/usr/share/gap/lib/mgmadj.gd is in gap-libs 4r6p5-3.
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 mgmadj.gd GAP library Andrew Solomon
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##
#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
##
## This file contains declarations for magmas with zero adjoined.
##
#############################################################################
##
#C IsMultiplicativeElementWithZero( <elt>)
##
## <#GAPDoc Label="IsMultiplicativeElementWithZero">
## <ManSection>
## <Filt Name="IsMultiplicativeElementWithZero" Arg='elt' Type='Category'/>
##
## <Description>
## Elements in a family which can be the operands of the
## <C>*</C> and the operation MultiplicativeZero.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory("IsMultiplicativeElementWithZero",IsMultiplicativeElement);
DeclareCategoryCollections("IsMultiplicativeElementWithZero");
#############################################################################
##
#O MultiplicativeZeroOp( <elt> )
##
## <#GAPDoc Label="MultiplicativeZeroOp">
## <ManSection>
## <Oper Name="MultiplicativeZeroOp" Arg='elt'/>
##
## <Description>
## for an element <A>elt</A> in the category
## <Ref Func="IsMultiplicativeElementWithZero"/>,
## returns the element <M>z</M> in the family <M>F</M> of <A>elt</A>
## with the property that <M>z * m = z = m * z</M> holds for all
## <M>m \in F</M>, if such an element is known.
## <P/>
## Families of elements in the category
## <Ref Func="IsMultiplicativeElementWithZero"/>
## often arise from adjoining a new zero to an existing magma.
## See <Ref Func="InjectionZeroMagma"/> for details.
## <P/>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareOperation( "MultiplicativeZeroOp", [IsMultiplicativeElementWithZero] );
#############################################################################
##
#A MultiplicativeZero( <M> )
##
## <#GAPDoc Label="MultiplicativeZero">
## <ManSection>
## <Attr Name="MultiplicativeZero" Arg='M'/>
##
## <Description>
## Returns the multiplicative zero of the magma which is the element
## <A>z</A> such that for all <A>m</A> in <A>M</A>, <C><A>z</A> * <A>m</A> = <A>m</A> * <A>z</A> = <A>z</A></C>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "MultiplicativeZero", IsMultiplicativeElementWithZero );
#############################################################################
##
#O IsMultiplicativeZero( <M>, <z> )
##
## <#GAPDoc Label="IsMultiplicativeZero">
## <ManSection>
## <Oper Name="IsMultiplicativeZero" Arg='M, z'/>
##
## <Description>
## returns true iff <C><A>z</A> * <A>m</A> = <A>m</A> * <A>z</A> = <A>z</A></C> for all <A>m</A> in <A>M</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareOperation( "IsMultiplicativeZero", [ IsMagma, IsMultiplicativeElement ] );
#############################################################################
##
#A InjectionZeroMagma( <M> )
##
## <#GAPDoc Label="InjectionZeroMagma">
## <ManSection>
## <Attr Name="InjectionZeroMagma" Arg='M'/>
##
## <Description>
## The canonical homomorphism <A>i</A> from the magma
## <A>M</A> into the magma formed from <A>M</A> with a single new element
## which is a multiplicative zero for the resulting magma.
## <P/>
## The elements of the new magma form a family of elements in the
## category IsMultiplicativeElementWithZero, and the
## new magma is obtained as Range(<A>i</A>).
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "InjectionZeroMagma", IsMagma );
#############################################################################
##
#E
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