## Search found 206 matches

18 Oct 2023, 15:53
Forum: Helpdesk
Topic: Recognizing the topology of surfaces
Replies: 8
Views: 8975

Could you please upload your $my_dual_sub and $my_signs? One way would be to save the $S_0 object and share the resulting JSON. I can't promise, but maybe we can do a bit more here. 23 Aug 2023, 11:27 Forum: General Discussion Topic: constructing the bisectors of angles in polyhedra Replies: 3 Views: 8385 ### Re: constructing the bisectors of angles in polyhedra I still don't understand. Let's postpone this. Concerning your tertatoid, I think I know a way, modulo some experimenting. Here are the steps. (1) Construct the regular tetrahedron as the convex hull of every other vertex of the cube [-1,1]^3. Call this polytope T. (2) From each edge of T construct ... 22 Aug 2023, 12:50 Forum: General Discussion Topic: constructing the bisectors of angles in polyhedra Replies: 3 Views: 8385 ### Re: constructing the bisectors of angles in polyhedra What is the "perpendicular bisector" of an edge? Do you mean the affine hyperplane which is perpendicular to a given edge, passing through the midpoint of that edge? Your "tetartoid" is given without coordinates, and from the description given on that web page I cannot deduce how... 26 Mar 2023, 19:17 Forum: Helpdesk Topic: Fourier-Motzkin Elimination and the projection method Replies: 7 Views: 7141 ### Re: Fourier-Motzkin Elimination and the projection method Of course, we will fix those errors in polymake. However, your specific computation can be rescued as follows: polytope >$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: 5549

### 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: 5549

### 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: 5549

### 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: 10057

### 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: 6578

### 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: 6578

### 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...