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PencilsOfQuadrics :: cliffordModule

cliffordModule -- makes a clifford Module

Synopsis

Description

The keys oddOperators evenOperators are the same as the two lists output by cliffordOperators(M1,M2)

The keys evenCenter oddCenter yield the action of the center of the even Clifford algebra of qq on the even, respectively odd parts of the Clifford module.

The key symmetricM yields the matrix of coefficients of the quadratic form qq

the key hyperellipticBranchEquation yields the branch equation in R -- that is, the equation of the set of points over which the quadratic form is singular.

i1 : kk = ZZ/101

o1 = kk

o1 : QuotientRing
i2 : g = 1

o2 = 1
i3 : (S, qq,  R,  u, M1, M2, Mu1, Mu2)=randomNicePencil(kk,g);
i4 : M = cliffordModule(M1,M2, R)

o4 = CliffordModule{...6...}

o4 : CliffordModule
i5 : Mu = cliffordModule(Mu1,Mu2, R)

o5 = CliffordModule{...6...}

o5 : CliffordModule

The symmetric matrices are the same for both:

i6 : Mu.symmetricM

o6 = | -5t  -50s 6t     -6t  |
     | -50s 0    -9t    5t   |
     | 6t   -9t  -s-30t 3t   |
     | -6t  5t   3t     -48t |

             4       4
o6 : Matrix R  <--- R
i7 : M.symmetricM

o7 = | -5t  -50s 6t     -6t  |
     | -50s 0    -9t    5t   |
     | 6t   -9t  -s-30t 3t   |
     | -6t  5t   3t     -48t |

             4       4
o7 : Matrix R  <--- R

But the operators are twice the size for M (in both cases the same size as the corresponding matrix factorization Mu.evenCenter numrows(Mu.evenCenter) == numrows(Mu1) M.evenCenter

See also

Ways to use cliffordModule :

For the programmer

The object cliffordModule is a method function.