%% %% 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 1.3e 2019/04/05 %% Copyright (C) 2013-2019 by Jean-Francois Burnol %% xintgcd: Euclidean algorithm with xint package %% --------------------------------------------------------------- \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 % : \let\z\endgroup \expandafter\let\expandafter\x\csname ver@xintgcd.sty\endcsname \expandafter\let\expandafter\w\csname ver@xintcore.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 xintcore.sty not yet loaded. \def\z{\endgroup\input xintcore.sty\relax}% \fi \else \def\empty {}% \ifx\x\empty % LaTeX, first loading, % variable is initialized, but \ProvidesPackage not yet seen \ifx\w\relax % xintcore.sty not yet loaded. \def\z{\endgroup\RequirePackage{xintcore}}% \fi \else \aftergroup\endinput % xintgcd already loaded. \fi \fi \fi \z% \XINTsetupcatcodes% defined in xintkernel.sty \XINT_providespackage \ProvidesPackage{xintgcd}% [2019/04/05 1.3e Euclide algorithm with xint package (JFB)]% \def\xintGCD {\romannumeral0\xintgcd }% \def\xintgcd #1#2{\xintiigcd {\xintNum{#1}}{\xintNum{#2}}}% \def\xintiiGCD {\romannumeral0\xintiigcd }% \def\xintiigcd #1{\expandafter\XINT_iigcd\romannumeral0\xintiiabs#1\xint:}% \def\XINT_iigcd #1#2\xint:#3% {% \expandafter\XINT_gcd_fork\expandafter#1% \romannumeral0\xintiiabs#3\xint:#1#2\xint: }% \def\XINT_gcd_fork #1#2% {% \xint_UDzerofork #1\XINT_gcd_Aiszero #2\XINT_gcd_Biszero 0\XINT_gcd_loop \krof #2% }% \def\XINT_gcd_AisZero #1\xint:#2\xint:{ #1}% \def\XINT_gcd_BisZero #1\xint:#2\xint:{ #2}% \def\XINT_gcd_loop #1\xint:#2\xint: {% \expandafter\expandafter\expandafter\XINT_gcd_CheckRem \expandafter\xint_secondoftwo \romannumeral0\XINT_div_prepare {#1}{#2}\xint:#1\xint: }% \def\XINT_gcd_CheckRem #1% {% \xint_gob_til_zero #1\XINT_gcd_end0\XINT_gcd_loop #1% }% \def\XINT_gcd_end0\XINT_gcd_loop #1\xint:#2\xint:{ #2}% \def\xintLCM {\romannumeral0\xintlcm}% \def\xintlcm #1#2{\xintiilcm{\xintNum{#1}}{\xintNum{#2}}}% \def\xintiiLCM {\romannumeral0\xintiilcm}% \def\xintiilcm #1{\expandafter\XINT_iilcm\romannumeral0\xintiiabs#1\xint:}% \def\XINT_iilcm #1#2\xint:#3% {% \expandafter\XINT_lcm_fork\expandafter#1% \romannumeral0\xintiiabs#3\xint:#1#2\xint: }% \def\XINT_lcm_fork #1#2% {% \xint_UDzerofork #1\XINT_lcm_iszero #2\XINT_lcm_iszero 0\XINT_lcm_notzero \krof #2% }% \def\XINT_lcm_iszero #1\xint:#2\xint:{ 0}% \def\XINT_lcm_notzero #1\xint:#2\xint: {% \expandafter\XINT_lcm_end\romannumeral0% \expandafter\expandafter\expandafter\XINT_gcd_CheckRem \expandafter\xint_secondoftwo \romannumeral0\XINT_div_prepare {#1}{#2}\xint:#1\xint: \xint:#1\xint:#2\xint: }% \def\XINT_lcm_end #1\xint:#2\xint:#3\xint:{\xintiimul {#2}{\xintiiQuo{#3}{#1}}}% \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 \krof #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 {#2}{#4}#1#3% #1#2=B, #3#4=A }% \def\XINT_bezout_botharezero #1\krof#2#300{{0}{0}{0}}% \def\XINT_bezout_firstiszero #1\krof#2#3#4#5% {% \xint_UDsignfork #4{{0}{-1}{#2}}% -{{0}{1}{#4#2}}% \krof }% \def\XINT_bezout_secondiszero #1\krof#2#3#4#5% {% \xint_UDsignfork #5{{-1}{0}{#3}}% -{{1}{0}{#5#3}}% \krof }% \def\XINT_bezout_minusminus #1#2#3#4% {% \expandafter\XINT_bezout_mm_post \romannumeral0\expandafter\XINT_bezout_preloop_a \romannumeral0\XINT_div_prepare {#1}{#2}{#1}% }% \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{#2}{#1}}% \def\XINT_bezout_minusplus #1#2#3#4% {% \expandafter\XINT_bezout_mp_post \romannumeral0\expandafter\XINT_bezout_preloop_a \romannumeral0\XINT_div_prepare {#1}{#4#2}{#1}% }% \def\XINT_bezout_mp_post #1#2% {% \expandafter\xint_exchangetwo_keepbraces\expandafter {\romannumeral0\xintiiopp {#2}}{#1}% }% \def\XINT_bezout_plusminus #1#2#3#4% {% \expandafter\XINT_bezout_pm_post \romannumeral0\expandafter\XINT_bezout_preloop_a \romannumeral0\XINT_div_prepare {#3#1}{#2}{#3#1}% }% \def\XINT_bezout_pm_post #1{\expandafter{\romannumeral0\xintiiopp{#1}}}% \def\XINT_bezout_plusplus #1#2#3#4% {% \expandafter\XINT_bezout_preloop_a \romannumeral0\XINT_div_prepare {#3#1}{#4#2}{#3#1}% }% \def\XINT_bezout_preloop_a #1#2#3% {% \if0#1\xint_dothis\XINT_bezout_preloop_exchange\fi \if0#2\xint_dothis\XINT_bezout_preloop_exit\fi \xint_orthat{\expandafter\XINT_bezout_loop_B}% \romannumeral0\XINT_div_prepare {#2}{#3}{#2}{#1}110% }% \def\XINT_bezout_preloop_exit \romannumeral0\XINT_div_prepare #1#2#3#4#5#6#7% {% {0}{1}{#2}% }% \def\XINT_bezout_preloop_exchange {% \expandafter\xint_exchangetwo_keepbraces \romannumeral0\expandafter\XINT_bezout_preloop_A }% \def\XINT_bezout_preloop_A #1#2#3#4% {% \if0#2\xint_dothis\XINT_bezout_preloop_exit\fi \xint_orthat{\expandafter\XINT_bezout_loop_B}% \romannumeral0\XINT_div_prepare {#2}{#3}{#2}{#1}% }% \def\XINT_bezout_loop_B #1#2% {% \if0#2\expandafter\XINT_bezout_exitA \else\expandafter\XINT_bezout_loop_C \fi {#1}{#2}% }% \def\XINT_bezout_loop_C #1#2#3#4#5#6#7% {% \expandafter\XINT_bezout_loop_D\expandafter {\romannumeral0\xintiiadd{\XINT_mul_plusplus{}{}#1\xint:#4\xint:}{#6}}% {\romannumeral0\xintiiadd{\XINT_mul_plusplus{}{}#1\xint:#5\xint:}{#7}}% {#2}{#3}{#4}{#5}% }% \def\XINT_bezout_loop_D #1#2% {% \expandafter\XINT_bezout_loop_E\expandafter{#2}{#1}% }% \def\XINT_bezout_loop_E #1#2#3#4% {% \expandafter\XINT_bezout_loop_b \romannumeral0\XINT_div_prepare {#3}{#4}{#3}{#2}{#1}% }% \def\XINT_bezout_loop_b #1#2% {% \if0#2\expandafter\XINT_bezout_exita \else\expandafter\XINT_bezout_loop_c \fi {#1}{#2}% }% \def\XINT_bezout_loop_c #1#2#3#4#5#6#7% {% \expandafter\XINT_bezout_loop_d\expandafter {\romannumeral0\xintiiadd{\XINT_mul_plusplus{}{}#1\xint:#4\xint:}{#6}}% {\romannumeral0\xintiiadd{\XINT_mul_plusplus{}{}#1\xint:#5\xint:}{#7}}% {#2}{#3}{#4}{#5}% }% \def\XINT_bezout_loop_d #1#2% {% \expandafter\XINT_bezout_loop_e\expandafter{#2}{#1}% }% \def\XINT_bezout_loop_e #1#2#3#4% {% \expandafter\XINT_bezout_loop_B \romannumeral0\XINT_div_prepare {#3}{#4}{#3}{#2}{#1}% }% \def\XINT_bezout_exita #1#2#3#4#5#6#7{{-#5}{#4}{#3}}% \def\XINT_bezout_exitA #1#2#3#4#5#6#7{{#5}{-#4}{#3}}% \def\xintEuclideAlgorithm {\romannumeral0\xinteuclidealgorithm }% \def\xinteuclidealgorithm #1% {% \expandafter\XINT_euc\expandafter{\romannumeral0\xintiiabs{\xintNum{#1}}}% }% \def\XINT_euc #1#2% {% \expandafter\XINT_euc_fork\romannumeral0\xintiiabs{\xintNum{#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\the\numexpr #1+\xint_c_i\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_a \romannumeral0% \XINT_rord_main {}#4{{#1}{#3}}% \xint: \xint_bye\xint_bye\xint_bye\xint_bye \xint_bye\xint_bye\xint_bye\xint_bye \xint: }% \def\XINT_euc_end_a #1#2#3{{#1}{#3}{#2}}% \def\xintBezoutAlgorithm {\romannumeral0\xintbezoutalgorithm }% \def\xintbezoutalgorithm #1% {% \expandafter \XINT_bezalg \expandafter{\romannumeral0\xintiiabs{\xintNum{#1}}}% }% \def\XINT_bezalg #1#2% {% \expandafter\XINT_bezalg_fork\romannumeral0\xintiiabs{\xintNum{#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\the\numexpr #1+\xint_c_i\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_a \romannumeral0% \XINT_rord_main {}#8{{#1}{#3}}% \xint: \xint_bye\xint_bye\xint_bye\xint_bye \xint_bye\xint_bye\xint_bye\xint_bye \xint: }% \def\XINT_bezalg_end_a #1#2#3#4{{#1}{#3}{0}{1}{#2}{#4}{1}{0}}% \def\xintGCDof {\romannumeral0\xintgcdof }% \def\xintgcdof #1{\expandafter\XINT_gcdof_a\romannumeral`&&@#1\xint:}% \def\XINT_gcdof_a #1{\expandafter\XINT_gcdof_b\romannumeral`&&@#1!}% \def\XINT_gcdof_b #1!#2{\expandafter\XINT_gcdof_c\romannumeral`&&@#2!{#1}!}% \def\XINT_gcdof_c #1{\xint_gob_til_xint: #1\XINT_gcdof_e\xint:\XINT_gcdof_d #1}% \def\XINT_gcdof_d #1!{\expandafter\XINT_gcdof_b\romannumeral0\xintgcd {#1}}% \def\XINT_gcdof_e #1!#2!{ #2}% \def\xintLCMof {\romannumeral0\xintlcmof }% \def\xintlcmof #1{\expandafter\XINT_lcmof_a\romannumeral`&&@#1\xint:}% \def\XINT_lcmof_a #1{\expandafter\XINT_lcmof_b\romannumeral`&&@#1!}% \def\XINT_lcmof_b #1!#2{\expandafter\XINT_lcmof_c\romannumeral`&&@#2!{#1}!}% \def\XINT_lcmof_c #1{\xint_gob_til_xint: #1\XINT_lcmof_e\xint:\XINT_lcmof_d #1}% \def\XINT_lcmof_d #1!{\expandafter\XINT_lcmof_b\romannumeral0\xintlcm {#1}}% \def\XINT_lcmof_e #1!#2!{ #2}% \def\xintTypesetEuclideAlgorithm {% \unless\ifdefined\xintAssignArray \errmessage {xintgcd: package xinttools is required for \string\xintTypesetEuclideAlgorithm}% \expandafter\xint_gobble_iii \fi \XINT_TypesetEuclideAlgorithm }% \def\XINT_TypesetEuclideAlgorithm #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 {% \unless\ifdefined\xintAssignArray \errmessage {xintgcd: package xinttools is required for \string\xintTypesetBezoutAlgorithm}% \expandafter\xint_gobble_iii \fi \XINT_TypesetBezoutAlgorithm }% \def\XINT_TypesetBezoutAlgorithm #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 }% \XINT_restorecatcodes_endinput% \endinput %% %% End of file `xintgcd.sty'.