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D.15.18.4 symExt
Procedure from library tateProdCplxNegGrad.lib (see tateProdCplxNegGrad_lib).
- Usage:
- symExt(m); m matrix
- Purpose:
- computes differential R(M_0) -> R(M_1) for the module M over S corresponding to the linear presentation matrix m, however, in order to
get the result, m has to be fetched to the exterior algebra E
- Assume:
- m a matrix, linear presentation matrix over S; Note: also works for nonlinear matrices, but makes no sense to use it in this case
- Return:
- matrix B representing R(M_0) -> R(M_1)
- Note:
- output lives in S (not as in Macaulay2 in the ring E, to get the same result, just fetch the matrix to E)
Example:
| | LIB "tateProdCplxNegGrad.lib";
intvec c = 1,2;
def (S,E) = productOfProjectiveSpaces(c);
setring(S);
matrix m[4][2] = x(0)(0), x(1)(0),x(0)(1),0,0,x(1)(1), 0,x(1)(2);
matrix A = symExt(m);
print(A);
==> 0, x(0)(0),0, 0,
==> 0, 0, x(0)(0), 0,
==> 0, 0, 0, x(0)(0),
==> x(0)(1), 0, 0, 0,
==> -x(0)(0),x(0)(1),0, 0,
==> 0, 0, x(0)(1), 0,
==> 0, 0, 0, x(0)(1),
==> 0, x(1)(0),0, 0,
==> 0, 0, x(1)(0), 0,
==> 0, 0, 0, x(1)(0),
==> x(1)(1), 0, 0, 0,
==> 0, x(1)(1),0, 0,
==> -x(1)(0),0, x(1)(1), 0,
==> 0, 0, 0, x(1)(1),
==> x(1)(2), 0, 0, 0,
==> 0, x(1)(2),0, 0,
==> 0, 0, x(1)(2), 0,
==> 0, 0, -x(1)(1),x(1)(2)
setring(E);
print(fetch(S,A));
==> 0, e(0)(0),0, 0,
==> 0, 0, e(0)(0), 0,
==> 0, 0, 0, e(0)(0),
==> e(0)(1), 0, 0, 0,
==> -e(0)(0),e(0)(1),0, 0,
==> 0, 0, e(0)(1), 0,
==> 0, 0, 0, e(0)(1),
==> 0, e(1)(0),0, 0,
==> 0, 0, e(1)(0), 0,
==> 0, 0, 0, e(1)(0),
==> e(1)(1), 0, 0, 0,
==> 0, e(1)(1),0, 0,
==> -e(1)(0),0, e(1)(1), 0,
==> 0, 0, 0, e(1)(1),
==> e(1)(2), 0, 0, 0,
==> 0, e(1)(2),0, 0,
==> 0, 0, e(1)(2), 0,
==> 0, 0, -e(1)(1),e(1)(2)
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