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D.13.6.6 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";
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
==> 0sh: xdg-open: Kommando nicht gefunden.
==>
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