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# matFact1 -- part of a RandomNicePencil

- Usage:
    `M1 = rNP.matFact1`
- Outputs:
  - 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 : setRandomSeed 0
     -- setting random seed to 0

    o1 = 0

    i2 : kk=ZZ/101;

    i3 : g=1;

    i4 : rNP=randNicePencil(kk,g);

    i5 : S=rNP.qqRing;

    i6 : qq=rNP.quadraticForm;

    i7 : M1=rNP.matFact1;

                 8      8
    o7 : Matrix S  <-- S

    i8 : M2=rNP.matFact2;

                 8      8
    o8 : Matrix S  <-- S

    i9 : M1*M2 - qq*id_(S^(2^(2*g+1)))

    o9 = 0

                 8      8
    o9 : Matrix S  <-- S

    i10 : M1*M2 - M2*M1

    o10 = 0

                  8      8
    o10 : Matrix S  <-- S

## See also

- qqRing -- part of a RandomNicePencil
- baseRing of a RandomNicePencil -- part of a RandomNicePencil
- quadraticForm -- part of a RandomNicePencil
- matFact2 -- part of a RandomNicePencil
- matFactu1 -- part of a RandomNicePencil
- matFactu2 -- part of a RandomNicePencil
- isotropicSpace -- part of a RandomNicePencil

## For the programmer

The object matFact1 is a symbol.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/PencilsOfQuadrics.m2:2515:0.