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hyperellipticBranchEquation -- part of a CliffordModule

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 : setRandomSeed 0
 -- setting random seed to 0

o1 = 0
 
i2 : kk=ZZ/101;
 
i3 : g=1;
 
i4 : rNP=randNicePencil(kk,g);
 
i5 : M=cliffordModule(rNP.matFact1,rNP.matFact2,rNP.baseRing)

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

o5 : CliffordModule
 
i6 : f=M.hyperellipticBranchEquation

          3       2 2        3      4
o6 = - 12s t - 50s t  - 16s*t  + 47t

o6 : kk[s, t]
 
i7 : sM=M.symmetricM

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

                      4               4
o7 : Matrix (kk[s, t])  <-- (kk[s, t])
 
i8 : f == det sM

o8 = true

See also

For the programmer

The object hyperellipticBranchEquation is a symbol.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/PencilsOfQuadrics.m2:2355:0.