Singular Manual: tropicalNewton_lib

> | ### D.15.37 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.15.37.1 setUniformizingParameter |  | sets the uniformizingParameter
> D.15.37.2 val |  | returns valuation of element in ground field
> D.15.37.3 newtonPolygonNegSlopes |  | returns negative of the Newton Polyong slopes
> D.15.37.4 cccMatrixToPositiveIntvec |  | helper function to turn a computed valuation vector into a usable weight vector in Singular
> D.15.37.5 tropicalPointNewton |  | computes point on tropical variety
> D.15.37.6 switchRingsAndComputeInitialIdeal |  | switches rings and computes initial ideal
> D.15.37.7 tropicalVarietyNewton |  | computes tropical variety of zero-dimensional ideal
> D.15.37.8 tropicalLinkNewton |  | computes tropical variety that is polyhedral fan and has codimension one lineality space
See also: tropicalVariety; tropical_lib.

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