BurchProjectiveDimension.g

## Bahman Engheta's Thesis: Bounds on Projective Dimension, Example 1.5
LoadPackage( "GradedRingForHomalg" );

R := GradedRing( HomalgFieldOfRationalsInDefaultCAS( ) * "a,b,c,d,e,f" );

LoadPackage( "GradedModules" );

I := GradedLeftSubmodule( "a*c*e, b*d*f, a*b*c*d + a*b*e*f + c*d*e*f", R );

M := FactorObject( I );

Assert( 0, ProjectiveDimension( M ) = 5 );