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# Modules, single 35
#
# 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("modules35.tst");
# doc/../examples/LTensorProduct_Z.g:2-116
gap> zz := HomalgRingOfIntegers( );
Z
gap> m := HomalgMatrix( [ [ 8, 0 ], [ 0, 2 ] ], zz );;
gap> M := LeftPresentation( m );
<A left module presented by 2 relations for 2 generators>
gap> Display( M );
Z/< 8 > + Z/< 2 >
gap> M;
<A torsion left module presented by 2 relations for 2 generators>
gap> a := HomalgMatrix( [ [ 2, 0 ] ], zz );;
gap> alpha := HomalgMap( a, "free", M );
<A homomorphism of left modules>
gap> pi := CokernelEpi( alpha );
<An epimorphism of left modules>
gap> Display( pi );
[ [ 1, 0 ],
[ 0, 1 ] ]
the map is currently represented by the above 2 x 2 matrix
gap> iota := KernelEmb( pi );
<A monomorphism of left modules>
gap> Display( iota );
[ [ 2, 0 ] ]
the map is currently represented by the above 1 x 2 matrix
gap> N := Kernel( pi );
<A cyclic torsion left module presented by yet unknown relations for a cyclic \
generator>
gap> Display( N );
Z/< 4 >
gap> C := HomalgComplex( pi );
<A left acyclic complex containing a single morphism of left modules at degree\
s [ 0 .. 1 ]>
gap> Add( C, iota );
gap> ByASmallerPresentation( C );
<A non-zero short exact sequence containing
2 morphisms of left modules at degrees [ 0 .. 2 ]>
gap> Display( C );
-------------------------
at homology degree: 2
Z/< 4 >
-------------------------
[ [ 0, 6 ] ]
the map is currently represented by the above 1 x 2 matrix
------------v------------
at homology degree: 1
Z/< 2 > + Z/< 8 >
-------------------------
[ [ 0, 1 ],
[ 1, 1 ] ]
the map is currently represented by the above 2 x 2 matrix
------------v------------
at homology degree: 0
Z/< 2 > + Z/< 2 >
-------------------------
gap> T := LTensorProduct( C, N );
<An exact triangle containing 3 morphisms of left complexes at degrees
[ 1, 2, 3, 1 ]>
gap> ByASmallerPresentation( T );
<A non-zero exact triangle containing
3 morphisms of left complexes at degrees [ 1, 2, 3, 1 ]>
gap> L := LongSequence( T );
<A sequence containing 5 morphisms of left modules at degrees [ 0 .. 5 ]>
gap> Display( L );
-------------------------
at homology degree: 5
Z/< 4 >
-------------------------
[ [ 0, 3 ] ]
the map is currently represented by the above 1 x 2 matrix
------------v------------
at homology degree: 4
Z/< 2 > + Z/< 4 >
-------------------------
[ [ 0, 1 ],
[ 0, 0 ] ]
the map is currently represented by the above 2 x 2 matrix
------------v------------
at homology degree: 3
Z/< 2 > + Z/< 2 >
-------------------------
[ [ 2 ],
[ 0 ] ]
the map is currently represented by the above 2 x 1 matrix
------------v------------
at homology degree: 2
Z/< 4 >
-------------------------
[ [ 0, 2 ] ]
the map is currently represented by the above 1 x 2 matrix
------------v------------
at homology degree: 1
Z/< 2 > + Z/< 4 >
-------------------------
[ [ 0, 1 ],
[ 1, 1 ] ]
the map is currently represented by the above 2 x 2 matrix
------------v------------
at homology degree: 0
Z/< 2 > + Z/< 2 >
-------------------------
gap> IsExactSequence( L );
true
gap> L;
<An exact sequence containing 5 morphisms of left modules at degrees
[ 0 .. 5 ]>
#
gap> STOP_TEST("modules35.tst", 1);
[ Dauer der Verarbeitung: 0.16 Sekunden
(vorverarbeitet)
]
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