This is a package for the computer algebra system Magma providing a toolkit for hypersurfaces and complete intersections in toric varieties.
Go to the directory with the spec file and start a Magma session.
The provided intrinsics are available after loading the package with the following command.
AttachSpec("spec");
This package provides the following user-defined intrinsics.
- For graded hypersurface rings
SearchPrimeBinomial: search for homogeneous prime binomialsDimHomComp: compute vector space dimension of homogeneous componentsGeneratorDegreeDimensionTuple: compute the dimension of the homogeneous components of the generator degreesHilbertCoeffs: compute the first coefficients of the Hilbert seriesIsMuAmbientSmooth: check if the mu-minimal ambient toric variety is smoothQuasismoothTest: check necessary conditions for quasismoothness
- For polynomial systems
FacePolynomial: compute the polynomial associated with a face of the Newton polytopeFaceSystem: compute the system associated with a face of the Newton polytopeIsNondegenerate: check the non-degeneracy condition
- For toric varieties and complete intersection Cox rings
ToricIntersectionProduct: compute intersection numbers on Q-factorial projective toric varietiesFanoDegree: compute anticanonical self-intersection number of a Fano variety with complete intersection Cox ring
- Miscellanea
IsZZGenerating: check if given elements form a generating set of an abelian groupFiberPoints: compute the lattice points of the positive orthant that live in the fiber of a group homomorphismIsDolgachevPolytope: check if a polytope is a Dolgachev polytopeIsHomPermutation: check if given subsets of a lattice are equal up to a certain permutation of coordinates
Examples can be found in the examples folder.
This library is provided as is and is still under development. There is no warranty. Use it at your own risk. If you find bugs or errors, please don't hesitate to contact me.