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PencilsOfQuadrics :: matFact1

matFact1 -- part of a RandomNicePencil

Synopsis

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
i9 : M1*M2 - M2*M1

o9 = 0

             8       8
o9 : Matrix S  <--- S

See also

For the programmer

The object matFact1 is a symbol.