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

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ren
Posts: 25
Joined: 03 May 2011, 15:21

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

Postby ren » 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.

ren
Posts: 25
Joined: 03 May 2011, 15:21

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

Postby ren » 11 Nov 2017, 09:51

Oops, the solution is quite apparent:

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

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gawrilow
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Posts: 311
Joined: 25 Dec 2010, 17:40

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

Postby gawrilow » 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.

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joswig
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Posts: 209
Joined: 24 Dec 2010, 11:10

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

Postby joswig » 13 Nov 2017, 09:45

Recall that polymake employs homogeneous polynomials for defining tropical hypersurfaces!


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