Quelle modules14.tst Sprache: unbekannt

# Modules, single 14
#
# 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("modules14.tst");

# doc/../gap/HomalgMap.gi:857-910
gap> zz := HomalgRingOfIntegers( );;
gap> M := HomalgMatrix( "[ 2, 3, 4,   5, 6, 7 ]", 2, 3, zz );
<A 2 x 3 matrix over an internal ring>
gap> M := LeftPresentation( M );
<A non-torsion left module presented by 2 relations for 3 generators>
gap> N := HomalgMatrix( "[ 2, 3, 4, 5,   6, 7, 8, 9 ]", 2, 4, zz );
<A 2 x 4 matrix over an internal ring>
gap> N := LeftPresentation( N );
<A non-torsion left module presented by 2 relations for 4 generators>
gap> mat := HomalgMatrix( "[ \
> 1, 0, -2, -4, \
> 0, 1,  4,  7, \
> 1, 0, -2, -4  \
> ]", 3, 4, zz );
<A 3 x 4 matrix over an internal ring>
gap> phi := HomalgMap( mat, M, N );
<A "homomorphism" of left modules>
gap> IsMorphism( phi );
true
gap> phi;
<A homomorphism of left modules>
gap> Display( phi );
[ [   1,   0,  -2,  -4 ],
  [   0,   1,   4,   7 ],
  [   1,   0,  -2,  -4 ] ]

the map is currently represented by the above 3 x 4 matrix
gap> ByASmallerPresentation( M );
<A rank 1 left module presented by 1 relation for 2 generators>
gap> Display( last );
Z/< 3 > + Z^(1 x 1)
gap> Display( phi );
[ [   2,   1,   0,  -1 ],
  [   1,   0,  -2,  -4 ] ]

the map is currently represented by the above 2 x 4 matrix
gap> ByASmallerPresentation( N );
<A rank 2 left module presented by 1 relation for 3 generators>
gap> Display( N );
Z/< 4 > + Z^(1 x 2)
gap> Display( phi );
[ [  -8,   0,   0 ],
  [  -3,  -1,  -2 ] ]

the map is currently represented by the above 2 x 3 matrix
gap> ByASmallerPresentation( phi );
<A non-zero homomorphism of left modules>
gap> Display( phi );
[ [   0,   0,   0 ],
  [   1,  -1,  -2 ] ]

the map is currently represented by the above 2 x 3 matrix

#
gap> STOP_TEST("modules14.tst", 1);

Quelle modules14.tst Sprache: unbekannt

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