal of Statistical Physics} }
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@article{KLS88, doi = {10.1007/bf01023854}, url = {https://doi.org/10.1007
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2Fbf01023854}, year = 1988, month = {dec}, publisher = {Springer Science and Business Media {LLC}}, volume = {53}, number = {5-6}, pages = {1019--1030}, author = {Tom Kennedy and Elliott H. Lieb and B. Sriram Shastry}, title = {Existence of N\'eel order in some spin-1/2 Heisenberg antiferromagnets}, journal = {Journal of Statistical Physics} }
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@article{LHY57, doi = {10.1103/physrev.106.1135}, url = {https://doi.org/10.1103
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2Fphysrev.106.1135}, year = 1957, month = {jun}, publisher = {American Physical Society ({APS})}, volume = {106}, number = {6}, pages = {1135--1145}, author = {T. D. Lee and Kerson Huang and C. N. Yang}, title = {Eigenvalues and Eigenfunctions of a Bose System of Hard Spheres and Its Low-Temperature Properties}, journal = {Physical Review} }
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@article{Li63, doi = {10.1103/physrev.130.2518}, url = {https://doi.org/10.1103
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2Fphysrev.130.2518}, year = 1963, month = {jun}, publisher = {American Physical Society ({APS})}, volume = {130}, number = {6}, pages = {2518--2528}, author = {Elliott H. Lieb}, title = {Simplified Approach to the Ground-State Energy of an Imperfect Bose Gas}, journal = {Physical Review} }
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@article{LL64, doi = {10.1103/physrev.134.a312}, url = {https://doi.org/10.1103
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2Fphysrev.134.a312}, year = 1964, month = {apr}, publisher = {American Physical Society ({APS})}, volume = {134}, number = {2A}, pages = {A312--A315}, author = {Elliott H. Lieb and Werner Liniger}, title = {Simplified Approach to the Ground-State Energy of an Imperfect Bose Gas. {III}. Application to the One-Dimensional Model}, journal = {Physical Review} }
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@article{LS64, doi = {10.1103/physrev.133.a899}, url = {https://doi.org/10.1103
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2Fphysrev.133.a899}, year = 1964, month = {feb}, publisher = {American Physical Society ({APS})}, volume = {133}, number = {4A}, pages = {A899--A906}, author = {Elliott H. Lieb and Arthur Y. Sakakura}, title = {Simplified Approach to the Ground-State Energy of an Imperfect Bose Gas. {II}. Charged Bose Gas at High Density}, journal = {Physical Review} }
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@article{LS02, doi = {10.1103/physrevlett.88.170409}, url = {https://doi.org/10.1103
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2Fphysrevlett.88.170409}, year = 2002, month = {apr}, publisher = {American Physical Society ({APS})}, volume = {88}, number = {17}, author = {Elliott H. Lieb and Robert Seiringer}, title = {Proof of Bose-Einstein Condensation for Dilute Trapped Gases}, journal = {Physical Review Letters} , pages={170409}}
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@book{LSe05,title={The Mathematics of the Bose Gas and its Condensation},author={Lieb, Elliott H. and Seiringer, Robert and Solovej, Jan Philip and Yngvason, Jakob},year={2005},publisher={Birkhauser},series={Oberwolfach Seminars},volume={34}}
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@article{LY98, doi = {10.1103/physrevlett.80.2504}, url = {https://doi.org/10.1103
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2Fphysrevlett.80.2504}, year = 1998, month = {mar}, publisher = {American Physical Society ({APS})}, volume = {80}, number = {12}, pages = {2504--2507}, author = {Elliott H. Lieb and Jakob Yngvason}, title = {Ground State Energy of the Low Density Bose Gas}, journal = {Physical Review Letters} , pages={}}
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@article{NE17, doi = {10.1088/1361-6633/aa50e8}, url = {https://doi.org/10.1088
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2F1361-6633
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2Faa50e8}, year = 2017, month = {mar}, publisher = {{IOP} Publishing}, volume = {80}, number = {5}, pages = {056001}, author = {Pascal Naidon and Shimpei Endo}, title = {Efimov physics: a review}, journal = {Reports on Progress in Physics}}
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@article{On63, doi = {10.1215/s0012-7094-63-03015-1}, url = {https://doi.org/10.1215
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2Fs0012-7094-63-03015-1}, year = 1963, month = {mar}, publisher = {Duke University Press}, volume = {30}, number = {1}, pages = {129--142}, author = {Richard O'Neil}, title = {Convolution operators and $L(p,q)$ spaces}, journal = {Duke Mathematical Journal} }
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@book{RS75b, title={Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness}, author={Reed, Michael and Simon, Barry}, edition={2}, year={1975}, publisher={Academic Press, New York}}
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@article{Se11, doi = {10.1007/s00220-011-1261-6}, url = {https://doi.org/10.1007
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2Fs00220-011-1261-6}, year = 2011, month = {may}, publisher = {Springer Science and Business Media {LLC}}, volume = {306}, number = {2}, pages = {565--578}, author = {Robert Seiringer}, title = {The Excitation Spectrum for Weakly Interacting Bosons}, journal = {Communications in Mathematical Physics} }
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@article{Ta08, doi = {10.1016/j.aop.2008.03.004}, url = {https://doi.org/10.1016
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2Fj.aop.2008.03.004}, year = 2008, month = {dec}, publisher = {Elsevier {BV}}, volume = {323}, number = {12}, pages = {2952--2970}, author = {Shina Tan}, title = {Energetics of a strongly correlated Fermi gas}, journal = {Annals of Physics} }
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@article{Ta08b, doi = {10.1016/j.aop.2008.03.005}, url = {https://doi.org/10.1016
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2Fj.aop.2008.03.005}, year = 2008, month = {dec}, publisher = {Elsevier {BV}}, volume = {323}, number = {12}, pages = {2971--2986}, author = {Shina Tan}, title = {Large momentum part of a strongly correlated Fermi gas}, journal = {Annals of Physics} }
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@article{Ta08c, doi = {10.1016/j.aop.2008.03.003}, url = {https://doi.org/10.1016
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2Fj.aop.2008.03.003}, year = 2008, month = {dec}, publisher = {Elsevier {BV}}, volume = {323}, number = {12}, pages = {2987--2990}, author = {Shina Tan}, title = {Generalized virial theorem and pressure relation for a strongly correlated Fermi gas}, journal = {Annals of Physics} }
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@article{YY09, doi = {10.1007/s10955-009-9792-3}, url = {https://doi.org/10.1007
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2Fs10955-009-9792-3}, year = 2009, month = {jul}, publisher = {Springer Science and Business Media {LLC}}, volume = {136}, number = {3}, pages = {453--503}, author = {Horng-Tzer Yau and Jun Yin}, title = {The Second Order Upper Bound for the Ground Energy of a Bose Gas}, journal = {Journal of Statistical Physics} }
