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D.15.21.6 tateResolution
Procedure from library tateProdCplxNegGrad.lib (see tateProdCplxNegGrad_lib).
- Usage:
- tateResolution(M,low,high); M module, L list, low intvec, high intvec
- Purpose:
- compute tate resolution of coker(M) where M is Z^t-graded S-module
- Assume:
- M a module over multigraded ring S
- Return:
- (E,tate), tate a multigradedcomplex, E the ring in which tate has to be viewed,
however note that tate is not ring dependent
Example:
| LIB "tateProdCplxNegGrad.lib";
// example 1
intvec c1 = 1,1,1;
intvec low1 = 0,0,0;
intvec high1 = 0,1,0;
def (S1,E1) = productOfProjectiveSpaces(c1);
setring(S1);
module M1 = 0;
intmat grading1[3][1] = -1,-1,-1;
M1 = setModuleGrading(M1,grading1);
multigradedcomplex tate1;
(E1,tate1) = tateResolution(M1,low1,high1);
setring(E1);
tate1;
tate1.differentials;
// example 2
intvec c2 = 1,2;
def (S2,E2) = productOfProjectiveSpaces(c2);
setring(S2);
intvec low2 = -3,-3;
intvec high2 = 0,0;
module M2 = x(0)(0),x(1)(0)^3 + x(1)(1)^3 +x(1)(2)^3;;
intmat grading2[2][1] = 0,0;
M2 = setModuleGrading(M2,grading2);
multigradedcomplex tate2;
(E2,tate2) = tateResolution(M2,low2,high2);
setring(E2);
tate2;
// example 3
intvec c3 = 1,1;
def (S3,E3) = productOfProjectiveSpaces(c3);
intvec low3 = -3,-3;
intvec high3 = 3,3;
setring(S3);
module M3 = 0;
intmat grading3[2][1] = -1,-1;
M3 = setModuleGrading(M3,grading3);
multigradedcomplex tate3;
(E3,tate3) = tateResolution(M3,low3,high3);
setring(E3);
tate3;
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