CliffordModule -- hash table holding details of a Clifford module

Description

the keys are oddOperators => uOdd', evenOperators => uEv', evenCenter=>c0', oddCenter => c1', symmetricM => Q, hyperellipticBranchEquation => f

i1 : kk = ZZ/101

o1 = kk

o1 : QuotientRing

i2 : setRandomSeed 0
 -- setting random seed to 0

o2 = 0

i3 : g = 1

o3 = 1

i4 : (S, qq, R, u, M1, M2, Mu1, Mu2) = randomNicePencil(kk,g);

i5 : C = cliffordModule(M1,M2,R)

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

o5 : CliffordModule

i6 : C.hyperellipticBranchEquation

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

o6 : R

cliffordModuleToCIResolution(CliffordModule,Ring,Ring) -- see cliffordModuleToCIResolution -- transforms a Clifford module to a resolution over a complete intersection ring
cliffordModuleToMatrixFactorization(CliffordModule,Ring) -- see cliffordModuleToMatrixFactorization -- reads off a matrix factorization from a Clifford module
randomIsotropicSubspace(CliffordModule,PolynomialRing) -- see randomIsotropicSubspace -- choose a random isotropic subspace
searchUlrich(CliffordModule,Ring) -- see searchUlrich -- searching an Ulrich module of smallest possible rank, or an Ulrich module of given rank.
searchUlrich(CliffordModule,Ring,ZZ) -- see searchUlrich -- searching an Ulrich module of smallest possible rank, or an Ulrich module of given rank.
tensorProduct(CliffordModule,VectorBundleOnE) -- see tensorProduct -- tensor product of sheaves on the elliptic curve or sheaf times CliffordModule
translateIsotropicSubspace(CliffordModule,VectorBundleOnE,PolynomialRing) -- see translateIsotropicSubspace -- choose a random isotropic subspace

The source of this document is in /build/reproducible-path/macaulay2-1.26.06+ds/M2/Macaulay2/packages/PencilsOfQuadrics.m2:2097:0.