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%%
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%% Points package:
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%% \point commands
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%%
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%% TeX format
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\NeedsTeXFormat{LaTeX2e}[1995/12/01]
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%% package name
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\ProvidesPackage{point}[2017/06/13]
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%% options
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\newif\ifresetatsection
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\DeclareOption{reset_at_section}{\resetatsectiontrue}
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\DeclareOption{no_reset_at_section}{\resetatsectionfalse}
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\newif\ifresetatsubsection
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\DeclareOption{reset_at_subsection}{\resetatsubsectiontrue}
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\DeclareOption{no_reset_at_subsection}{\resetatsubsectionfalse}
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\newif\ifresetattheo
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\DeclareOption{reset_at_theo}{\resetattheotrue}
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\DeclareOption{no_reset_at_theo}{\resetattheofalse}
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\def\point@defaultoptions{
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\ExecuteOptions{reset_at_section, reset_at_subsection, no_reset_at_theo}
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\ProcessOptions
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%% reset at every new section
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\ifresetatsection
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\let\point@oldsection\section
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\gdef\section{\resetpointcounter\point@oldsection}
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\fi
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%% reset at every new subsection
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\ifresetatsubsection
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\let\point@oldsubsection\subsection
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\gdef\subsection{\resetpointcounter\point@oldsubsection}
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\fi
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%% reset at every new theorem
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\ifresetattheo
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\ifdefined\iantheotrue
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\let\point@oldtheo\theo
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\gdef\theo{\resetpointcounter\point@oldtheo}
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\fi
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\fi
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}
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%% point
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% counter
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\newcounter{pointcount}
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\def\point{
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\stepcounter{pointcount}
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\setcounter{subpointcount}{0}
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% hyperref anchor (only if the class is 'ian')
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\ifdefined\ifianclass
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\hrefanchor
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% define tag (for \label)
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\xdef\tag{\arabic{pointcount}}
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\fi
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% header
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\indent{\bf \arabic{pointcount}\ - }
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}
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%% subpoint
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% counter
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\newcounter{subpointcount}
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\def\subpoint{
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\stepcounter{subpointcount}
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\setcounter{subsubpointcount}0
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% hyperref anchor (only if the class is 'ian')
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\ifdefined\ifianclass
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\hrefanchor
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% define tag (for \label)
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\xdef\tag{\arabic{pointcount}-\arabic{subpointcount}}
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\fi
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% header
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\indent\hskip.5cm{\bf \arabic{pointcount}-\arabic{subpointcount}\ - }
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}
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%% subsubpoint
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% counter
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\newcounter{subsubpointcount}
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\def\subsubpoint{
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\stepcounter{subsubpointcount}
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% hyperref anchor (only if the class is 'ian')
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\ifdefined\ifianclass
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\hrefanchor
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% define tag (for \label)
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\xdef\tag{\arabic{pointcount}-\arabic{subpointcount}-\arabic{subsubpointcount}}
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\fi
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\indent\hskip1cm{\bf
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\arabic{pointcount}-\arabic{subpointcount}-\arabic{subsubpointcount}\ - }
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}
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%% reset point counters
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\def\resetpointcounter{
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\setcounter{pointcount}{0}
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\setcounter{subpointcount}{0}
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\setcounter{subsubpointcount}{0}
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}
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%% end
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\point@defaultoptions
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\endinput
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