Add NaturalGModule helper

Also fix usage error message for GModuleByMats
gap-system · Oct 14, 2024 · 6343f96 · 6343f96
1 parent 19484a7
commit 6343f96
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diff --git a/doc/ref/meataxe.xml b/doc/ref/meataxe.xml
@@ -77,6 +77,16 @@ bases used are needed as well.
 <Section Label="Module Constructions">
 <Heading>Module Constructions</Heading>
 
+<ManSection>
+<Heading>NaturalGModule</Heading>
+<Func Name="NaturalGModule" Arg='group[, field]' Label="for matrix group and a field"/>
+<Description>
+creates a MeatAxe module over <A>field</A> from the generators of the matrix
+group <A>group</A>. If <A>field</A> is not provided then the value returned by
+<Ref Filt="DefaultFieldOfMatrixGroup"/> is used instead.
+</Description>
+</ManSection>
+
 <ManSection>
 <Func Name="PermutationGModule" Arg='G, F'/>
 

diff --git a/lib/meataxe.gd b/lib/meataxe.gd
@@ -35,6 +35,14 @@ DeclareGlobalFunction("TrivialGModule");
 ## The induced module for g is calculated.
 DeclareGlobalFunction("InducedGModule");
 
+#############################################################################
+##
+#F  NaturalGModule ( g[, F] )
+##
+## g is a matrix group, F a field.
+## The corresponding natural module is output.
+DeclareGlobalFunction("NaturalGModule");
+
 #############################################################################
 ##
 #F PermutationGModule ( g, F) . permutation module

diff --git a/lib/meataxe.gi b/lib/meataxe.gi
@@ -128,6 +128,26 @@ InstallGlobalFunction(InducedGModule,function(g, h, m)
 
 end);
 
+#############################################################################
+##
+#F  NaturalGModule ( g[, F] )
+##
+## g is a matrix group, F a field.
+## The corresponding natural module is output.
+InstallGlobalFunction(NaturalGModule,function(group, field...)
+  if not IsMatrixGroup(group) then
+    Error("<group> must be a matrix group");
+  fi;
+  if Length(field) = 0 then
+    field := DefaultFieldOfMatrixGroup(group);
+  elif Length(field) = 1 then
+    field := field[1];
+  else
+    Error("too many arguments");
+  fi;
+  return GModuleByMats(GeneratorsOfGroup(group), DimensionOfMatrixGroup(group), field);
+end);
+
 #############################################################################
 ##
 #F PermutationGModule( g, F) . permutation module
@@ -3413,18 +3433,18 @@ end;
 ##  <P/>
 ##  <Example><![CDATA[
 ##  gap> g:= SO(-1, 4, 2);;
-##  gap> m:= GModuleByMats( GeneratorsOfGroup( g ), GF(2) );;
+##  gap> m:= NaturalGModule( g );;
 ##  gap> Display( MTX.InvariantQuadraticForm( m ) );
 ##   . . . .
 ##   1 . . .
 ##   . . 1 .
 ##   . . 1 1
-##  gap> g:= SP(4, 2);;
-##  gap> m:= GModuleByMats( GeneratorsOfGroup( g ), GF(2) );;
+##  gap> g:= Sp(4, 2);;
+##  gap> m:= NaturalGModule( g );;
 ##  gap> MTX.InvariantQuadraticForm( m );
 ##  fail
-##  gap> g:= SP(4, 3);;
-##  gap> m:= GModuleByMats( GeneratorsOfGroup( g ), GF(3) );;
+##  gap> g:= Sp(4, 3);;
+##  gap> m:= NaturalGModule( g );;
 ##  gap> q:= MTX.InvariantQuadraticForm( m );;
 ##  gap> q = - TransposedMat( q );  # antisymmetric inv. bilinear form
 ##  true