%% %% This is file `xintgcd.sty', %% generated with the docstrip utility. %% %% The original source files were: %% %% xint.dtx (with options: `xintgcd') %% %% IMPORTANT NOTICE: %% %% For the copyright see the source file. %% %% Any modified versions of this file must be renamed %% with new filenames distinct from xintgcd.sty. %% %% For distribution of the original source see the terms %% for copying and modification in the file xint.dtx. %% %% This generated file may be distributed as long as the %% original source files, as listed above, are part of the %% same distribution. (The sources need not necessarily be %% in the same archive or directory.) %%---------------------------------------------------------------- %% The xint bundle (version 1.09n of April 1st, 2014) %% xintgcd: Euclidean algorithm with xint package %% Copyright (C) 2013-2014 by Jean-Francois Burnol %%---------------------------------------------------------------- \begingroup\catcode61\catcode48\catcode32=10\relax% \catcode13=5 % ^^M \endlinechar=13 % \catcode123=1 % { \catcode125=2 % } \catcode64=11 % @ \catcode35=6 % # \catcode44=12 % , \catcode45=12 % - \catcode46=12 % . \catcode58=12 % : \def\space { }% \let\z\endgroup \expandafter\let\expandafter\x\csname ver@xintgcd.sty\endcsname \expandafter\let\expandafter\w\csname ver@xint.sty\endcsname \expandafter \ifx\csname PackageInfo\endcsname\relax \def\y#1#2{\immediate\write-1{Package #1 Info: #2.}}% \else \def\y#1#2{\PackageInfo{#1}{#2}}% \fi \expandafter \ifx\csname numexpr\endcsname\relax \y{xintgcd}{\numexpr not available, aborting input}% \aftergroup\endinput \else \ifx\x\relax % plain-TeX, first loading of xintgcd.sty \ifx\w\relax % but xint.sty not yet loaded. \y{xintgcd}{now issuing \string\input\space xint.sty}% \def\z{\endgroup\input xint.sty\relax}% \fi \else \def\empty {}% \ifx\x\empty % LaTeX, first loading, % variable is initialized, but \ProvidesPackage not yet seen \ifx\w\relax % xint.sty not yet loaded. \y{xintgcd}{now issuing \string\RequirePackage{xint}}% \def\z{\endgroup\RequirePackage{xint}}% \fi \else \y{xintgcd}{I was already loaded, aborting input}% \aftergroup\endinput \fi \fi \fi \z% \begingroup\catcode61\catcode48\catcode32=10\relax% \catcode13=5 % ^^M \endlinechar=13 % \catcode123=1 % { \catcode125=2 % } \catcode64=11 % @ \catcode35=6 % # \catcode44=12 % , \catcode45=12 % - \catcode46=12 % . \catcode58=12 % : \ifdefined\PackageInfo \def\y#1#2{\PackageInfo{#1}{#2}}% \else \def\y#1#2{\immediate\write-1{Package #1 Info: #2.