| #### D.15.24.4 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);
    setring(E);
    print(fetch(S,A));

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