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# GradedModules, single 4
#
# DO NOT EDIT THIS FILE - EDIT EXAMPLES IN THE SOURCE INSTEAD!
#
# This file has been generated by AutoDoc. It contains examples extracted from
# the package documentation. Each example is preceded by a comment which gives
# the name of a GAPDoc XML file and a line range from which the example were
# taken. Note that the XML file in turn may have been generated by AutoDoc
# from some other input.
#
gap> START_TEST("gradedmodules04.tst");
# doc/../examples/doc/SubmoduleGeneratedByHomogeneousPart.g:2-66
gap> R := HomalgFieldOfRationalsInDefaultCAS( ) * "x,y,z";;
gap> S := GradedRing( R );;
gap> M := HomalgMatrix( "[ x^3, y^2, z, z, 0, 0 ]", 2, 3, S );;
gap> M := LeftPresentationWithDegrees( M, [ -1, 0, 1 ] );
<A graded non-torsion left module presented by 2 relations for 3 generators>
gap> n := SubmoduleGeneratedByHomogeneousPart( 1, M );
<A graded left submodule given by 7 generators>
gap> Display( M );
z, 0, 0,
0, y^2*z,z^2,
x^3,y^2, z
Cokernel of the map
Q[x,y,z]^(1x3) --> Q[x,y,z]^(1x3),
currently represented by the above matrix
(graded, degrees of generators: [ -1, 0, 1 ])
gap> Display( n );
x^2,0,0,
x*y,0,0,
y^2,0,0,
0, x,0,
0, y,0,
0, z,0,
0, 0,1
A left submodule generated by the 7 rows of the above matrix
(graded, degrees of generators: [ 1, 1, 1, 1, 1, 1, 1 ])
gap> N := UnderlyingObject( n );
<A graded left module presented by yet unknown relations for 7 generators>
gap> Display( N );
0, 0, z,0, 0, 0,0,
0, z, 0,0, 0, 0,0,
z, 0, 0,0, 0, 0,0,
0, 0, 0,0, -z, y,0,
0, 0, 0,-z,0, x,0,
0, 0, 0,-y,x, 0,0,
0, -y,x,0, 0, 0,0,
-y,x, 0,0, 0, 0,0,
x, 0, 0,0, y, 0,z,
0, 0, 0,0, y*z,0,z^2
Cokernel of the map
Q[x,y,z]^(1x10) --> Q[x,y,z]^(1x7),
currently represented by the above matrix
(graded, degrees of generators: [ 1, 1, 1, 1, 1, 1, 1 ])
gap> gens := GeneratorsOfModule( N );
<A set of 7 generators of a homalg left module>
gap> Display( gens );
x^2,0,0,
x*y,0,0,
y^2,0,0,
0, x,0,
0, y,0,
0, z,0,
0, 0,1
a set of 7 generators given by the rows of the above matrix
#
gap> STOP_TEST("gradedmodules04.tst", 1);
[ Dauer der Verarbeitung: 0.17 Sekunden
(vorverarbeitet)
]
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