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PencilsOfQuadrics :: hyperellipticBranchEquation

hyperellipticBranchEquation -- part of a CliffordModule

Synopsis

Description

Gives the branch equation of the set of points over which the associated quadratic form is singular. It is same as the determinant of the symmetric matrix M.symmetricM.

i1 : kk=ZZ/101;
i2 : g=1;
i3 : rNP=randNicePencil(kk,g);
i4 : M=cliffordModule(rNP.matFact1,rNP.matFact2,rNP.baseRing)

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

o4 : CliffordModule
i5 : f=M.hyperellipticBranchEquation

          3       2 2        3      4
o5 = - 12s t - 50s t  - 16s*t  + 47t

o5 : kk[s, t]
i6 : sM=M.symmetricM

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

                      4                4
o6 : Matrix (kk[s, t])  <--- (kk[s, t])
i7 : f == det sM

o7 = true

See also

For the programmer

The object hyperellipticBranchEquation is a symbol.