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Posted: **11 Nov 2017, 08:04**

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

thanks in advance, Yue.

Posted: **11 Nov 2017, 09:51**

Oops, the solution is quite apparent:

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

Posted: **11 Nov 2017, 18:48**

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.

Posted: **13 Nov 2017, 09:45**

Recall that polymake employs homogeneous polynomials for defining tropical hypersurfaces!

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

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

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

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

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