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by joswig
26 Jun 2022, 22:10
Forum: Helpdesk
Topic: orientation of dual polyhedra to each other
Replies: 2
Views: 71

Re: orientation of dual polyhedra to each other

The compose command puts several visualized objects into the same coordinate system. Should work with all backends.

Code: Select all

$J = johnson_solid(90); $PJ = polarize($J); compose($J->VISUAL(FacetColor=>"red",VertexLabels=>"hidden"), $PJ->VISUAL(FacetColor=>"blue",VertexLabels=>"hidden"));
by joswig
21 Apr 2022, 19:10
Forum: Helpdesk
Topic: Is this the fastest way to compute the Betti numbers ?
Replies: 4
Views: 313

Re: Is this the fastest way to compute the Betti numbers ?

polymake thinks of objects (here tropical::Hypersurface) as a list of properties (each of which comes with a type). There are defining properties (here MONOMIALS and COEFFICIENTS) which just specify what it is that you are talking about. Then there are derived properties (such as, e.g., the dimensio...
by joswig
20 Apr 2022, 18:41
Forum: Helpdesk
Topic: Is this the fastest way to compute the Betti numbers ?
Replies: 4
Views: 313

Re: Is this the fastest way to compute the Betti numbers ?

Indeed, the triangulation (induced by MONOMIALS and COEFFICIENTS) is the same. Yet your code already exploits this automatically. The property PATCHWORK is declared multiple (see apps/tropical/rules/patchwork.rules) which means that all the patchworks for all your choices of signs will be kept. Prob...
by joswig
11 Apr 2022, 16:45
Forum: General Discussion
Topic: My polymake is running for more than 12hours
Replies: 1
Views: 368

Re: My polymake is running for more than 12hours

A polytope in 70 dimensions with 200 inequalities may have as many as 983858800923516812309510979394668240 vertices (by McMullen's upper bound theorem). Of course that number can also be much smaller. In general, there is no good way to tell ahead of time if such a computation is possible and how lo...
by joswig
30 Mar 2022, 11:56
Forum: General Discussion
Topic: Scaling of mixed volume
Replies: 1
Views: 302

Re: Scaling of mixed volume

All known algorithms for computing the mixed volume are exponential in the dimension. Since even computing the volume is known to be #P-hard there is no hope for any improvement.
by joswig
06 Mar 2022, 20:37
Forum: Helpdesk
Topic: Static library/Linking Polymake C++ code for windows machine
Replies: 5
Views: 628

Re: Static library/Linking Polymake C++ code for windows machine

One comment: to run polymake code on a pure Windows machine you could employ some live version of Linux, e.g., Ubuntu . And a question: which computation do you want to do with CPLEX? polymake is capable of solving (mixed integer) linear programs exactly. Of course, CPLEX is much faster (as it uses ...
by joswig
04 Mar 2022, 17:36
Forum: Helpdesk
Topic: Equivalence between a PORTA output and Polymake output for same input
Replies: 1
Views: 289

Re: Equivalence between a PORTA output and Polymake output for same input

If "0 >= -1" occurs as a facet, then your polyhedron is necessarily unbounded. The converse, by the way, is not true. The thing is that combinatorially polymake treats all polyhedra as bounded polytopes (with a marked face at infinity, which may have any dimension). This has a number of algorithmic ...
by joswig
03 Mar 2022, 18:42
Forum: Helpdesk
Topic: Accessing facets and affine hull data structures in C++
Replies: 6
Views: 629

Re: Accessing facets and affine hull data structures in C++

There are several things to consider then: (1) If you pass float coordinates as point coordinates of a Polytope object, then they will be converted to exact rationals automatically. (2) In general, there is no way (known) to "approximately" compute convex hulls with floats throughout. In dimension 3...
by joswig
03 Mar 2022, 17:01
Forum: Helpdesk
Topic: Accessing facets and affine hull data structures in C++
Replies: 6
Views: 629

Re: Accessing facets and affine hull data structures in C++

(1)Is it safe to simply cast the Rational scalar to a double for further usage in my application? In general: no. Rational is an exact type, double is not. If a conversion makes sense or not will depend on what you want to compute. Usually, you just want to stick with Rational. polymake supports ar...
by joswig
03 Mar 2022, 10:08
Forum: Helpdesk
Topic: Accessing facets and affine hull data structures in C++
Replies: 6
Views: 629

Re: Accessing facets and affine hull data structures in C++

A few more remarks: (1) Specifying polytopes in terms of a V-description works by providing POINTS. Using VERTICES is potentially more efficient, but this requires that the points (i.e., rows of the matrix) are actually, the vertices, and without repetitions. (2) We use a homogeneous coordinate mode...

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