## Search found 203 matches

26 Mar 2023, 19:17
Forum: Helpdesk
Topic: Fourier-Motzkin Elimination and the projection method
Replies: 7
Views: 465

Of course, we will fix those errors in polymake. However, your specific computation can be rescued as follows: polytope > $C = new Cone(INEQUALITIES =>[[1,0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,00,0,0,0],[0,0,0,0,1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,... 30 Jan 2023, 15:34 Forum: Helpdesk Topic: Computational Complexity of VERTICES_IN_FACETS Replies: 3 Views: 422 ### Re: Computational Complexity of VERTICES_IN_FACETS OK, so for fixed dimension d, assuming the resulting polytope to be simplicial (with prob 1) is indeed crucial for the algorithms to run in linear time? This is not what I said. Note that in the expression O(mnd) the parameter m (number of facets) depends on n (number of vertices/input points). Rou... 03 Jan 2023, 16:57 Forum: Helpdesk Topic: Computational Complexity of VERTICES_IN_FACETS Replies: 3 Views: 422 ### Re: Computational Complexity of VERTICES_IN_FACETS Indeed, polymake employs a convex hull computation to compute the vertex-facet incidences from input points. Most algorithms/implementations produce FACETS and VERTICES_IN_FACETS together. If this is not the case there is a second step to compute scalar products between each row of VERTICES and each... 03 Jan 2023, 16:32 Forum: Helpdesk Topic: Computational Complexity of VERTICES_IN_FACETS Replies: 3 Views: 422 ### Computational Complexity of VERTICES_IN_FACETS Here is a question that I received: I was wondering what computational complexity I can expect from VERTICES_IN_FACETS for m vertices on the d sphere. Does it rely on a convex hull algorithm? If yes, on which? As I am using this wonderfully practicable function as a non-specialist in convex geometry... 23 Sep 2022, 18:19 Forum: General Discussion Topic: How to define Newton polytopes of a list of polynomials and compute the vertices, rays? Replies: 3 Views: 2094 ### Re: How to define Newton polytopes of a list of polynomials and compute the vertices, rays? A google search for "polymake" and "newton polytope" reveals: https://polymake.org/doku.php/user_guid ... s_tutorial 06 Sep 2022, 09:39 Forum: Helpdesk Topic: How we can get the integer hull facets by using Polymake? Replies: 5 Views: 1085 ### Re: How we can get the integer hull facets by using Polymake? The code of the client gc_closure can be viewed on github. The algorithm is described in §22.3 and §23.1 of Schrijver's book on integer and linear programming (Wiley 1986). 22 Aug 2022, 09:47 Forum: Helpdesk Topic: How we can get the integer hull facets by using Polymake? Replies: 5 Views: 1085 ### Re: How we can get the integer hull facets by using Polymake? The first description is the facet description of your input. Here it is essentially the same as your input, as the given inequalities proved to be irredundant. For an overview of how to apply polymake in the context of integer linear programming, including integer hulls, see this tutorial . More de... 08 Aug 2022, 13:50 Forum: Helpdesk Topic: Error realize()-ing a Harnack curve defined via its dual subdivision Replies: 2 Views: 981 ### Re: Error realize()-ing a Harnack curve defined via its dual subdivision There are two "issues" here which come together: (1) As you already assumed there are no canonical embeddings (defined). Hence that operation cannot be done by polymake. (2) Due to the combination of a very general abstract framework (implemented in a standard programming language; here: p... 26 Jun 2022, 22:10 Forum: Helpdesk Topic: orientation of dual polyhedra to each other Replies: 2 Views: 967 ### 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.$J = johnson_solid(90); $PJ = polarize($J); compose($J->VISUAL(FacetColor=>"red",VertexLabels=>"hidden"),$PJ->VISUAL(FacetColor=>"blue",VertexLabels=>&qu...
21 Apr 2022, 19:10
Forum: Helpdesk
Topic: Is this the fastest way to compute the Betti numbers ?
Replies: 4
Views: 1374

### 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...