/usr/share/gap/lib/matobj1.gd is in gap-libs 4r7p9-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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#
# matobj1.gd
# by Max Neunhöffer
#
## Copyright (C) 2007 Max Neunhöffer, Lehrstuhl D f. Math., RWTH Aachen
## This file is free software, see license information at the end.
#
# This file together with matobj2.gd formally define the interface to the
# new style vectors and matrices in GAP.
# In this file the categories are defined, it is read earlier in the
# GAP library reading process.
#
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# Categories for vectors and matrices:
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DeclareCategory( "IsRowVectorObj", IsVector and IsCopyable );
# All the arithmetical filters come from IsVector.
# RowVectors are no longer necessarily lists, since they do not promise all
# list operations. Of course, in specific implementations the objects
# may still be lists. But beware: Some matrix representations might
# rely on the fact that vectors cannot change their length!
# The family of an object in IsRowVectorObj is the same as the family of
# the base domain.
# There are one main category for matrices and two disjoint sub-categories:
DeclareCategory( "IsMatrixObj", IsVector and IsScalar and IsCopyable );
# All the arithmetical filters come from IsVector and IsScalar.
# In particular, matrices are in "IsMultiplicativeElement" which defines
# powering with a positive integer by the (kernel) method for POW_OBJ_INT.
# Note that this is at least strange for non-associative base domains.
# Matrices are no longer necessarily lists, since they do not promise all list
# operations! Of course, in specific implementations the objects may
# still be lists.
# The family of an object in IsMatrixObj is the collections family of
# the family of its base domain.
InstallTrueMethod(IsAssociativeElement,
IsMatrixObj and IsAssociativeElementCollColl);
DeclareCategory( "IsRowListMatrix", IsMatrixObj );
# The category of matrices behaving like lists of rows which are GAP objects.
# Different matrices in this category can share rows and the same row can
# occur more than once in a matrix. Row access just gives a reference
# to the row object.
DeclareCategory( "IsFlatMatrix", IsMatrixObj );
# The category of "flatly" stored matrices. They behave as if all their rows
# were in one single chunk of memory, such that rows are not individual
# GAP objects. Writing row access and slicing always copies.
# Note that read-accessing the i-th row of a flat matrix twice can
# yield two non-identical objects!
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