%% %% This is file `mathtools.sty', %% generated with the docstrip utility. %% %% The original source files were: %% %% mathtools.dtx (with options: `package') %% %% It may be distributed and/or modified under the %% conditions of the LaTeX Project Public License, either version 1.3 %% of this license or (at your option) any later version. %% The latest version of this license is in %% http://www.latex-project.org/lppl.txt %% and version 1.3 or later is part of all distributions of LaTeX %% version 2003/12/01 or later. %% %% This work has the LPPL maintenance status "maintained". %% %% The Current Maintainer of this work is Morten H\o gholm. %% %% This work consists of the files mathtools.dtx and mathtools.ins %% and the derived file mathtools.sty. %% \NeedsTeXFormat{LaTeX2e} \ProvidesPackage{mathtools} [2004/10/10 v1.01a mathematical typesetting tools (MH)] \RequirePackage{keyval,calc} \RequirePackage{mhsetup}[2004/10/10] \MHInternalSyntaxOn \def\MT_options_name:{mathtools} \newcommand*\mathtoolsset[1]{\setkeys{\MT_options_name:}{#1}} \MH_new_boolean:n {fixamsmath} \DeclareOption{fixamsmath}{ \MH_set_boolean_T:n {fixamsmath} } \DeclareOption{donotfixamsmathbugs}{ \MH_set_boolean_F:n {fixamsmath} } \DeclareOption{allowspaces}{ \MH_let:NwN \MaybeMHPrecedingSpacesOff \relax \MH_let:NwN \MH_maybe_nospace_ifnextchar:Nnn \kernel@ifnextchar } \DeclareOption{disallowspaces}{ \MH_let:NwN \MaybeMHPrecedingSpacesOff \MHPrecedingSpacesOff \MH_let:NwN \MH_maybe_nospace_ifnextchar:Nnn \MH_nospace_ifnextchar:Nnn } \DeclareOption*{ \PassOptionsToPackage{\CurrentOption}{amsmath} } \ExecuteOptions{fixamsmath,disallowspaces} \ProcessOptions\relax \MHInternalSyntaxOff \RequirePackage{amsmath}[2000/07/18] \MHInternalSyntaxOn \AtEndOfPackage{\MHInternalSyntaxOff} \def\MT_true_false_error:{ \PackageError{mathtools} {You~ have~ to~ select~ either~ `true'~ or~ `false'} {I'll~ assume~ you~ chose~ `false'~ for~ now.} } \def\MT_define_tagform:nwnn #1[#2]#3#4{ \@namedef{MT_tagform_#1:n}##1 {\maketag@@@{#3\ignorespaces#2{##1}\unskip\@@italiccorr#4}} } \providecommand*\newtagform[1]{% \@ifundefined{MT_tagform_#1:n} {\@ifnextchar[% {\MT_define_tagform:nwnn #1}% {\MT_define_tagform:nwnn #1[]}% }{\PackageError{mathtools} {The~ tag~ form~ `#1'~ is~ already~ defined\MessageBreak You~ probably~ want~ to~ look~ up~ \@backslashchar renewtagform~ instead} {I~ will~ just~ ignore~ your~ wish~ for~ now.}} } \newtagform{default}{(}{)} \providecommand*\renewtagform[1]{% \@ifundefined{MT_tagform_#1:n} {\PackageError{mathtools} {The~ tag~ form~ `#1'~ is~ not~ defined\MessageBreak You~ probably~ want~ to~ look~ up~ \@backslashchar newtagform~ instead} {I~ will~ just~ ignore~ your~ wish~ for~ now.}} {\@ifnextchar[% {\MT_define_tagform:nwnn #1}% {\MT_define_tagform:nwnn #1[]}% } } \providecommand*\usetagform[1]{% \@ifundefined{MT_tagform_#1:n} { \PackageError{mathtools}{% You~ have~ chosen~ the~ tag~ form~ `#1'\MessageBreak but~ it~ appears~ to~ be~ undefined} {I~ will~ use~ the~ default~ tag~ form~ instead.}% \@namedef{tagform@}{\@nameuse{MT_tagform_default:n}} } { \@namedef{tagform@}{\@nameuse{MT_tagform_#1:n}} } \MH_if_boolean:nT {show_only_refs}{ \MH_let:NwN \MT_prev_tagform:n \tagform@ \def\tagform@##1{\MT_extended_tagform:n {##1}} } } \MH_new_boolean:n {manual_tag} \MH_new_boolean:n {raw_maketag} \MH_let:NwN \MT_AmS_tag_in_align: \tag@in@align \def\tag@in@align{ \global\MH_set_boolean_T:n {manual_tag} \MT_AmS_tag_in_align: } \def\tag@in@display#1#{ \relax \global\MH_set_boolean_T:n {manual_tag} \tag@in@display@a{#1} } \def\MT_extended_tagform:n #1{ \MH_set_boolean_F:n {raw_maketag} \if_meaning:NN \df@label\@empty \MH_if_boolean:nT {manual_tag} { \MH_if_boolean:nTF {show_manual_tags} { \MT_prev_tagform:n {#1} } { \stepcounter{equation} } } \else: \MH_if_boolean:nTF {manual_tag} { \MH_if_boolean:nTF {show_manual_tags} { \MT_prev_tagform:n {#1} } { \@ifundefined{MT_r_\df@label} { } { \MT_prev_tagform:n {#1} } } } { \@ifundefined{MT_r_\df@label} { } { \refstepcounter{equation}\MT_prev_tagform:n {#1} } } \fi: \global\MH_set_boolean_T:n {raw_maketag} } \def\MT_extended_maketag:n #1{ \ifx\df@label\@empty \MT_maketag:n {#1} \else: \MH_if_boolean:nTF {raw_maketag} { \MH_if_boolean:nTF {show_manual_tags} { \MT_maketag:n {#1} } { \@ifundefined{MT_r_\df@label} { } { \MT_maketag:n {#1} } } } { \MT_maketag:n {#1} } \fi: \global\MH_set_boolean_F:n {manual_tag} } \def\MT_extended_eqref:n #1{ \protected@write\@auxout{} {\string\MT@newlabel{#1}} \textup{\MT_prev_tagform:n {\ref{#1}}} } \newcommand*\refeq[1]{ \textup{\ref{#1}} } \def\MT_extended_refeq:n #1{ \protected@write\@auxout{} {\string\MT@newlabel{#1}} \textup{\ref{#1}} } \newcommand*\MT@newlabel[1]{ \global\@namedef{MT_r_#1}{} } \MH_new_boolean:n {show_only_refs} \MH_new_boolean:n {show_manual_tags} \define@key{\MT_options_name:}{showmanualtags}[true]{ \@ifundefined{boolean_show_manual_tags_#1:} { \MT_true_false_error: \@nameuse{boolean_show_manual_tags_false:} } { \@nameuse{boolean_show_manual_tags_#1:} } } \newcommand*\MT_showonlyrefs_true:{ \MH_if_boolean:nF {show_only_refs}{ \MH_set_boolean_T:n {show_only_refs} \MH_let:NwN \MT_incr_eqnum: \incr@eqnum \MH_let:NwN \incr@eqnum \@empty \MH_let:NwN \MT_array_parbox_restore: \@arrayparboxrestore \@xp\def\@xp\@arrayparboxrestore\@xp{\@arrayparboxrestore \MH_let:NwN \incr@eqnum \@empty } \MH_let:NwN \MT_prev_tagform:n \tagform@ \MH_let:NwN \MT_eqref:n \eqref \MH_let:NwN \MT_refeq:n \refeq \MH_let:NwN \MT_maketag:n \maketag@@@ \MH_let:NwN \maketag@@@ \MT_extended_maketag:n \def\tagform@##1{\MT_extended_tagform:n {##1}} \MH_let:NwN \eqref \MT_extended_eqref:n \MH_let:NwN \refeq \MT_extended_refeq:n } } \def\MT_showonlyrefs_false: { \MH_if_boolean:nT {show_only_refs}{ \MH_set_boolean_F:n {show_only_refs} \MH_let:NwN \tagform@ \MT_prev_tagform:n \MH_let:NwN \eqref \MT_eqref:n \MH_let:NwN \refeq \MT_refeq:n \MH_let:NwN \maketag@@@ \MT_maketag:n \MH_let:NwN \incr@eqnum \MT_incr_eqnum: \MH_let:NwN \@arrayparboxrestore \MT_array_parbox_restore: } } \define@key{\MT_options_name:}{showonlyrefs}[true]{ \@nameuse{MT_showonlyrefs_#1:} } \renewcommand\nonumber{ \if@eqnsw \if_meaning:NN \incr@eqnum\@empty \MH_if_boolean:nF {show_only_refs} {\addtocounter{equation}\m@ne} \fi: \fi: \MH_let:NwN \print@eqnum\@empty \MH_let:NwN \incr@eqnum\@empty \global\@eqnswfalse } \providecommand*\xleftrightarrow[2][]{% \ext@arrow 3095\MT_leftrightarrow_fill:{#1}{#2}} \def\MT_leftrightarrow_fill:{% \arrowfill@\leftarrow\relbar\rightarrow} \providecommand*\xLeftarrow[2][]{% \ext@arrow 0055{\Leftarrowfill@}{#1}{#2}} \providecommand*\xRightarrow[2][]{% \ext@arrow 0055{\Rightarrowfill@}{#1}{#2}} \providecommand*\xLeftrightarrow[2][]{% \ext@arrow 0055{\Leftrightarrowfill@}{#1}{#2}} \def\MT_rightharpoondown_fill:{% \arrowfill@\relbar\relbar\rightharpoondown} \def\MT_rightharpoonup_fill:{% \arrowfill@\relbar\relbar\rightharpoonup} \def\MT_leftharpoondown_fill:{% \arrowfill@\leftharpoondown\relbar\relbar} \def\MT_leftharpoonup_fill:{% \arrowfill@\leftharpoonup\relbar\relbar} \providecommand*\xrightharpoondown[2][]{% \ext@arrow 0359\MT_rightharpoondown_fill:{#1}{#2}} \providecommand*\xrightharpoonup[2][]{% \ext@arrow 0359\MT_rightharpoonup_fill:{#1}{#2}} \providecommand*\xleftharpoondown[2][]{% \ext@arrow 3095\MT_leftharpoondown_fill:{#1}{#2}} \providecommand*\xleftharpoonup[2][]{% \ext@arrow 