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D.13.6.7 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 xdg-open;
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";
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
drawNewtonSubdivision(f);
// 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;
drawNewtonSubdivision(tropical_g);
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