## tropicalizing a polynomial g(x1,x2) in K[x0,x1,x2]

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ren
Posts: 30
Joined: 03 May 2011, 15:21

### tropicalizing a polynomial g(x1,x2) in K[x0,x1,x2]

How can I tropicalize a polynomial g(x1,x2) in a polynomial ring K[x0,x1,x2]? I have two polynomials f(x0,x1) and g(x1,x2) in K[x0,x1,x2] and want to visualize the intersection of their hypersurfaces in R^3.

The command "toTropicalPolynomial" tropicalizes x1 to x_0 and x2 to x_1:

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tropical > $g = toTropicalPolynomial("max(x1,x2,0)"); tropical > print$g; x_0 + x_1 + 0 

ren
Posts: 30
Joined: 03 May 2011, 15:21

### Re: tropicalizing a polynomial g(x1,x2) in K[x0,x1,x2]

Oops, the solution is quite apparent:

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\$g = toTropicalPolynomial("max(x1,x2,0+0*x0)");

gawrilow
Main Author
Posts: 349
Joined: 25 Dec 2010, 17:40

### Re: tropicalizing a polynomial g(x1,x2) in K[x0,x1,x2]

toTropicalPolynomial can be called with an explicit list of variable names, in your case it would be:

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 toTropicalPolynomial("max(x1,x2)", qw(x0 x1 x2));
Pressing F1 in the polymake shell (after having typed in the function name) would reveal this trick to you fully free of charge.

joswig
Main Author
Posts: 216
Joined: 24 Dec 2010, 11:10

### Re: tropicalizing a polynomial g(x1,x2) in K[x0,x1,x2]

Recall that polymake employs homogeneous polynomials for defining tropical hypersurfaces!