Reid's theorem says that the set of maximal isotropic subspaces on a complete intersection of two quadrics in (2g+2) variables is isomorphic to the set of degree 0 line bundles on the associated hyperelliptic curve E of genus g. The method chooses a random line bundle L of degree 0 on E, and computes the maximal isotropic subspace ru corresponding to the translation of u by L.
i1 : kk=ZZ/101; |
i2 : g=2; |
i3 : (S,qq,R,u, M1,M2, Mu1,Mu2) = randomNicePencil(kk,g); |
i4 : M=cliffordModule (Mu1, Mu2, R); |
i5 : ru=randomIsotropicSubspace(M,S) o5 = | y_1-36z_1-2z_2 y_0+20z_1+17z_2 x_1+25z_1-12z_2 x_0+40z_1-43z_2 | 1 4 o5 : Matrix S <--- S |
i6 : assert (betti ru == betti u) |
The ground field kk (=coefficientRing S) has to be finite, since it uses the method randomLineBundle.
The object randomIsotropicSubspace is a method function.