extensions:tropicalcubics

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extensions:tropicalcubics [2019/05/28 13:29] – [Download] joswigextensions:tropicalcubics [2021/01/12 14:34] (current) – external edit 127.0.0.1
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-====== Tropical Cubics ======+====== TropicalCubics ======
  
-This is the software companion to the article "The Schäfli fan" by +This is the software companion to the article "The Schläfli fan" by 
-[[https://page.math.tu-berlin.de/~joswig/|Michael Joswig]], [[https://page.math.tu-berlin.de/~panizzut/|Marta Panizzut]] and [[https://math.berkeley.edu/~bernd/|Bernd Sturmfels]], arXiv:1905.xyz+[[https://page.math.tu-berlin.de/~joswig/|Michael Joswig]], [[https://page.math.tu-berlin.de/~panizzut/|Marta Panizzut]] and [[https://math.berkeley.edu/~bernd/|Bernd Sturmfels]], [[https://arxiv.org/abs/1905.11951|arXiv:1905.11951]]
  
 Smooth tropical cubic surfaces are parameterized by maximal cones in the unimodular secondary fan of the triple tetrahedron.  There are 344 843 867 such cones, organized into a [[https://db.polymake.org|database]] of 14 373 645 symmetry classes. The Schläfli fan gives a further refinement of these cones. It reveals all possible patterns of the 27 Smooth tropical cubic surfaces are parameterized by maximal cones in the unimodular secondary fan of the triple tetrahedron.  There are 344 843 867 such cones, organized into a [[https://db.polymake.org|database]] of 14 373 645 symmetry classes. The Schläfli fan gives a further refinement of these cones. It reveals all possible patterns of the 27
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 ===== Download ===== ===== Download =====
  
-[[http://http://page.math.tu-berlin.de/~joswig/software/polymake/TropicalCubics-0.1.tar.xz|TropicalCubics-0.1.tar.xz]] [28 May 2019]+[[http://page.math.tu-berlin.de/~joswig/software/polymake/TropicalCubics-0.2.tar.xz|TropicalCubics-0.2.tar.xz]] [04 Feb 2020], for polymake version 4.0 
 + 
 +[[http://page.math.tu-berlin.de/~joswig/software/polymake/TropicalCubics-0.1.tar.xz|TropicalCubics-0.1.tar.xz]] [28 May 2019], for polymake versions 3.5 and 3.6
  
 ===== Installation ===== ===== Installation =====
  
-This requires an installation of polymake, version 3.5 (or a developer'version no later than 28 May 2019).+This requires an installation of polymake, version 4.0.  For polymake 3.5 or 3.6 use version 0.1 of this extension instead.
  
 After download you first need to extract the code. After download you first need to extract the code.
 <code> <code>
-tar Jxpf TropicalCubics-0.1.tar.xz+tar Jxpf TropicalCubics-0.2.tar.xz
 </code> </code>
-Suppose this ends up at ''/your/path/TropicalCubics'' Then you start up polymake.  Within the polymake shell do:+Suppose this ends up at ''/your/path/TropicalCubics-0.2'' Then you start up polymake.  Within the polymake shell do:
 <code> <code>
-import_extension "/your/path/TropicalCubics";+import_extension "/your/path/TropicalCubics-0.2";
 </code> </code>
-Afterwards you are good to run the code.  This import needs to be performed only once.  The reference to the extension is permanently stored in ''$HOME/.polymake/prefer.pl'' For more details there is a [[user_guide/extend/extensions|guide to polymake's extension system]].+Do not forget to use an absolute path!  Afterwards you are good to run the code.  This import needs to be performed only once.  The reference to the extension is permanently stored in ''$HOME/.polymake/settings'' For more details there is a [[user_guide/extend/extensions|guide to polymake's extension system]].
 ===== Examples ===== ===== Examples =====
  
-This extension makes contributions to the applications ''fan'' and ''tropical''.+This extension contributes to the applications ''fan'' and ''tropical''.
  
 In the application ''tropical'' you can create a dense tropical cubic surface by just specifying the coordinates. In the application ''tropical'' you can create a dense tropical cubic surface by just specifying the coordinates.
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 The bulk of the functionality sits in the application ''fan'' and the type ''DualSubdivisionOfCubic''. The bulk of the functionality sits in the application ''fan'' and the type ''DualSubdivisionOfCubic''.
 +The latter is derived from ''SubdivisionOfPoints''.
 <code> <code>
 > print $S->DUAL_SUBDIVISION->type->full_name; > print $S->DUAL_SUBDIVISION->type->full_name;
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 </code> </code>
  
-Suppose you have a triangulation of $3 \Delta_3$ and you want to find it.  This example comes from §6.2 of [[https://link.springer.com/chapter/10.1007/978-3-319-70566-8_14|Hampe & Joswig: Tropical computations in polymake, in: Algorithmic and experimental methods in algebra, geometry, and number theory, Springer 2017]].  This is again in application ''tropical''.+Suppose you have a triangulation of $3 \Delta_3$ and you want to find it.  The next example comes from §6.2 of [[https://link.springer.com/chapter/10.1007/978-3-319-70566-8_14|Hampe & Joswig: Tropical computations in polymake, in: Algorithmic and experimental methods in algebra, geometry, and number theory, Springer 2017]].  This is again in application ''tropical''.
 <code> <code>
 > $F = toTropicalPolynomial("min(12+3*x0,-131+2*x0+x1, > $F = toTropicalPolynomial("min(12+3*x0,-131+2*x0+x1,
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 </code> </code>
 So this corresponds to the triangulation #5054117 constructed above (and stored in the variable ''$X''). So this corresponds to the triangulation #5054117 constructed above (and stored in the variable ''$X'').
 +For about 99.5% of all triangulations the canonical hash value (computed by [[http://pallini.di.uniroma1.it/|nauty]]) identifies the triangulations uniquely.  In the remaining cases the function ''retrieve_by_canonical_hash'' returns the first triangulation and issues a warning.
 +
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  • Last modified: 2019/05/28 13:29
  • by joswig