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D.5.10.1 truncate
Procedure from library sheafcoh.lib (see sheafcoh_lib).
- Usage:
- truncate(M,d); M module, d int
- Assume:
M is graded, and it comes assigned with an admissible degree
vector as an attribute
- Return:
- module
- Note:
- Output is a presentation matrix for the truncation of coker(M)
at degree d.
Example:
| | LIB "sheafcoh.lib";
ring R=0,(x,y,z),dp;
module M=maxideal(3);
homog(M);
==> 1
// compute presentation matrix for truncated module (R/<x,y,z>^3)_(>=2)
module M2=truncate(M,2);
print(M2);
==> z,0,0,0,0,0,y, 0, 0,0, 0,0,x, 0, 0, 0, 0, 0,
==> 0,z,0,0,0,0,-z,y, 0,0, 0,0,0, x, 0, 0, 0, 0,
==> 0,0,z,0,0,0,0, -z,y,0, 0,0,0, 0, x, 0, 0, 0,
==> 0,0,0,z,0,0,0, 0, 0,y, 0,0,-z,0, 0, x, 0, 0,
==> 0,0,0,0,z,0,0, 0, 0,-z,y,0,0, -z,-y,0, x, 0,
==> 0,0,0,0,0,z,0, 0, 0,0, 0,y,0, 0, 0, -z,-y,x
dimGradedPart(M2,1);
==> 0
dimGradedPart(M2,2);
==> 6
// this should coincide with:
dimGradedPart(M,2);
==> 6
// shift grading by 1:
intvec v=1;
attrib(M,"isHomog",v);
M2=truncate(M,2);
print(M2);
==> 0, -y,-z,z2,0, 0, yz,0, xz,y2,0, xy,x2,
==> -z,x, 0, 0, z2,0, 0, yz,0, 0, y2,0, 0,
==> y, 0, x, 0, 0, z2,0, 0, 0, 0, 0, 0, 0
dimGradedPart(M2,3);
==> 6
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