Singular Manual: drawTropicalCurve

| #### D.13.4.6 drawTropicalCurve Procedure from library `tropical.lib` (see tropical_lib). Usage: drawTropicalCurve(f[,#]); f poly or list, # 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/tropicalcurveNUMBER.tex and /tmp/tropicalcurveNUMBER.ps, where NUMBER is a random four digit integer; moreover it displays the tropical curve via xdg-open; if you wish to remove all these files from /tmp, call the procedure cleanTmp - edges with multiplicity greater than one carry this multiplicity - 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 - if the last optional argument is 'onlytexfile' then only the latex file is produced; this option should be used if xdg-utils is not installed on your system - 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 xdg-open
    drawTropicalCurve(f);
    ==> This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017) (preloaded\
        format=latex)
    ==>  restricted \write18 enabled.
    ==> entering extended mode
    ==> (/tmp/tropicalcurve6034.tex
    ==> LaTeX2e <2017/01/01> patch level 3
    ==> Babel <3.10> and hyphenation patterns for 3 language(s) loaded.
    ==> (/usr/share/texmf-dist/tex/latex/amscls/amsart.cls
    ==> Document Class: amsart 2015/03/04 v2.20.2
    ==> (/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 \setlength
    ==>               {\topmargin}{30mm}^^M
    ==> No pages of output.
    ==> Transcript written on tropicalcurve6034.log.
    ==> This is dvips(k) 5.997 Copyright 2017 Radical Eye Software (www.radicaley\
       e.com)
    ==> dvips: DVI file can't be opened: /tmp/tropicalcurve6034.dvi: No such file\
        or directory
    ==> rm: das Entfernen von 'tropicalcurve6034.aux' ist nicht möglich: Datei o\
       der Verzeichnis nicht gefunden
    ==> rm: das Entfernen von 'tropicalcurve6034.ps?' ist nicht möglich: Datei o\
       der Verzeichnis nicht gefunden
    ==> rm: das Entfernen von 'tropicalcurve6034.dvi' ist nicht möglich: Datei o\
       der Verzeichnis nicht gefunden
    ==> 0
    ==> sh: xdg-open: Kommando nicht gefunden.
    // we can instead apply the procedure to a tropical polynomial and use "maximum"
    poly g=1/t3*(x7+y7+1)+t3*(x4+y4+x2+y2+x3y+xy3)+t21*x2y2;
    list tropical_g=tropicalise(g);
    tropical_g;
    ==> [1]:
    ==>    7*x-3
    ==> [2]:
    ==>    7*y-3
    ==> [3]:
    ==>    4*x+3
    ==> [4]:
    ==>    3*x+y+3
    ==> [5]:
    ==>    2*x+2*y+21
    ==> [6]:
    ==>    x+3*y+3
    ==> [7]:
    ==>    4*y+3
    ==> [8]:
    ==>    2*x+3
    ==> [9]:
    ==>    2*y+3
    ==> [10]:
    ==>    -3
    drawTropicalCurve(tropical_g,"max");
    ==> This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017) (preloaded\
        format=latex)
    ==>  restricted \write18 enabled.
    ==> entering extended mode
    ==> (/tmp/tropicalcurve9641.tex
    ==> LaTeX2e <2017/01/01> patch level 3
    ==> Babel <3.10> and hyphenation patterns for 3 language(s) loaded.
    ==> (/usr/share/texmf-dist/tex/latex/amscls/amsart.cls
    ==> Document Class: amsart 2015/03/04 v2.20.2
    ==> (/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 \setlength
    ==>               {\topmargin}{30mm}^^M
    ==> No pages of output.
    ==> Transcript written on tropicalcurve9641.log.
    ==> This is dvips(k) 5.997 Copyright 2017 Radical Eye Software (www.radicaley\
       e.com)
    ==> dvips: DVI file can't be opened: /tmp/tropicalcurve9641.dvi: No such file\
        or directory
    ==> rm: das Entfernen von 'tropicalcurve9641.aux' ist nicht möglich: Datei o\
       der Verzeichnis nicht gefunden
    ==> rm: das Entfernen von 'tropicalcurve9641.ps?' ist nicht möglich: Datei o\
       der Verzeichnis nicht gefunden
    ==> rm: das Entfernen von 'tropicalcurve9641.dvi' ist nicht möglich: Datei o\
       der Verzeichnis nicht gefunden
    ==> 0
    ==> sh: xdg-open: Kommando nicht gefunden.

User manual for Singular version 4-1-3, 2020, generated by texi2html.