Merge pull request #1471 from TKuh/manual_group_congruence

`AddIsCongruentForMorphisms` for the groups example in the manual

Manual/GAP_code/group_example/complete_example.g

@@ -3,6 +3,8 @@ grps := CreateCapCategory( "groups" );
 AddPreCompose( grps, { cat, mor1, mor2 } -> mor1 * mor2 );
 identity_func := { cat, grp } -> GroupHomomorphismByImages( grp, grp );
 AddIdentityMorphism( grps, identity_func );
+congruence_func := { cat, mor1, mor2 } -> mor1 = mor2;
+AddIsCongruentForMorphisms( grps, congruence_func );
 EnableAddForCategoricalOperations( grps );
 Finalize( grps );
 S3 := SymmetricGroup( 3 );

Manual/GAP_tex/group_example/AddIsCongruentForMorphisms.g

@@ -0,0 +1,5 @@
+## gapcolor ##
+gap> congruence_func := { cat, mor1, mor2 } -> mor1 = mor2;
+function( grp ) ... end
+gap> AddIsCongruentForMorphisms( grps, congruence_func );
+## endgapcolor ##

Manual/GAP_tex/group_example/AddIsCongruentForMorphisms.tex

@@ -0,0 +1,20 @@
+\documentclass[12pt]{amsart}
+\usepackage{graphicx}
+\usepackage{a4wide}
+\usepackage{amssymb}
+\usepackage{xcolor}
+\usepackage{fancyvrb}
+
+\title{GAP Code}
+\author{}
+
+\begin{document}
+\maketitle
+
+\begin{Verbatim}[commandchars=!@\%,frame=single]
+!color@blue%@gap>%!color@red%@ congruence_func := { cat, mor1, mor2 } -> mor1 = mor2;%
+function( grp ) ... end
+!color@blue%@gap>%!color@red%@ AddIsCongruentForMorphisms( grps, congruence_func );%
+\end{Verbatim}
+
+\end{document}

Manual/GAP_tex/group_example/AddIsCongruentForMorphisms_main.tex

@@ -0,0 +1,6 @@
+\begin{Verbatim}[commandchars=!@\%,frame=single]
+!color@blue%@gap>%!color@red%@ congruence_func := { cat, mor1, mor2 } -> mor1 = mor2;%
+function( grp ) ... end
+!color@blue%@gap>%!color@red%@ AddIsCongruentForMorphisms( grps, congruence_func );%
+\end{Verbatim}
+

Manual/GAP_tex/group_example/AddPreCompose.g

@@ -1,3 +1,3 @@
 ## gapcolor ##
-gap> AddPreCompose( grps, \* );
+gap> AddPreCompose( grps, { cat, mor1, mor2 } -> mor1 * mor2 );
 ## endgapcolor ##

Manual/GAP_tex/group_example/AddPreCompose.tex

@@ -12,7 +12,7 @@
 \maketitle
 
 \begin{Verbatim}[commandchars=!@\%,frame=single]
-!color@blue%@gap>%!color@red%@ AddPreCompose( grps, \* );%
+!color@blue%@gap>%!color@red%@ AddPreCompose( grps, { cat, mor1, mor2 } -> mor1 * mor2 );%
 \end{Verbatim}
 
 \end{document}

Manual/Tutorial.tex

@@ -28,6 +28,10 @@ \section{The category of groups}\label{section:groups}
 \input{GAP_tex/group_example/AddIdentityMorphism_main}
 
 The command used above exactly creates the identity morphism of a group.
+Additionally, we want to decide the mathematical equality of morphisms, which in CAP is called ``congruence of morphisms''.
+
+\input{GAP_tex/group_example/AddIsCongruentForMorphisms_main}
+
 Next, we tell \CapPkg that every output of a basic operation for the category \texttt{grps} should automatically be added to the category \texttt{grps}.
 This step is necessary since in this example, we simply integrate already existing algorithms and data structures of \GAP to
 \CapPkg's infrastructure.