M1, a matrix, a matrix over S such that (M1, M2) gives a matrix factorization of qq of size 2^{2g+1}.
Description
M1, M2 are consecutive high syzygy matrices in the minimal periodic resolution of the base ring R=S/(ideal matrix x_0..y_{(g-1)},z_1,z_2) as a module over S/(ideal qq). These are used to construct the Clifford algebra of qq.
i1 : kk=ZZ/101;
i2 : g=1;
i3 : rNP=randNicePencil(kk,g);
i4 : S=rNP.qqRing;
i5 : qq=rNP.quadraticForm;
i6 : M1=rNP.matFact1;
8 8
o6 : Matrix S <-- S
i7 : M2=rNP.matFact2;
8 8
o7 : Matrix S <-- S
i8 : M1*M2 - qq*id_(S^(2^(2*g+1)))
o8 = 0
8 8
o8 : Matrix S <-- S