Constructing tropical complex

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julsoles

Constructing tropical complex

Postby julsoles » 14 Mar 2016, 02:04

I am trying to construct a tropical complex from given points. I define the points in a matrix as follows and try to call the function "tropical_complex" but get the following error:

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tropical> $p1 = new Matrix<Rational>([[0,0,2],[0,2,0],[0,1,-2]]); tropical> print tropical_complex($p1); ERROR: Undefined subroutine &Polymake::User::tropical_complex called at input line 1.
Could anyone tell me why this error is happening and how I could solve it?

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hampe
Developer
Posts: 48
Joined: 29 Apr 2011, 10:42

Re: Constructing tropical complex

Postby hampe » 14 Mar 2016, 11:29

The whole tropical functionality has been heavily remodeled and some older functions have been removed/refactored into other objects/functions.

As far as I can tell from the old code, the function tropical_complex was supposed to compute the subdivision of the tropical torus obtained by putting a max-tropical hyperplane at each of the given points - is that what you want?

In that case, this is now part of the functionality of the Cone object in application tropical This represents a tropical convex hull of points in tropical projective coordinates. Among other things, one can also ask for the type subdivision of the tropical torus induced by the points. This is exactly the operation described above. In your example (I assume your points are points in the plane already in homogeneous coordinates? Otherwise you have to add another zero coordinate):

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tropical> $c = new Cone<Min>(POINTS=>[[0,0,2],[0,2,0],[0,1,-2]]); tropical> $t = $c->torus_subdivision_as_complex(); tropical> $t->VISUAL;
Note that putting max-hyperplanes at each point corresponds to considering the Min-convex-hull, thus the <Min> in the code.


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