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ToricInvariants :: ToricInvariants

ToricInvariants -- Given a projective toric variety, the package computes the degree and codimension of the dual, the Euclidean distance degree, polar degrees, and Chern-Mather class

Description

Given a projective toric variety XA defined by a full rank integer matrix A with the vector (1,1,...,1) in its row space, the package computes the degree and codimension of the dual (i.e. the A-discriminant variety), the Euclidean distance degree of XA, the polar degrees of XA, and the Chern-Mather class of XA. Note that we do not require that XA is normal. This package uses the algorithms described in [1] and [2]. For definitions of the objects computed by the package see [1,2].

References:
[1] Martin Helmer and Bernd Sturmfels. "Nearest points on toric varieties." Mathematica Scandinavica 122, no. 2 (2018): 213-238. Arxiv version: https://arxiv.org/abs/1603.06544.
[2] Martin Helmer and Bernt Ivar Utstol Nodland. "Polar degrees and closest points in codimension two." Journal of Algebra and Its Applications (2017): 1950095. Arxiv version: https://arxiv.org/abs/1711.02381.

Author

Version

This documentation describes version 3.01 of ToricInvariants.

Source code

The source code from which this documentation is derived is in the file ToricInvariants.m2.

Exports

  • Functions and commands
    • cmClass -- Computes the Chern-Mather class of a projective toric variety
    • cmVolumes -- Computes the Chern-Mather volumes of a projective toric variety
    • dualDegCodim -- Computes the degree and codimension of the dual to a projective toric variety
    • edDeg -- Computes the (generic) Euclidean distance degree of a projective toric variety
    • polarDegrees -- Computes the polar degrees of a projective toric variety
  • Symbols
    • ForceAmat (missing documentation)
    • Output (missing documentation)
    • TextOutput (missing documentation)