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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.