# LoadPackage( "RingsForHomalg" );
# 
# Qxyz := HomalgFieldOfRationalsInDefaultCAS( ) * "x,y,z";
# 
# LoadPackage( "LocalizeRingForHomalg" );
# 
# R0:=LocalizePolynomialRingAtZeroWithMora( Qxyz );
# 
# wmat := HomalgMatrix( "[ \
# x*y,  y*z,    z,        0,         0,    \
# x^3*z,x^2*z^2,0,        x*z^2,     -z^2, \
# x^4,  x^3*z,  0,        x^2*z,     -x*z, \
# 0,    0,      x*y,      -y^2,      x^2-1,\
# 0,    0,      x^2*z,    -x*y*z,    y*z,  \
# 0,    0,      x^2*y-x^2,-x*y^2+x*y,y^2-y \
# ]", 6, 5, Qxyz );
# 
# wmat := HomalgLocalMatrix( wmat, R0 );
# 
# W := LeftPresentation( wmat );
# 
# ## the module is isomorphic to LeftPresentation of the multiple extension:
# ## x,z,1,0, 0, 0,0, 0,    0,  0, 
# ## 0,0,y,-z,0, 0,0, 0,    0,  0, 
# ## 0,0,x,0, -z,1,0, 0,    0,  0, 
# ## 0,0,0,x, -y,0,1, 0,    0,  0, 
# ## 0,0,0,0, 0, y,-z,0,    0,  0, 
# ## 0,0,0,0, 0, x,0, -z,   0,  -1,
# ## 0,0,0,0, 0, 0,x, -y,   -1, 0, 
# ## 0,0,0,0, 0, 0,-y,x^2-1,0,  0, 
# ## 0,0,0,0, 0, 0,0, 0,    z,  0, 
# ## 0,0,0,0, 0, 0,0, 0,    y-1,0, 
# ## 0,0,0,0, 0, 0,0, 0,    0,  z, 
# ## 0,0,0,0, 0, 0,0, 0,    0,  y, 
# ## 0,0,0,0, 0, 0,0, 0,    0,  x
# 
# BasisOfModule( W );
# syz := SyzygiesGenerators( W );
# Y := Hom( R0, W );
# iota := TorsionObjectEmb( W );
# pi := TorsionFreeFactorEpi( W );
# C := HomalgComplex( pi, 0 );
# Add( C, iota );
# T := TorsionObject( W );
# F := TorsionFreeFactor( W );
# O := HomalgCocomplex( iota, -1 );
# Add( O, pi );

Read( "ReducedBasisOfModuleMora.g" );


filt := PurityFiltration( W );

II_E := SpectralSequence( filt );

m := IsomorphismOfFiltration( filt );
