The quadratic relations computed in the procedure getRelationsAndNormalForm depend only on the unknown entries of the matrix a. In almost all cases, each of these relations is the Pfaffian of skew-symmetric matrix of size 4. The procedure fixes a choice of skew-symmetric matrices whose Pfaffians coincides with the given quadrics.
i1 : kk = ZZ/197; |
i2 : s = "22"; |
i3 : (A,B,subs0) = globalVariables(kk,s); |
i4 : SR = ring(A); |
i5 : D = complexModuloRegularSequence(SR,s); |
i6 : (d1',d2) = setupGeneralMatrices(D,A,B); |
i7 : (relLin,relPfaf,d1'nor,d2nor) = getRelationsAndNormalForm(d1',d2,subs0); |
i8 : Ms = setupSkewMatrices(relPfaf,s); |