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D.15.21.13 regionComplex
Procedure from library tateProdCplxNegGrad.lib (see tateProdCplxNegGrad_lib).
- Usage:
- regionComplex(T,d,I,J,K); T multigradedcomplex, d intvec, I intvec, J intvec, K intvec
- Purpose:
- compute the region complex of T w.r.t. the sets I,J,K and the vector d
- Assume:
- I,J,K are intvecs representing disjoint subsets of {1,...,t}, T is a complex in ring E, zero represents the empty set
- Return:
- multigraded complex which is the region complex T_d(I,J,K) of T
Example:
| | LIB "tateProdCplxNegGrad.lib";
intvec f = 1,1;
def (S,E) = productOfProjectiveSpaces(f);
intvec low = -3,-3;
intvec high = 3,3;
setring(S);
module M = 0;
intmat MGrading[2][1] = -1,-1;
M = setModuleGrading(M,MGrading);
multigradedcomplex tate;
(E,tate) = tateResolution(M,low,high);
setring(E);
tate;
==> E^25 <-- E^40 <-- E^46 <-- E^44 <-- E^35 <-- E^30 <-- E^38 <\
-- E^56 <-- E^81 <-- E^110 <-- E^141 <-- E^174 <-- E^210
==> -6 -5 -4 -3 -2 -1 0 \
1 2 3 4 5 6
==>
ring Z = cohomologyMatrixFromResolution(tate,low,high);
setring(Z);
print(cohomologymat);
==> 5h,0,5,10,15,20,25,
==> 4h,0,4,8, 12,16,20,
==> 3h,0,3,6, 9, 12,15,
==> 2h,0,2,4, 6, 8, 10,
==> h, 0,1,2, 3, 4, 5,
==> 0, 0,0,0, 0, 0, 0,
==> h2,0,h,2h,3h,4h,5h
setring(E);
intvec c= 0,-3;
intvec I = 0;
intvec J = 0,1;
intvec K = 0,2;
multigradedcomplex U = regionComplex(tate,c,I,J,K);
U;
==> 0 <-- E^10 <-- E^8 <-- E^6 <-- E^4 <-- E^2 <-- E^2 <-- 0
==> -4 -3 -2 -1 0 1 2 3
==>
Z = cohomologyMatrixFromResolution(U,low,high);
setring(Z);
print(cohomologymat);
==> 0,0,0,10,0,0,0,
==> 0,0,0,8, 0,0,0,
==> 0,0,0,6, 0,0,0,
==> 0,0,0,4, 0,0,0,
==> 0,0,0,2, 0,0,0,
==> 0,0,0,0, 0,0,0,
==> 0,0,0,2h,0,0,0
setring(E);
multigradedcomplex V = regionComplex(tate,c,I,J,J);
==> ? I,J,K have to be disjoint.
==> ? leaving tateProdCplxNegGrad.lib::regionComplex (0)
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