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## <#GAPDoc Label="LTensorProduct_Z">
## <Example><![CDATA[
## 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 ]>
## ]]></Example>
## <#/GAPDoc>
LoadPackage( "Modules" );
zz := HomalgRingOfIntegers( );
m := HomalgMatrix( [ [ 8, 0 ], [ 0, 2 ] ], zz );
M := LeftPresentation( m );
a := HomalgMatrix( [ [ 2, 0 ] ], zz );
alpha := HomalgMap( a, "free", M );
pi := CokernelEpi( alpha );
iota := KernelEmb( pi );
N := Kernel( pi );
C := HomalgComplex( pi );
Add( C, iota );
ByASmallerPresentation( C );
T := LTensorProduct( C, N );
ByASmallerPresentation( T );
L := LongSequence( T );
IsExactSequence( L );
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