Singular

D.13.4.7 drawNewtonSubdivision

Procedure from library tropical.lib (see tropical_lib).

Usage:
drawTropicalCurve(f[,#]); f poly, # optional list

Assume:
f is list of linear polynomials of the form ax+by+c with integers a, b and a rational number c representing a tropical Laurent polynomial defining a tropical plane curve;
alternatively f can be a polynomial in Q(t)[x,y] defining a tropical plane curve via the valuation map;
the basering must have a global monomial ordering, two variables and up to one parameter!

Return:
NONE

Note:
- the procedure creates the files /tmp/newtonsubdivisionNUMBER.tex, and /tmp/newtonsubdivisionNUMBER.ps, where NUMBER is a random four digit integer;
moreover it desplays the tropical curve defined by f via kghostview; if you wish to remove all these files from /tmp, call the procedure cleanTmp;
if # is empty, then the tropical curve is computed w.r.t. minimum, if #[1] is the string 'max', then it is computed w.r.t. maximum
- note that lattice points in the Newton subdivision which are black correspond to markings of the marked subdivision, while lattice points in grey are not marked

Example:
 LIB "tropical.lib"; ==> Welcome to polymake version ==> Copyright (c) 1997-2015 ==> Ewgenij Gawrilow, Michael Joswig (TU Darmstadt) ==> http://www.polymake.org ring r=(0,t),(x,y),dp; poly f=t*(x3+y3+1)+1/t*(x2+y2+x+y+x2y+xy2)+1/t2*xy; // the command drawTropicalCurve(f) computes the graph of the tropical curve // given by f and displays a post script image, provided you have kghostview drawNewtonSubdivision(f); ==> This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2014) (preloaded\ format=latex) ==> restricted \write18 enabled. ==> entering extended mode ==> (/tmp/newtonsubdivision6034.tex ==> LaTeX2e <2014/05/01> ==> Babel <3.9l> and hyphenation patterns for 2 languages loaded. ==> (/usr/share/texmf-dist/tex/latex/amscls/amsart.cls ==> Document Class: amsart 2009/07/02 v2.20.1 ==> (/usr/share/texmf-dist/tex/latex/amsmath/amsmath.sty ==> For additional information on amsmath, use the ?' option. ==> (/usr/share/texmf-dist/tex/latex/amsmath/amstext.sty ==> (/usr/share/texmf-dist/tex/latex/amsmath/amsgen.sty)) ==> (/usr/share/texmf-dist/tex/latex/amsmath/amsbsy.sty) ==> (/usr/share/texmf-dist/tex/latex/amsmath/amsopn.sty)) ==> (/usr/share/texmf-dist/tex/latex/amsfonts/umsa.fd) ==> (/usr/share/texmf-dist/tex/latex/amsfonts/amsfonts.sty)) ==> ==> ! LaTeX Error: File texdraw.sty' not found. ==> ==> Type X to quit or to proceed, ==> or enter new name. (Default extension: sty) ==> ==> Enter file name: warning: kpathsea: $.sty: Unrecognized variable construc\ t $.'. ==> ==> ! LaTeX Error: File \$.sty' not found. ==> ==> Type X to quit or to proceed, ==> or enter new name. (Default extension: sty) ==> ==> Enter file name: ==> ! Emergency stop. ==> ==> ==> l.3 \begin ==> {document}^^M ==> No pages of output. ==> Transcript written on newtonsubdivision6034.log. ==> This is dvips(k) 5.994 Copyright 2014 Radical Eye Software (www.radicaley\ e.com) ==> dvips: DVI file can't be opened: /tmp/newtonsubdivision6034.dvi: No such \ file or directory ==> rm: das Entfernen von „newtonsubdivision6034.aux“ ist nicht möglich:\ Datei oder Verzeichnis nicht gefunden ==> rm: das Entfernen von „newtonsubdivision6034.ps?“ ist nicht möglich:\ Datei oder Verzeichnis nicht gefunden ==> rm: das Entfernen von „newtonsubdivision6034.dvi“ ist nicht möglich:\ Datei oder Verzeichnis nicht gefunden ==> sh: kghostview: Kommando nicht gefunden. ==> 0 // we can instead apply the procedure to a tropical polynomial poly g=x+y+x2y+xy2+1/t*xy; list tropical_g=tropicalise(g); tropical_g; ==> [1]: ==> 2*x+y ==> [2]: ==> x+2*y ==> [3]: ==> x+y-1 ==> [4]: ==> x ==> [5]: ==> y drawNewtonSubdivision(tropical_g); ==> This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2014) (preloaded\ format=latex) ==> restricted \write18 enabled. ==> entering extended mode ==> (/tmp/newtonsubdivision9641.tex ==> LaTeX2e <2014/05/01> ==> Babel <3.9l> and hyphenation patterns for 2 languages loaded. ==> (/usr/share/texmf-dist/tex/latex/amscls/amsart.cls ==> Document Class: amsart 2009/07/02 v2.20.1 ==> (/usr/share/texmf-dist/tex/latex/amsmath/amsmath.sty ==> For additional information on amsmath, use the ?' option. ==> (/usr/share/texmf-dist/tex/latex/amsmath/amstext.sty ==> (/usr/share/texmf-dist/tex/latex/amsmath/amsgen.sty)) ==> (/usr/share/texmf-dist/tex/latex/amsmath/amsbsy.sty) ==> (/usr/share/texmf-dist/tex/latex/amsmath/amsopn.sty)) ==> (/usr/share/texmf-dist/tex/latex/amsfonts/umsa.fd) ==> (/usr/share/texmf-dist/tex/latex/amsfonts/amsfonts.sty)) ==> ==> ! LaTeX Error: File texdraw.sty' not found. ==> ==> Type X to quit or to proceed, ==> or enter new name. (Default extension: sty) ==> ==> Enter file name: ==> ! Emergency stop. ==> ==> ==> l.3 \begin ==> {document}^^M ==> No pages of output. ==> Transcript written on newtonsubdivision9641.log. ==> This is dvips(k) 5.994 Copyright 2014 Radical Eye Software (www.radicaley\ e.com) ==> dvips: DVI file can't be opened: /tmp/newtonsubdivision9641.dvi: No such \ file or directory ==> rm: das Entfernen von „newtonsubdivision9641.aux“ ist nicht möglich:\ Datei oder Verzeichnis nicht gefunden ==> rm: das Entfernen von „newtonsubdivision9641.ps?“ ist nicht möglich:\ Datei oder Verzeichnis nicht gefunden ==> rm: das Entfernen von „newtonsubdivision9641.dvi“ ist nicht möglich:\ Datei oder Verzeichnis nicht gefunden ==> sh: kghostview: Kommando nicht gefunden. ==> 0 ==> > fgets() failed with errno 9