user_guide:tutorials:apps_tropical

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tutorial:apps_tropical [2015/10/29 10:32] – hampetutorial:apps_tropical [2017/06/12 18:29] – [Tropical arithmetics] removed faulty polynomial syntax oroehrig
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   * Tropical convex hull computations   * Tropical convex hull computations
   * Tropical cycles and hypersurfaces.   * Tropical cycles and hypersurfaces.
 +
 +To use the full palette of tools for tropical geometry, switch to the corresponding application by typing the following in the ''polymake'' shell:
 +<code>
 +> application 'tropical';
 +</code>
  
 === Disclaimer: Min or Max - you have to choose! === === Disclaimer: Min or Max - you have to choose! ===
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 === Disclaimer 2: Newest version required === === Disclaimer 2: Newest version required ===
  
-Most of the features described here only work in polymake version 2.15beta3 or newer (i.e. you should get the [[:perpetualbeta|perpetual beta]]).+Most of the features described here only work in polymake version 3.0 or newer.
  
 ==== Tropical arithmetics ==== ==== Tropical arithmetics ====
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 </code> </code>
  
-Finally, you can also create tropical polynomials. This can either be done in the [[polynomials_tutorial|usual manner]] or with a special parser:+Finally, you can also create tropical polynomials. This can be done with the special toTropicalPolynomial parser:
  
 <code> <code>
-tropical > $r = new Ring<TropicalNumber<Min> >(3); #Tropical polynomial ring in 3 variables 
-tropical > ($x, $y, $z) = $r->variables; 
-tropical > $p = $x*$x + $y * $z; 
-tropical > print $p; 
-x0^2 + x1*x2 
 tropical > $q = toTropicalPolynomial("min(2a,b+c)"); tropical > $q = toTropicalPolynomial("min(2a,b+c)");
 tropical > print $q; tropical > print $q;
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 A tropical cone should always be created via ''POINTS'' (i.e. not ''VERTICES''), since they determine the combinatorial structure. The following creates a tropical line segment in the tropical projective plane. Note that the point (0,1,1) is not a vertex, as it is in the tropical convex hull of the other two points. However, it does play a role when computing the corresponding subdivision of the tropical projective torus into covector cells (see the [[apps_tropical#A note on coordinates|note]] below to understand the different coordinates): A tropical cone should always be created via ''POINTS'' (i.e. not ''VERTICES''), since they determine the combinatorial structure. The following creates a tropical line segment in the tropical projective plane. Note that the point (0,1,1) is not a vertex, as it is in the tropical convex hull of the other two points. However, it does play a role when computing the corresponding subdivision of the tropical projective torus into covector cells (see the [[apps_tropical#A note on coordinates|note]] below to understand the different coordinates):
 <code> <code>
-tropical > $c = new Cone<Min>(POINTS=>[[0,0,0],[0,1,1][0,2,1]]);+tropical > $c = new Cone<Min>(POINTS=>[[0,0,0],[0,1,1],[0,2,1]]);
 tropical > print $c->VERTICES; tropical > print $c->VERTICES;
 0 0 0 0 0 0
  • user_guide/tutorials/apps_tropical.txt
  • Last modified: 2019/02/04 22:55
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