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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
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