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D.15.18.12 beilinsonWindow
Procedure from library tateProdCplxNegGrad.lib (see tateProdCplxNegGrad_lib).
- Usage:
- beilinsonWindow(T); T multigradedcomplex
- Purpsose:
- compute the subquotient complex of T consisting of summands generated in degrees 0 <= a <= n
- Assume:
- T is a multigraded complex of free E-modules
- Return:
- multigradedcomplex, the Beilinson window of T
- Note:
- The returend summands are the only ones that contribute to the Beilinson monad.
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);
multigradedcomplex W = beilinsonWindow(tate);
W;
==> 0 <-- E^4 <-- E^4 <-- E^1 <-- 0
==> -1 0 1 2 3
==>
intvec c = 1,1,1;
intvec low2 = 0,0,0;
intvec high2 = 0,1,0;
def (S2,E2) = productOfProjectiveSpaces(c);
setring(S2);
module M2 = 0;
intmat gradeM[3][1] = -1,-1,-1;
M2 = setModuleGrading(M2,gradeM);
multigradedcomplex tate2;
(E2,tate2) = tateResolution(M2,low2,high2);
setring(E2);
multigradedcomplex W2 = beilinsonWindow(tate2);
W2;
==> 0 <-- E^8
==> -1 0
==>
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