3095\MT_leftharpoonup_fill:{#1}{#2}} \providecommand*\xleftrightharpoons[2][]{\mathrel{% \raise.22ex\hbox{% $\ext@arrow 3095\MT_leftharpoonup_fill:{\phantom{#1}}{#2}$}% \setbox0=\hbox{% $\ext@arrow 0359\MT_rightharpoondown_fill:{#1}{\phantom{#2}}$}% \kern-\wd0 \lower.22ex\box0}} \providecommand*\xrightleftharpoons[2][]{\mathrel{% \raise.22ex\hbox{% $\ext@arrow 3095\MT_rightharpoonup_fill:{\phantom{#1}}{#2}$}% \setbox0=\hbox{% $\ext@arrow 0359\MT_leftharpoondown_fill:{#1}{\phantom{#2}}$}% \kern-\wd0 \lower.22ex\box0}} \providecommand*\xhookleftarrow[2][]{% \ext@arrow 3095\MT_hookleft_fill:{#1}{#2}} \def\MT_hookleft_fill:{% \arrowfill@\leftarrow\relbar{\relbar\joinrel\rhook}} \providecommand*\xhookrightarrow[2][]{% \ext@arrow 3095\MT_hookright_fill:{#1}{#2}} \def\MT_hookright_fill:{% \arrowfill@{\lhook\joinrel\relbar}\relbar\rightarrow} \providecommand*\xmapsto[2][]{% \ext@arrow 0395\MT_mapsto_fill:{#1}{#2}} \def\MT_mapsto_fill:{% \arrowfill@{\mapstochar\relbar}\relbar\rightarrow} \providecommand*\underbracket{ \@ifnextchar[ {\MT_underbracket_I:w} {\MT_underbracket_I:w[\l_MT_bracketheight_fdim]}} \def\MT_underbracket_I:w[#1]{ \@ifnextchar[ {\MT_underbracket_II:w[#1]} {\MT_underbracket_II:w[#1][.7\fontdimen5\textfont2]}} \def\MT_underbracket_II:w[#1][#2]#3{% \mathop{\vtop{\m@th\ialign{## \crcr $\hfil\displaystyle{#3}\hfil$% \crcr \noalign{\kern .2\fontdimen5\textfont2 \nointerlineskip}% \upbracketfill {#1}{#2}% \crcr}}} \limits} \def\upbracketfill#1#2{% \sbox\z@{$\braceld$} \edef\l_MT_bracketheight_fdim{\the\ht\z@}% \upbracketend{#1}{#2} \leaders \vrule \@height \z@ \@depth #1 \hfill \upbracketend{#1}{#2}% } \def\upbracketend#1#2{\vrule \@height #2 \@width #1\relax} \providecommand*\overbracket{ \@ifnextchar[ {\MT_overbracket_I:w} {\MT_overbracket_I:w[\l_MT_bracketheight_fdim]}} \def\MT_overbracket_I:w[#1]{ \@ifnextchar[ {\MT_overbracket_II:w[#1]} {\MT_overbracket_II:w[#1][.7\fontdimen5\textfont2]}} \def\MT_overbracket_II:w[#1][#2]#3{% \mathop{\vbox{\m@th\ialign{## \crcr \downbracketfill{#1}{#2}% \crcr \noalign{\kern .2\fontdimen5\textfont2 \nointerlineskip}% $\hfil\displaystyle{#3}\hfil$ \crcr}}}% \limits} \def\downbracketfill#1#2{% \sbox\z@{$\braceld$}\edef\l_MT_bracketheight_fdim{\the\ht\z@} \downbracketend{#1}{#2} \leaders \vrule \@height #1 \@depth \z@ \hfill \downbracketend{#1}{#2}% } \def\downbracketend#1#2{\vrule \@width #1\@depth #2\relax} \MH_let:NwN \LaTeXunderbrace \underbrace \def\underbrace#1{\mathop{\vtop{\m@th\ialign{##\crcr $\hfil\displaystyle{#1}\hfil$\crcr \noalign{\kern.7\fontdimen5\textfont2\nointerlineskip}% \upbracefill\crcr\noalign{\kern.5\fontdimen5\textfont2}}}}\limits} \MH_let:NwN \LaTeXoverbrace \overbrace \def\overbrace#1{\mathop{\vbox{\m@th\ialign{##\crcr \noalign{\kern.5\fontdimen5\textfont2}% \downbracefill\crcr \noalign{\kern.7\fontdimen5\textfont2\nointerlineskip}% $\hfil\displaystyle{#1}\hfil$\crcr}}}\limits} \providecommand*\lparen{(} \providecommand*\rparen{)} \def\vcentcolon{\mathrel{\mathop\ordinarycolon}} \begingroup \catcode`\:=\active \lowercase{\endgroup \ifnum\mathcode`\:=32768\relax \let\ordinarycolon= :% \else \mathchardef\ordinarycolon\mathcode`\: % \fi \let :\vcentcolon } \MH_new_boolean:n {center_colon} \define@key{\MT_options_name:}{centercolon}[true]{ \@ifundefined{MT_active_colon_#1:} { \MT_true_false_error:n \@nameuse{MT_active_colon_false:} } { \@nameuse{MT_active_colon_#1:} } } \def\MT_active_colon_true: { \MH_if_boolean:nF {center_colon}{ \MH_set_boolean_T:n {center_colon} \edef\MT_active_colon_false: {\mathcode`\noexpand\:=\the\mathcode`\:\relax} \mathcode`\:=32768 } } \AtBeginDocument{ \providecommand*\dblcolon{\vcentcolon\mkern-.9mu\vcentcolon} \providecommand*\coloneqq{\vcentcolon\mkern-1.2mu=} \providecommand*\Coloneqq{\dblcolon\mkern-1.2mu=} \providecommand*\coloneq{\vcentcolon\mkern-1.2mu\mathrel{-}} \providecommand*\Coloneq{\dblcolon\mkern-1.2mu\mathrel{-}} \providecommand*\eqqcolon{=\mkern-1.2mu\vcentcolon} \providecommand*\Eqqcolon{=\mkern-1.2mu\dblcolon} \providecommand*\eqcolon{\mathrel{-}\mkern-1.2mu\vcentcolon} \providecommand*\Eqcolon{\mathrel{-}\mkern-1.2mu\dblcolon} \providecommand*\colonapprox{\vcentcolon\mkern-1.2mu\approx} \providecommand*\Colonapprox{\dblcolon\mkern-1.2mu\approx} \providecommand*\colonsim{\vcentcolon\mkern-1.2mu\sim} \providecommand*\Colonsim{\dblcolon\mkern-1.2mu\sim} } \MH_new_boolean:n {mult_firstline} \MH_new_boolean:n {outer_mult} \newcount\g_MT_multlinerow_int \newdimen\l_MT_multwidth_dim \newcommand*\MT_test_for_tcb_other:nnnnn [1]{ \if:w t#1\relax \expandafter\MH_use_choice_i:nnnn \else: \if:w c#1\relax \expandafter\expandafter\expandafter\MH_use_choice_ii:nnnn \else: \if:w b#1\relax \expandafter\expandafter\expandafter \expandafter\expandafter\expandafter\expandafter \MH_use_choice_iii:nnnn \else: \expandafter\expandafter\expandafter \expandafter\expandafter\expandafter\expandafter \MH_use_choice_iv:nnnn \fi: \fi: \fi: } \def\MT_mult_invisible_line: { \crcr \global\MH_set_boolean_F:n {mult_firstline} \hbox to \l_MT_multwidth_dim{}\crcr \noalign{\vskip-\baselineskip \vskip-\normallineskip} } \def\MT_mult_mathcr_atat:w [#1]{% \if_num:w 0=`{\fi: \iffalse}\fi: \MH_if_boolean:nT {mult_firstline}{ \kern\l_MT_mult_left_fdim \MT_mult_invisible_line: } \crcr \noalign{\vskip#1\relax} \global\advance\g_MT_multlinerow_int\@ne \if_num:w \g_MT_multlinerow_int=\l_MT_multline_lastline_fint \MH_let:NwN \math@cr@@\MT_mult_last_mathcr:w \fi: } \def\MT_mult_firstandlast_mathcr:w [#1]{% \if_num:w 0=`{\fi: \iffalse}\fi: \kern\l_MT_mult_left_fdim \MT_mult_invisible_line: \noalign{\vskip#1\relax} \kern\l_MT_mult_right_fdim } \def\MT_mult_last_mathcr:w [#1]{ \if_num:w 0=`{\fi: \iffalse}\fi:\math@cr@@@ \noalign{\vskip#1\relax} \kern\l_MT_mult_right_fdim} \newcommand\MT_start_mult:N [1]{ \MT_test_for_tcb_other:nnnnn {#1} { \MH_let:NwN \MT_next:\vtop } { \MH_let:NwN \MT_next:\vcenter } { \MH_let:NwN \MT_next:\vbox } { \PackageError{mathtools} {Invalid~ position~ specifier.~ I'll~ try~ to~ recover~ with~ `c'}\@ehc } \collect@body\MT_mult_internal:n } \newcommand*\MT_shoveright:wn [2][0pt]{% #2\hfilneg \setlength\@tempdima{#1} \kern\@tempdima } \newcommand*\MT_shoveleft:wn [2][0pt]{% \hfilneg \setlength\@tempdima{#1} \kern\@tempdima #2 } \newcommand*\MT_mult_internal:n [1]{ \MH_if_boolean:nF {outer_mult}{\null\,} \MT_next: \bgroup \Let@ \def\l_MT_multline_lastline_fint{0 } \chardef\dspbrk@context\@ne \restore@math@cr \MH_let:NwN \math@cr@@\MT_mult_mathcr_atat:w \MH_let:NwN \shoveleft\MT_shoveleft:wn \MH_let:NwN \shoveright\MT_shoveright:wn \spread@equation \MH_set_boolean_F:n {mult_firstline} \MT_measure_mult:n {#1} \if_dim:w \l_MT_multwidth_dim<\l_MT_multline_measure_fdim \MH_setlength:dn \l_MT_multwidth_dim{\l_MT_multline_measure_fdim} \fi \MH_set_boolean_T:n {mult_firstline} \if_num:w \l_MT_multline_lastline_fint=\@ne \MH_let:NwN \math@cr@@ \MT_mult_firstandlast_mathcr:w \fi: \ialign\bgroup \hfil\strut@$\m@th\displaystyle{}##$\hfil \crcr \hfilneg #1 } \newcommand\MT_measure_mult:n [1]{ \begingroup \g_MT_multlinerow_int\@ne \MH_let:NwN \label\MT_gobblelabel:w \MH_let:NwN \tag\gobble@tag \setbox\z@\vbox{ \ialign{\strut@$\m@th\displaystyle{}##$ \crcr #1 \crcr } } \xdef\l_MT_multline_measure_fdim{\the\wdz@} \advance\g_MT_multlinerow_int\m@ne \xdef\l_MT_multline_lastline_fint{\number\g_MT_multlinerow_int} \endgroup \g_MT_multlinerow_int\@ne } \MaybeMHPrecedingSpacesOff \newcommand*\MT_multlined_second_arg:w [1][\@empty]{ \MT_test_for_tcb_other:nnnnn {#1} {\def\MT_mult_default_pos:{#1}} {\def\MT_mult_default_pos:{#1}} {\def\MT_mult_default_pos:{#1}} { \if_meaning:NN \@empty#1\@empty \else: \setlength \l_MT_multwidth_dim{#1} \fi: } \MT_start_mult:N \MT_mult_default_pos: } \newenvironment{multlined}[1][] { \MT_test_for_tcb_other:nnnnn {#1} {\def\MT_mult_default_pos:{#1}} {\def\MT_mult_default_pos:{#1}} {\def\MT_mult_default_pos:{#1}} { \if_meaning:NN \@empty#1\@empty \else: \setlength \l_MT_multwidth_dim{#1} \fi: } \MT_multlined_second_arg:w } { \hfilneg \endaligned } \MHPrecedingSpacesOn \define@key{\MT_options_name:} {firstline-afterskip}{\def\l_MT_mult_left_fdim{#1}} \define@key{\MT_options_name:} {lastline-preskip}{\def\l_MT_mult_right_fdim{#1}} \define@key{\MT_options_name:} {multlined-width}{\setlength \l_MT_multwidth_dim{#1}} \define@key{\MT_options_name:} {multlined-pos}{\def\MT_mult_default_pos:{#1}} \setkeys{\MT_options_name:}{ firstline-afterskip=\multlinegap, lastline-preskip=\multlinegap, multlined-width=0pt, multlined-pos=c, } \def\MT_gobblelabel:w #1{} \newcommand*\DeclarePairedDelimiter[3]{% \@ifdefinable{#1}{ \edef\MT_next: {\MH_cs_to_str:N #1} \@namedef{MT_delim_\MT_next: _star:}##1 {\left#2 ##1 \right #3}% \@xp\@xp\@xp \newcommand \@xp\csname MT_delim_\MT_next: _nostar:\endcsname[2][\\@gobble] { \edef\MT_next: {\MH_cs_to_str:N ##1} \@nameuse {\MT_next: l} #2 ##2 \@nameuse {\MT_next: r} #3} \newcommand{#1}{ \@ifstar {\@nameuse{MT_delim_\MH_cs_to_str:N #1 _star:}} {\@nameuse{MT_delim_\MH_cs_to_str:N #1 _nostar:}} } } } \def\MT_start_cases:nn #1#2{ \RIfM@\else \nonmatherr@{\begin{\@currenvir}}% \fi \left\lbrace \vcenter \bgroup \Let@ \chardef\dspbrk@context\@ne \restore@math@cr \spread@equation \ialign\bgroup \strut@$\m@th\displaystyle{##}$\hfil\strut@ #2 \crcr } \newcommand*\newcases[3]{ \newenvironment{#1} {\MT_start_cases:nn {#2}{#3}} {\endaligned\right.} } \newcommand*\renewcases[3]{ \renewenvironment{#1} {\MT_start_cases:nn {#2}{#3}} {\endaligned\right.} } \newcases{dcases}{\quad}{$\m@th\displaystyle{##}$\hfil} \newcases{dcases*}{\quad}{{##}\hfil} \def\MT_matrix_begin:N #1{% \hskip -\arraycolsep \MH_let:NwN \@ifnextchar \MH_nospace_ifnextchar:Nnn \array{*\c@MaxMatrixCols #1}} \def\MT_matrix_end:{\endarray \hskip -\arraycolsep} \MaybeMHPrecedingSpacesOff \newenvironment{matrix*}[1][c] {\MT_matrix_begin:N #1} {\MT_matrix_end:} \newenvironment{pmatrix*}[1][c] {\left(\MT_matrix_begin:N #1} {\MT_matrix_end:\right)} \newenvironment{bmatrix*}[1][c] {\left[\MT_matrix_begin:N #1} {\MT_matrix_end:\right]} \newenvironment{Bmatrix*}[1][c] {\left\lbrace\MT_matrix_begin:N #1} {\MT_matrix_end:\right\rbrace} \newenvironment{vmatrix*}[1][c] {\left\lvert\MT_matrix_begin:N #1} {\MT_matrix_end:\right\rvert} \newenvironment{Vmatrix*}[1][c] {\left\lVert\MT_matrix_begin:N #1} {\MT_matrix_end:\right\lVert} \MHPrecedingSpacesOn \newcommand*\smashoperator[2][lr]{ \def\MT_smop_use:NNNNN {\@nameuse{MT_smop_smash_#1:NNNNN}} \toks@{#2} \expandafter\MT_smop_get_args:wwwNnNn \the\toks@\@nil\@nil\@nil\@nil\@nil\@nil\@@nil } \def\MT_smop_remove_nil_vi:N #1\@nil\@nil\@nil\@nil\@nil\@nil{#1} \def\MT_smop_mathop:n {\mathop} \def\MT_smop_limits: {\limits} \MH_new_boolean:n {smop_one} \MH_new_boolean:n {smop_two} \def\MT_smop_get_args:wwwNnNn #1#2#3#4#5#6#7\@@nil{% \begingroup \def\MT_smop_arg_A: {#1} \def\MT_smop_arg_B: {#2} \def\MT_smop_arg_C: {#3} \def\MT_smop_arg_D: {#4} \def\MT_smop_arg_E: {#5} \def\MT_smop_arg_F: {#6} \def\MT_smop_arg_G: {#7} \if_meaning:NN \MT_smop_arg_A: \MT_smop_mathop:n \if_meaning:NN \MT_smop_arg_C:\MT_smop_limits: \def\MT_smop_final_arg_A:{#1{#2}}% \if_meaning:NN \MT_smop_arg_D: \@nnil \else: \MH_set_boolean_T:n {smop_one} \MH_let:NwN \MT_smop_final_arg_B: \MT_smop_arg_D: \MH_let:NwN \MT_smop_final_arg_C: \MT_smop_arg_E: \if_meaning:NN \MT_smop_arg_F: \@nnil \else: \MH_set_boolean_T:n {smop_two} \MH_let:NwN \MT_smop_final_arg_D: \MT_smop_arg_F: \edef\MT_smop_final_arg_E: {\expandafter\MT_smop_remove_nil_vi:N \MT_smop_arg_G: } \fi: \fi: \else: \def\MT_smop_final_arg_A:{#1{#2}}% \if_meaning:NN \MT_smop_arg_D: \@nnil \else: \MH_set_boolean_T:n {smop_one} \MH_let:NwN \MT_smop_final_arg_B: \MT_smop_arg_C: \MH_let:NwN \MT_smop_final_arg_C: \MT_smop_arg_D: \if_meaning:NN \MT_smop_arg_F: \@nnil \else: \MH_set_boolean_T:n {smop_two} \MH_let:NwN \MT_smop_final_arg_D: \MT_smop_arg_E: \MH_let:NwN \MT_smop_final_arg_E: \MT_smop_arg_F: \fi: \fi: \fi: \else: \if_meaning:NN \MT_smop_arg_B:\MT_smop_limits: \def\MT_smop_final_arg_A:{#1}% \if_meaning:NN \MT_smop_arg_D: \@nnil \else: \MH_set_boolean_T:n {smop_one} \MH_let:NwN \MT_smop_final_arg_B: \MT_smop_arg_C: \MH_let:NwN \MT_smop_final_arg_C: \MT_smop_arg_D: \if_meaning:NN \MT_smop_arg_F: \@nnil \else: \MH_set_boolean_T:n {smop_two} \MH_let:NwN \MT_smop_final_arg_D: \MT_smop_arg_E: \MH_let:NwN \MT_smop_final_arg_E: \MT_smop_arg_F: \fi: \fi: \else: \def\MT_smop_final_arg_A:{#1}% \if_meaning:NN \MT_smop_arg_C: \@nnil \else: \MH_set_boolean_T:n {smop_one} \MH_let:NwN \MT_smop_final_arg_B: \MT_smop_arg_B: \MH_let:NwN \MT_smop_final_arg_C: \MT_smop_arg_C: \if_meaning:NN \MT_smop_arg_D: \@nnil \else: \MH_set_boolean_T:n {smop_two} \MH_let:NwN \MT_smop_final_arg_D: \MT_smop_arg_D: \MH_let:NwN \MT_smop_final_arg_E: \MT_smop_arg_E: \fi: \fi: \fi: \fi: \MH_if_boolean:nT {smop_one}{ \MT_smop_measure:NNNNN \MT_smop_final_arg_A: \MT_smop_final_arg_B: \MT_smop_final_arg_C: \MT_smop_final_arg_D: \MT_smop_final_arg_E: } \MT_smop_use:NNNNN \MT_smop_final_arg_A: \MT_smop_final_arg_B: \MT_smop_final_arg_C: \MT_smop_final_arg_D: \MT_smop_final_arg_E: \endgroup } \def\MT_smop_needed_args:NNNNN #1#2#3#4#5{% \displaystyle #1 \MH_if_boolean:nT {smop_one}{ \limits#2{\MT_cramped_clap_internal:Nn \scriptstyle{#3}} \MH_if_boolean:nT {smop_two}{ #4{\MT_cramped_clap_internal:Nn \scriptstyle{#5}} } } } \def\MT_smop_measure:NNNNN #1#2#3#4#5{% \MH_let:NwN \MT_saved_mathclap:Nn \MT_cramped_clap_internal:Nn \MH_let:NwN \MT_cramped_clap_internal:Nn \@secondoftwo \sbox\z@{$\m@th\MT_smop_needed_args:NNNNN #1#2#3#4#5$} \MH_let:NwN \MT_cramped_clap_internal:Nn \MT_saved_mathclap:Nn \sbox\tw@{$\m@th\displaystyle#1$} \@tempdima=.5\wd0 \advance\@tempdima-.5\wd2 } \def\MT_smop_smash_l:NNNNN #1#2#3#4#5{ \MT_smop_needed_args:NNNNN #1#2#3#4#5\kern\@tempdima } \def\MT_smop_smash_r:NNNNN #1#2#3#4#5{ \kern\@tempdima\MT_smop_needed_args:NNNNN #1#2#3#4#5 } \def\MT_smop_smash_lr:NNNNN #1#2#3#4#5{ \MT_smop_needed_args:NNNNN #1#2#3#4#5 } \def\MT_vphantom:Nn {\v@true\h@false\MT_internal_phantom:N} \def\MT_hphantom:Nn {\v@false\h@true\MT_internal_phantom:N} \def\MT_phantom:Nn {\v@true\h@true\MT_internal_phantom:N} \def\MT_internal_phantom:N #1{ \ifmmode \expandafter\mathph@nt\expandafter#1 \else \expandafter\makeph@nt \fi } \newcommand*\adjustlimits[6]{ \sbox\z@{$\m@th \displaystyle #1$} \sbox\tw@{$\m@th \displaystyle #4$} \@tempdima=\dp\z@ \advance\@tempdima-\dp\tw@ \if_dim:w \@tempdima>\z@ \mathop{#1}\limits#2{#3} \else: \mathop{#1\MT_vphantom:Nn \displaystyle{#4}}\limits #2{ \def\finsm@sh{\ht\z@\z@ \box\z@} \mathsm@sh\scriptstyle{\MT_cramped_internal:Nn \scriptstyle{#3}} \MT_vphantom:Nn \scriptstyle {\MT_cramped_internal:Nn \scriptstyle{#6}} } \fi: \if_dim:w \@tempdima>\z@ \mathop{#4\MT_vphantom:Nn \displaystyle{#1}}\limits #5 { \MT_vphantom:Nn \scriptstyle {\MT_cramped_internal:Nn \scriptstyle{#3}} \def\finsm@sh{\ht\z@\z@ \box\z@} \mathsm@sh\scriptstyle{\MT_cramped_internal:Nn \scriptstyle{#6}} } \else: \mathop{#4}\limits#5{#6} \fi: } \def\shortintertext#1{% \ifvmode\else\\\@empty\fi \noalign{% \penalty\postdisplaypenalty\vskip\abovedisplayshortskip \vbox{\normalbaselines \if_dim:w \linewidth=\columnwidth \else: \parshape\@ne \@totalleftmargin \linewidth \fi: \noindent#1\par}% \penalty\predisplaypenalty\vskip\abovedisplayshortskip% }% } \providecommand*\clap[1]{\hb@xt@\z@{\hss#1\hss}} \providecommand*\mathllap[1][\@empty]{ \ifx\@empty#1\@empty \expandafter \mathpalette \expandafter \MT_mathllap:Nn \else \expandafter \MT_mathllap:Nn \expandafter #1 \fi } \providecommand*\mathrlap[1][\@empty]{ \ifx\@empty#1\@empty \expandafter \mathpalette \expandafter \MT_mathrlap:Nn \else \expandafter \MT_mathrlap:Nn \expandafter #1 \fi } \providecommand*\mathclap[1][\@empty]{ \ifx\@empty#1\@empty \expandafter \mathpalette \expandafter \MT_mathclap:Nn \else \expandafter \MT_mathclap:Nn \expandafter #1 \fi } \def\MT_mathllap:Nn #1#2{{}\llap{$\m@th#1{#2}$}} \def\MT_mathrlap:Nn #1#2{{}\rlap{$\m@th#1{#2}$}} \def\MT_mathclap:Nn #1#2{{}\clap{$\m@th#1{#2}$}} \providecommand*\mathmbox{\mathpalette\MT_mathmbox:nn} \def\MT_mathmbox:nn #1#2{\mbox{$\m@th#1#2$}} \providecommand*\mathmakebox{ \@ifnextchar[ \MT_mathmakebox_I:w \mathmbox} \def\MT_mathmakebox_I:w[#1]{% \@ifnextchar[ {\MT_mathmakebox_II:w[#1]} {\MT_mathmakebox_II:w[#1][c]}} \def\MT_mathmakebox_II:w[#1][#2]{ \mathpalette{\MT_mathmakebox_III:w[#1][#2]}} \def\MT_mathmakebox_III:w[#1][#2]#3#4{% \@begin@tempboxa\hbox{$\m@th#3#4$}% \setlength\@tempdima{#1}% \hbox{\hb@xt@\@tempdima{\csname bm@#2\endcsname}}% \@end@tempboxa} \def\mathsm@sh#1#2{% \setbox\z@\hbox{$\m@th#1{#2}$}{}\finsm@sh} \providecommand*\cramped[1][\@empty]{ \ifx\@empty#1\@empty \expandafter \mathpalette \expandafter \MT_cramped_internal:Nn \else \expandafter \MT_cramped_internal:Nn \expandafter #1 \fi } \def\MT_cramped_internal:Nn #1#2{ \sbox\z@{$\m@th#1\nulldelimiterspace=\z@\radical\z@{#2}$} \ifx#1\displaystyle \dimen@=\fontdimen8\textfont3 \advance\dimen@ .25\fontdimen5\textfont2 \else \dimen@=1.25\fontdimen8 \ifx#1\textstyle\textfont \else \ifx#1\scriptstyle \scriptfont \else \scriptscriptfont \fi \fi 3 \fi \advance\dimen@-\ht\z@ \ht\z@=-\dimen@ \box\z@ } \providecommand*\crampedllap[1][\@empty]{ \ifx\@empty#1\@empty \expandafter \mathpalette \expandafter \MT_cramped_llap_internal:Nn \else \expandafter \MT_cramped_llap_internal:Nn \expandafter #1 \fi } \def\MT_cramped_llap_internal:Nn #1#2{ {}\llap{\MT_cramped_internal:Nn #1{#2}} } \providecommand*\crampedclap[1][\@empty]{ \ifx\@empty#1\@empty \expandafter \mathpalette \expandafter \MT_cramped_clap_internal:Nn \else \expandafter \MT_cramped_clap_internal:Nn \expandafter #1 \fi } \def\MT_cramped_clap_internal:Nn #1#2{ {}\clap{\MT_cramped_internal:Nn #1{#2}} } \providecommand*\crampedrlap[1][\@empty]{ \ifx\@empty#1\@empty \expandafter \mathpalette \expandafter \MT_cramped_rlap_internal:Nn \else \expandafter \MT_cramped_rlap_internal:Nn \expandafter #1 \fi } \def\MT_cramped_rlap_internal:Nn #1#2{ {}\rlap{\MT_cramped_internal:Nn #1{#2}} } \DeclareRobustCommand{\prescript}[3]{ \@mathmeasure\z@\scriptstyle{\MT_prescript_sup:{#1}} \@mathmeasure\tw@\scriptstyle{\MT_prescript_sub:{#2}} \if_dim:w \wd\tw@>\wd\z@ \setbox\z@\hbox to\wd\tw@{\hfil\unhbox\z@} \else: \setbox\tw@\hbox to\wd\z@{\hfil\unhbox\tw@} \fi: \mathop{} \mathopen{\vphantom{\MT_prescript_arg:{#3}}}^{\box\z@}\sb{\box\tw@} \MT_prescript_arg:{#3} } \define@key{\MT_options_name:} {prescript-sup-format}{\def\MT_prescript_sup:{#1}} \define@key{\MT_options_name:} {prescript-sub-format}{\def\MT_prescript_sub:{#1}} \define@key{\MT_options_name:} {prescript-arg-format}{\def\MT_prescript_arg:{#1}} \setkeys{\MT_options_name:}{ prescript-sup-format={}, prescript-sub-format={}, prescript-arg-format={}, } \def\@DeclareMathSizes #1#2#3#4#5{% \@defaultunits\dimen@ #2pt\relax\@nnil \if:w $#3$% \MH_let:cN {S@\strip@pt\dimen@}\math@fontsfalse \else: \@defaultunits\dimen@ii #3pt\relax\@nnil \@defaultunits\@tempdima #4pt\relax\@nnil \@defaultunits\@tempdimb #5pt\relax\@nnil \toks@{#1}% \expandafter\xdef\csname S@\strip@pt\dimen@\endcsname{% \gdef\noexpand\tf@size{\strip@pt\dimen@ii}% \gdef\noexpand\sf@size{\strip@pt\@tempdima}% \gdef\noexpand\ssf@size{\strip@pt\@tempdimb}% \the\toks@ }% \fi: } \def\MT_mathic_true: { \MH_if_boolean:nF {math_italic_corr}{ \MH_set_boolean_T:n {math_italic_corr} \MH_let:NwN \MT_begin_inlinemath: \( \renewcommand*\({\relax\ifmmode\@badmath\else \ifhmode \if_dim:w \fontdimen\@ne\font>\z@ \if_dim:w \lastskip>\z@ \skip@\lastskip\unskip \@@italiccorr \hskip\skip@ \else: \@@italiccorr \fi: \fi: \fi: $\fi: } } } \def\MT_mathic_false: { \MH_if_boolean:nT {math_italic_corr}{ \MH_set_boolean_F:n {math_italic_corr} \MH_let:NwN \( \MT_begin_inlinemath: } } \MH_new_boolean:n {math_italic_corr} \define@key{\MT_options_name:}{mathic}[true]{ \@ifundefined{MT_mathic_#1:} { \MT_true_false_error: \@nameuse{MT_mathic_false:} } { \@nameuse{MT_mathic_#1:} } } \newenvironment{spreadlines}[1]{ \setlength{\jot}{#1} \ignorespaces }{ \ignorespacesafterend } \MaybeMHPrecedingSpacesOff \newenvironment{MT_gathered_env}[1][c]{% \RIfM@\else \nonmatherr@{\begin{\@currenvir}}% \fi \null\,% \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi\fi \bgroup \Let@ \chardef\dspbrk@context\@ne \restore@math@cr \spread@equation \ialign\bgroup \MT_gathered_pre: \strut@$\m@th\displaystyle##$ \MT_gathered_post: \crcr }{% \endaligned \MT_gathered_env_end: } \MHPrecedingSpacesOn \newcommand*\newgathered[4]{ \newenvironment{#1} { \def\MT_gathered_pre:{#2} \def\MT_gathered_post:{#3} \def\MT_gathered_env_end:{#4} \MT_gathered_env }{\endMT_gathered_env} } \newcommand*\renewgathered[4]{ \renewenvironment{#1} { \def\MT_gathered_pre:{#2} \def\MT_gathered_post:{#3} \def\MT_gathered_env_end:{#4} \MT_gathered_env }{\endMT_gathered_env} } \newgathered{lgathered}{}{\hfil}{} \newgathered{rgathered}{\hfil}{}{} \renewgathered{gathered}{\hfil}{\hfil}{} \newcommand*\splitfrac[2]{% \genfrac{}{}{0pt}{1}% {\textstyle#1\quad\hfill}% {\textstyle\hfill\quad\mathstrut#2}% } \newcommand*\splitdfrac[2]{% \genfrac{}{}{0pt}{0}{#1\quad\hfill}{\hfill\quad\mathstrut #2}% } \MH_if_boolean:nT {fixamsmath}{ \def\place@tag{% \iftagsleft@ \kern-\tagshift@ \if@fleqn \if_num:w \xatlevel@=\tw@ \kern-\@mathmargin \fi: \fi: \if:w 1\shift@tag\row@\relax \rlap{\vbox{% \normalbaselines \boxz@ \vbox to\lineht@{}% \raise@tag }}% \else: \rlap{\boxz@}% \fi: \kern\displaywidth@ \else: \kern-\tagshift@ \if:w 1\shift@tag\row@\relax \llap{\vtop{% \raise@tag \normalbaselines \setbox\@ne\null \dp\@ne\lineht@ \box\@ne \boxz@ }}% \else: \llap{\boxz@}% \fi: \fi: } \def\x@calc@shift@lf{% \if_dim:w \eqnshift@=\z@ \global\eqnshift@\@mathmargin\relax \alignsep@\displaywidth \advance\alignsep@-\totwidth@ \if_num:w \@tempcntb=0 \else: \global\divide\alignsep@\@tempcntb % original line \fi: \if_dim:w \alignsep@<\minalignsep\relax \global\alignsep@\minalignsep\relax \fi: \fi: \if_dim:w \tag@width\row@>\@tempdima \saveshift@1% \else: \saveshift@0% \fi:}% } \MaybeMHPrecedingSpacesOff \renewcommand\aligned@a[1][c]{\start@aligned{#1}\m@ne} \MHPrecedingSpacesOn \endinput %% %% End of file `mathtools.sty'.