Revision 9cb4a2a33ffaf8c93958e021a5558aa3eafb6d56 authored by Mohamed Barakat on 12 September 2021, 12:47:39 UTC, committed by Mohamed Barakat on 12 September 2021, 12:47:39 UTC
1 parent d4384af
WhySpectral.g
LoadPackage( "Modules" );
ZZ := HomalgRingOfIntegers( );
F := 1 * ZZ;
T := 0 * ZZ;
lambda := HomalgMatrix( "[ 2 ]", 1, 1, ZZ );
lambda := HomalgMap( lambda, F, F );
id := HomalgIdentityMap( F, F );
zz := HomalgZeroMap( T, T );
zf := HomalgZeroMap( T, F );
fz := HomalgZeroMap( F, T );
C_2 := HomalgComplex( zz, 1 );
Add( C_2, fz );
Add( C_2, lambda );
C_1 := HomalgComplex( fz, 1 );
Add( C_1, -lambda );
Add( C_1, zf );
C_0 := HomalgComplex( lambda, 1 );
Add( C_0, zf );
Add( C_0, zz );
c_1 := HomalgChainMorphism( zz, C_1, C_2 );
Add( c_1, fz );
Add( c_1, id );
Add( c_1, zf );
c_0 := HomalgChainMorphism( fz, C_0, C_1 );
Add( c_0, id );
Add( c_0, zf );
Add( c_0, zz );
C := HomalgComplex( c_1, -1 );
Add( C, c_0 );
Assert( 0, IsComplex( C ) );
BC := HomalgBicomplex( C );
tBC := TransposedBicomplex( BC );
Tot := TotalComplex( BC );
## converges after 1 step
I_E := SpectralSequenceWithFiltrationOfCollapsedToZeroTransposedSpectralSequence( BC );
filt := FiltrationBySpectralSequence( I_E, 0 );
ByASmallerPresentation( filt );
m := IsomorphismOfFiltration( filt );
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