Singular

D.13.7 tropicalNewton_lib

Library:

tropicalNewton.lib

Purpose:

Computations in Tropical Geometry using Newton Polygon methods

Authors:

Tommy Hofman, email: [email protected] Yue Ren, email: [email protected]

Overview:

This libraries contains algorithms for computing
- non-trivial points on tropical varieties,
- zero-dimensional tropical varieties,
- one-codimensional links of tropical varieties
based on Newton polygon methods.

References:

Hofmann, Ren: Computing tropical points and tropical links, arXiv:1611.02878 (WARNING: this library follows the max convention instead and triangular sets follow the definition of the Singular book)

Procedures:

D.13.7.1 setUniformizingParameter		sets the uniformizingParameter
D.13.7.2 val		returns valuation of element in ground field
D.13.7.3 newtonPolygonNegSlopes		returns negative of the Newton Polyong slopes
D.13.7.4 cccMatrixToPositiveIntvec		helper function to turn a computed valuation vector into a usable weight vector in Singular
D.13.7.5 tropicalPointNewton		computes point on tropical variety
D.13.7.6 switchRingsAndComputeInitialIdeal		switches rings and computes initial ideal
D.13.7.7 tropicalVarietyNewton		computes tropical variety of zero-dimensional ideal
D.13.7.8 tropicalLinkNewton		computes tropical variety that is polyhedral fan and has codimension one lineality space