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 |
The object hyperellipticBranchEquation is a symbol.