### D.13.7 tropicalNewton_lib

Library:
  tropicalNewton.lib
Purpose:
  Computations in Tropical Geometry using Newton Polygon methods

Authors:
  Tommy Hofman, email: thofmann@mathematik.uni.kl.de Yue Ren, email: reny@cs.bgu.ac.il

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

See also: tropicalVariety; tropical_lib.

User manual for Singular version 4.4.1, 2025, generated by texi2html.