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D.5.10.8 dimGradedPart

Procedure from library sheafcoh.lib (see sheafcoh_lib).

Usage:
dimGradedPart(M,d); M module, d int

Assume:
M is graded, and it comes assigned with an admissible degree vector as an attribute

Return:
int

Note:
Output is the vector space dimension of the graded part of degree d of coker(M).

Example:
 
LIB "sheafcoh.lib";
ring R=0,(x,y,z),dp;
module M=maxideal(3);
// assign compatible weight vector (here: 0)
homog(M);
==> 1
// compute dimension of graded pieces of R/<x,y,z>^3 :
dimGradedPart(M,0);
==> 1
dimGradedPart(M,1);
==> 3
dimGradedPart(M,2);
==> 6
dimGradedPart(M,3);
==> 0
// shift grading:
attrib(M,"isHomog",intvec(2));
dimGradedPart(M,2);
==> 1