/usr/share/gap/lib/twocohom.gd is in gap-libs 4r7p5-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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##
#W twocohom.gd GAP library Bettina Eick
##
#Y Copyright (C) 1997, Lehrstuhl D für Mathematik, RWTH Aachen, Germany
#Y (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland
#Y Copyright (C) 2002 The GAP Group
##
#############################################################################
##
#F CollectedWordSQ( <C>, <u>, <v> )
##
## <ManSection>
## <Func Name="CollectedWordSQ" Arg='C, u, v'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareGlobalFunction( "CollectedWordSQ" );
#############################################################################
##
#F CollectorSQ( <G>, <M>, <isSplit> )
##
## <ManSection>
## <Func Name="CollectorSQ" Arg='G, M, isSplit'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareGlobalFunction( "CollectorSQ" );
#############################################################################
##
#F AddEquationsSQ( <eq>, <t1>, <t2> )
##
## <ManSection>
## <Func Name="AddEquationsSQ" Arg='eq, t1, t2'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareGlobalFunction( "AddEquationsSQ" );
#############################################################################
##
#F SolutionSQ( <C>, <eq> )
##
## <ManSection>
## <Func Name="SolutionSQ" Arg='C, eq'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareGlobalFunction( "SolutionSQ" );
#############################################################################
##
#F TwoCocyclesSQ( <C>, <G>, <M> )
##
## <ManSection>
## <Func Name="TwoCocyclesSQ" Arg='C, G, M'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareGlobalFunction( "TwoCocyclesSQ" );
#############################################################################
##
#F TwoCoboundariesSQ( <C>, <G>, <M> )
##
## <ManSection>
## <Func Name="TwoCoboundariesSQ" Arg='C, G, M'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareGlobalFunction( "TwoCoboundariesSQ" );
#############################################################################
##
#F TwoCohomologySQ( <C>, <G>, <M> )
##
## <ManSection>
## <Func Name="TwoCohomologySQ" Arg='C, G, M'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareGlobalFunction( "TwoCohomologySQ" );
#############################################################################
##
#O TwoCocycles( <G>, <M> )
##
## <#GAPDoc Label="TwoCocycles">
## <ManSection>
## <Oper Name="TwoCocycles" Arg='G, M'/>
##
## <Description>
## returns the <M>2</M>-cocycles of a pc group <A>G</A> by the
## <A>G</A>-module <A>M</A>.
## The generators of <A>M</A> must correspond to the <Ref Func="Pcgs"/>
## value of <A>G</A>. The operation
## returns a list of vectors over the field underlying <A>M</A> and the
## additive group generated by these vectors is the group of
## <M>2</M>-cocyles.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareOperation( "TwoCocycles", [ IsPcGroup, IsObject ] );
#############################################################################
##
#O TwoCoboundaries( <G>, <M> )
##
## <#GAPDoc Label="TwoCoboundaries">
## <ManSection>
## <Oper Name="TwoCoboundaries" Arg='G, M'/>
##
## <Description>
## returns the group of <M>2</M>-coboundaries of a pc group <A>G</A> by the
## <A>G</A>-module <A>M</A>.
## The generators of <A>M</A> must correspond to the <Ref Func="Pcgs"/>
## value of <A>G</A>.
## The group of coboundaries is given as vector space over the field
## underlying <A>M</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareOperation( "TwoCoboundaries", [ IsPcGroup, IsObject ] );
#############################################################################
##
#O TwoCohomology( <G>, <M> )
##
## <#GAPDoc Label="TwoCohomology">
## <ManSection>
## <Oper Name="TwoCohomology" Arg='G, M'/>
##
## <Description>
## returns a record defining the second cohomology group as factor space of
## the space of cocycles by the space of coboundaries.
## <A>G</A> must be a pc group and the generators of <A>M</A> must
## correspond to the pcgs of <A>G</A>.
## <Example><![CDATA[
## gap> G := SmallGroup( 4, 2 );
## <pc group of size 4 with 2 generators>
## gap> mats := List( Pcgs( G ), x -> IdentityMat( 1, GF(2) ) );
## [ <a 1x1 matrix over GF2>, <a 1x1 matrix over GF2> ]
## gap> M := GModuleByMats( mats, GF(2) );
## rec( dimension := 1, field := GF(2),
## generators := [ <an immutable 1x1 matrix over GF2>,
## <an immutable 1x1 matrix over GF2> ], isMTXModule := true )
## gap> TwoCoboundaries( G, M );
## [ ]
## gap> TwoCocycles( G, M );
## [ [ Z(2)^0, 0*Z(2), 0*Z(2) ], [ 0*Z(2), Z(2)^0, 0*Z(2) ],
## [ 0*Z(2), 0*Z(2), Z(2)^0 ] ]
## gap> cc := TwoCohomology( G, M );;
## gap> cc.cohom;
## <linear mapping by matrix, <vector space of dimension 3 over GF(
## 2)> -> ( GF(2)^3 )>
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareOperation( "TwoCohomology", [ IsPcGroup, IsObject ] );
#############################################################################
##
#E
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