Singular Manual: drawNewtonSubdivision

| #### 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 <RETURN> 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 <RETURN> to proceed,
    ==> or enter new name. (Default extension: sty)
    ==>
    ==> Enter file name:
    ==> ! Emergency stop.
    ==> <read *>
    ==>
    ==> 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 <RETURN> to proceed,
    ==> or enter new name. (Default extension: sty)
    ==>
    ==> Enter file name:
    ==> ! Emergency stop.
    ==> <read *>
    ==>
    ==> 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

User manual for Singular version 4-1-0, 2016, generated by texi2html.