}}% \fi \def\empty {}% \expandafter\let\expandafter\w\csname ver@xint.sty\endcsname \ifx\w\relax % Plain TeX, user gave a file name at the prompt \y{xintgcd}{Loading of package xint failed, aborting input}% \aftergroup\endinput \fi \ifx\w\empty % LaTeX, user gave a file name at the prompt \y{xintgcd}{Loading of package xint failed, aborting input}% \aftergroup\endinput \fi \endgroup% \XINTsetupcatcodes% \XINT_providespackage \ProvidesPackage{xintgcd}% [2014/04/01 v1.09n Euclide algorithm with xint package (jfB)]% \def\xintGCD {\romannumeral0\xintgcd }% \def\xintgcd #1% {% \expandafter\XINT_gcd\expandafter{\romannumeral0\xintiabs {#1}}% }% \def\XINT_gcd #1#2% {% \expandafter\XINT_gcd_fork\romannumeral0\xintiabs {#2}\Z #1\Z }% \def\XINT_gcd_fork #1#2\Z #3#4\Z {% \xint_UDzerofork #1\XINT_gcd_BisZero #3\XINT_gcd_AisZero 0\XINT_gcd_loop \krof {#1#2}{#3#4}% }% \def\XINT_gcd_AisZero #1#2{ #1}% \def\XINT_gcd_BisZero #1#2{ #2}% \def\XINT_gcd_CheckRem #1#2\Z {% \xint_gob_til_zero #1\xint_gcd_end0\XINT_gcd_loop {#1#2}% }% \def\xint_gcd_end0\XINT_gcd_loop #1#2{ #2}% \def\XINT_gcd_loop #1#2% {% \expandafter\expandafter\expandafter \XINT_gcd_CheckRem \expandafter\xint_secondoftwo \romannumeral0\XINT_div_prepare {#1}{#2}\Z {#1}% }% \def\xintGCDof {\romannumeral0\xintgcdof }% \def\xintgcdof #1{\expandafter\XINT_gcdof_a\romannumeral-`0#1\relax }% \def\XINT_gcdof_a #1{\expandafter\XINT_gcdof_b\romannumeral-`0#1\Z }% \def\XINT_gcdof_b #1\Z #2{\expandafter\XINT_gcdof_c\romannumeral-`0#2\Z {#1}\Z}% \def\XINT_gcdof_c #1{\xint_gob_til_relax #1\XINT_gcdof_e\relax\XINT_gcdof_d #1}% \def\XINT_gcdof_d #1\Z {\expandafter\XINT_gcdof_b\romannumeral0\xintgcd {#1}}% \def\XINT_gcdof_e #1\Z #2\Z { #2}% \def\xintLCM {\romannumeral0\xintlcm}% \def\xintlcm #1% {% \expandafter\XINT_lcm\expandafter{\romannumeral0\xintiabs {#1}}% }% \def\XINT_lcm #1#2% {% \expandafter\XINT_lcm_fork\romannumeral0\xintiabs {#2}\Z #1\Z }% \def\XINT_lcm_fork #1#2\Z #3#4\Z {% \xint_UDzerofork #1\XINT_lcm_BisZero #3\XINT_lcm_AisZero 0\expandafter \krof \XINT_lcm_notzero\expandafter{\romannumeral0\XINT_gcd_loop {#1#2}{#3#4}}% {#1#2}{#3#4}% }% \def\XINT_lcm_AisZero #1#2#3#4#5{ 0}% \def\XINT_lcm_BisZero #1#2#3#4#5{ 0}% \def\XINT_lcm_notzero #1#2#3{\xintiimul {#2}{\xintiiQuo{#3}{#1}}}% \def\xintLCMof {\romannumeral0\xintlcmof }% \def\xintlcmof #1{\expandafter\XINT_lcmof_a\romannumeral-`0#1\relax }% \def\XINT_lcmof_a #1{\expandafter\XINT_lcmof_b\romannumeral-`0#1\Z }% \def\XINT_lcmof_b #1\Z #2{\expandafter\XINT_lcmof_c\romannumeral-`0#2\Z {#1}\Z}% \def\XINT_lcmof_c #1{\xint_gob_til_relax #1\XINT_lcmof_e\relax\XINT_lcmof_d #1}% \def\XINT_lcmof_d #1\Z {\expandafter\XINT_lcmof_b\romannumeral0\xintlcm {#1}}% \def\XINT_lcmof_e #1\Z #2\Z { #2}% \def\xintBezout {\romannumeral0\xintbezout }% \def\xintbezout #1% {% \expandafter\xint_bezout\expandafter {\romannumeral0\xintnum{#1}}% }% \def\xint_bezout #1#2% {% \expandafter\XINT_bezout_fork \romannumeral0\xintnum{#2}\Z #1\Z }% \def\XINT_bezout_fork #1#2\Z #3#4\Z {% \xint_UDzerosfork #1#3\XINT_bezout_botharezero #10\XINT_bezout_secondiszero #30\XINT_bezout_firstiszero 00{\xint_UDsignsfork #1#3\XINT_bezout_minusminus % A < 0, B < 0 #1-\XINT_bezout_minusplus % A > 0, B < 0 #3-\XINT_bezout_plusminus % A < 0, B > 0 --\XINT_bezout_plusplus % A > 0, B > 0 \krof }% \krof {#2}{#4}#1#3{#3#4}{#1#2}% #1#2=B, #3#4=A }% \edef\XINT_bezout_botharezero #1#2#3#4#5#6% {% \noexpand\xintError:NoBezoutForZeros\space {0}{0}{0}{0}{0}% }% \def\XINT_bezout_firstiszero #1#2#3#4#5#6% {% \xint_UDsignfork #3{ {0}{#3#1}{0}{1}{#1}}% -{ {0}{#3#1}{0}{-1}{#1}}% \krof }% \def\XINT_bezout_secondiszero #1#2#3#4#5#6% {% \xint_UDsignfork #4{ {#4#2}{0}{-1}{0}{#2}}% -{ {#4#2}{0}{1}{0}{#2}}% \krof }% \def\XINT_bezout_minusminus #1#2#3#4% {% \expandafter\XINT_bezout_mm_post \romannumeral0\XINT_bezout_loop_a 1{#1}{#2}1001% }% \def\XINT_bezout_mm_post #1#2% {% \expandafter\XINT_bezout_mm_postb\expandafter {\romannumeral0\xintiiopp{#2}}{\romannumeral0\xintiiopp{#1}}% }% \def\XINT_bezout_mm_postb #1#2% {% \expandafter\XINT_bezout_mm_postc\expandafter {#2}{#1}% }% \edef\XINT_bezout_mm_postc #1#2#3#4#5% {% \space {#4}{#5}{#1}{#2}{#3}% }% \def\XINT_bezout_minusplus #1#2#3#4% {% \expandafter\XINT_bezout_mp_post \romannumeral0\XINT_bezout_loop_a 1{#1}{#4#2}1001% }% \def\XINT_bezout_mp_post #1#2% {% \expandafter\XINT_bezout_mp_postb\expandafter {\romannumeral0\xintiiopp {#2}}{#1}% }% \edef\XINT_bezout_mp_postb #1#2#3#4#5% {% \space {#4}{#5}{#2}{#1}{#3}% }% \def\XINT_bezout_plusminus #1#2#3#4% {% \expandafter\XINT_bezout_pm_post \romannumeral0\XINT_bezout_loop_a 1{#3#1}{#2}1001% }% \def\XINT_bezout_pm_post #1% {% \expandafter \XINT_bezout_pm_postb \expandafter {\romannumeral0\xintiiopp{#1}}% }% \edef\XINT_bezout_pm_postb #1#2#3#4#5% {% \space {#4}{#5}{#1}{#2}{#3}% }% \def\XINT_bezout_plusplus #1#2#3#4% {% \expandafter\XINT_bezout_pp_post \romannumeral0\XINT_bezout_loop_a 1{#3#1}{#4#2}1001% }% \edef\XINT_bezout_pp_post #1#2#3#4#5% {% \space {#4}{#5}{#1}{#2}{#3}% }% \def\XINT_bezout_loop_a #1#2#3% {% \expandafter\XINT_bezout_loop_b \expandafter{\the\numexpr -#1\expandafter }% \romannumeral0\XINT_div_prepare {#2}{#3}{#2}% }% \def\XINT_bezout_loop_b #1#2#3#4#5#6#7#8% {% \expandafter \XINT_bezout_loop_c \expandafter {\romannumeral0\xintiiadd{\XINT_Mul{#5}{#2}}{#7}}% {\romannumeral0\xintiiadd{\XINT_Mul{#6}{#2}}{#8}}% {#1}{#3}{#4}{#5}{#6}% }% \def\XINT_bezout_loop_c #1#2% {% \expandafter \XINT_bezout_loop_d \expandafter {#2}{#1}% }% \def\XINT_bezout_loop_d #1#2#3#4#5% {% \XINT_bezout_loop_e #4\Z {#3}{#5}{#2}{#1}% }% \def\XINT_bezout_loop_e #1#2\Z {% \xint_gob_til_zero #1\xint_bezout_loop_exit0\XINT_bezout_loop_f {#1#2}% }% \def\XINT_bezout_loop_f #1#2% {% \XINT_bezout_loop_a {#2}{#1}% }% \def\xint_bezout_loop_exit0\XINT_bezout_loop_f #1#2% {% \ifcase #2 \or \expandafter\XINT_bezout_exiteven \else\expandafter\XINT_bezout_exitodd \fi }% \edef\XINT_bezout_exiteven #1#2#3#4#5% {% \space {#5}{#4}{#1}% }% \edef\XINT_bezout_exitodd #1#2#3#4#5% {% \space {-#5}{-#4}{#1}% }% \def\xintEuclideAlgorithm {\romannumeral0\xinteuclidealgorithm }% \def\xinteuclidealgorithm #1% {% \expandafter \XINT_euc \expandafter{\romannumeral0\xintiabs {#1}}% }% \def\XINT_euc #1#2% {% \expandafter\XINT_euc_fork \romannumeral0\xintiabs {#2}\Z #1\Z }% \def\XINT_euc_fork #1#2\Z #3#4\Z {% \xint_UDzerofork #1\XINT_euc_BisZero #3\XINT_euc_AisZero 0\XINT_euc_a \krof {0}{#1#2}{#3#4}{{#3#4}{#1#2}}{}\Z }% \def\XINT_euc_AisZero #1#2#3#4#5#6{ {1}{0}{#2}{#2}{0}{0}}% \def\XINT_euc_BisZero #1#2#3#4#5#6{ {1}{0}{#3}{#3}{0}{0}}% \def\XINT_euc_a #1#2#3% {% \expandafter\XINT_euc_b \expandafter {\the\numexpr #1+1\expandafter }% \romannumeral0\XINT_div_prepare {#2}{#3}{#2}% }% \def\XINT_euc_b #1#2#3#4% {% \XINT_euc_c #3\Z {#1}{#3}{#4}{{#2}{#3}}% }% \def\XINT_euc_c #1#2\Z {% \xint_gob_til_zero #1\xint_euc_end0\XINT_euc_a }% \def\xint_euc_end0\XINT_euc_a #1#2#3#4\Z% {% \expandafter\xint_euc_end_ \romannumeral0% \XINT_rord_main {}#4{{#1}{#3}}% \xint_relax \xint_bye\xint_bye\xint_bye\xint_bye \xint_bye\xint_bye\xint_bye\xint_bye \xint_relax }% \edef\xint_euc_end_ #1#2#3% {% \space {#1}{#3}{#2}% }% \def\xintBezoutAlgorithm {\romannumeral0\xintbezoutalgorithm }% \def\xintbezoutalgorithm #1% {% \expandafter \XINT_bezalg \expandafter{\romannumeral0\xintiabs {#1}}% }% \def\XINT_bezalg #1#2% {% \expandafter\XINT_bezalg_fork \romannumeral0\xintiabs {#2}\Z #1\Z }% \def\XINT_bezalg_fork #1#2\Z #3#4\Z {% \xint_UDzerofork #1\XINT_bezalg_BisZero #3\XINT_bezalg_AisZero 0\XINT_bezalg_a \krof 0{#1#2}{#3#4}1001{{#3#4}{#1#2}}{}\Z }% \def\XINT_bezalg_AisZero #1#2#3\Z{ {1}{0}{0}{1}{#2}{#2}{1}{0}{0}{0}{0}{1}}% \def\XINT_bezalg_BisZero #1#2#3#4\Z{ {1}{0}{0}{1}{#3}{#3}{1}{0}{0}{0}{0}{1}}% \def\XINT_bezalg_a #1#2#3% {% \expandafter\XINT_bezalg_b \expandafter {\the\numexpr #1+1\expandafter }% \romannumeral0\XINT_div_prepare {#2}{#3}{#2}% }% \def\XINT_bezalg_b #1#2#3#4#5#6#7#8% {% \expandafter\XINT_bezalg_c\expandafter {\romannumeral0\xintiiadd {\xintiiMul {#6}{#2}}{#8}}% {\romannumeral0\xintiiadd {\xintiiMul {#5}{#2}}{#7}}% {#1}{#2}{#3}{#4}{#5}{#6}% }% \def\XINT_bezalg_c #1#2#3#4#5#6% {% \expandafter\XINT_bezalg_d\expandafter {#2}{#3}{#4}{#5}{#6}{#1}% }% \def\XINT_bezalg_d #1#2#3#4#5#6#7#8% {% \XINT_bezalg_e #4\Z {#2}{#4}{#5}{#1}{#6}{#7}{#8}{{#3}{#4}{#1}{#6}}% }% \def\XINT_bezalg_e #1#2\Z {% \xint_gob_til_zero #1\xint_bezalg_end0\XINT_bezalg_a }% \def\xint_bezalg_end0\XINT_bezalg_a #1#2#3#4#5#6#7#8\Z {% \expandafter\xint_bezalg_end_ \romannumeral0% \XINT_rord_main {}#8{{#1}{#3}}% \xint_relax \xint_bye\xint_bye\xint_bye\xint_bye \xint_bye\xint_bye\xint_bye\xint_bye \xint_relax }% \edef\xint_bezalg_end_ #1#2#3#4% {% \space {#1}{#3}{0}{1}{#2}{#4}{1}{0}% }% \def\xintTypesetEuclideAlgorithm #1#2% {% l'algo remplace #1 et #2 par |#1| et |#2| \par \begingroup \xintAssignArray\xintEuclideAlgorithm {#1}{#2}\to\U \edef\A{\U2}\edef\B{\U4}\edef\N{\U1}% \setbox 0 \vbox{\halign {$##$\cr \A\cr \B \cr}}% \count 255 1 \xintloop \indent\hbox to \wd 0 {\hfil$\U{\numexpr 2*\count255\relax}$}% ${} = \U{\numexpr 2*\count255 + 3\relax} \times \U{\numexpr 2*\count255 + 2\relax} + \U{\numexpr 2*\count255 + 4\relax}$% \ifnum \count255 < \N \par \advance \count255 1 \repeat \endgroup }% \def\xintTypesetBezoutAlgorithm #1#2% {% \par \begingroup \xintAssignArray\xintBezoutAlgorithm {#1}{#2}\to\BEZ \edef\A{\BEZ2}\edef\B{\BEZ6}\edef\N{\BEZ1}% A = |#1|, B = |#2| \setbox 0 \vbox{\halign {$##$\cr \A\cr \B \cr}}% \count255 1 \xintloop \indent\hbox to \wd 0 {\hfil$\BEZ{4*\count255 - 2}$}% ${} = \BEZ{4*\count255 + 5} \times \BEZ{4*\count255 + 2} + \BEZ{4*\count255 + 6}$\hfill\break \hbox to \wd 0 {\hfil$\BEZ{4*\count255 +7}$}% ${} = \BEZ{4*\count255 + 5} \times \BEZ{4*\count255 + 3} + \BEZ{4*\count255 - 1}$\hfill\break \hbox to \wd 0 {\hfil$\BEZ{4*\count255 +8}$}% ${} = \BEZ{4*\count255 + 5} \times \BEZ{4*\count255 + 4} + \BEZ{4*\count255 }$ \par \ifnum \count255 < \N \advance \count255 1 \repeat \edef\U{\BEZ{4*\N + 4}}% \edef\V{\BEZ{4*\N + 3}}% \edef\D{\BEZ5}% \ifodd\N $\U\times\A - \V\times \B = -\D$% \else $\U\times\A - \V\times\B = \D$% \fi \par \endgroup }% \def\xintGCDof:csv #1{\expandafter\XINT_gcdof:_b\romannumeral-`0#1,,}% \def\XINT_gcdof:_b #1,#2,{\expandafter\XINT_gcdof:_c\romannumeral-`0#2,{#1},}% \def\XINT_gcdof:_c #1{\if #1,\expandafter\XINT_of:_e \else\expandafter\XINT_gcdof:_d\fi #1}% \def\XINT_gcdof:_d #1,{\expandafter\XINT_gcdof:_b\romannumeral0\xintgcd {#1}}% \def\xintLCMof:csv #1{\expandafter\XINT_lcmof:_a\romannumeral-`0#1,,}% \def\XINT_lcmof:_a #1,#2,{\expandafter\XINT_lcmof:_c\romannumeral-`0#2,{#1},}% \def\XINT_lcmof:_c #1{\if#1,\expandafter\XINT_of:_e \else\expandafter\XINT_lcmof:_d\fi #1}% \def\XINT_lcmof:_d #1,{\expandafter\XINT_lcmof:_a\romannumeral0\xintlcm {#1}}% \XINT_restorecatcodes_endinput% \endinput %% %% End of file `xintgcd.sty'.