## Search found 210 matches

08 May 2024, 09:47
Forum: Helpdesk
Topic: union of cones
Replies: 1
Views: 252

### Re: union of cones

Here is a simple example (not mathematically interesting):

Code: Select all

polytope > @list_of_cones = (); for (my $i=0;$i<5; ++$i) { my$C = new Cone(INPUT_RAYS=>[[1,0],[1,$i]]); push @list_of_cones,$C; } polytope > $u = fan::union_of_cones(\@list_of_cones); polytope > print$u->F_VECTOR; 5 4 
15 Apr 2024, 09:54
Forum: General Discussion
Topic: Plotting Icosahedron in Polymake
Replies: 2
Views: 1435

### Re: Plotting Icosahedron in Polymake

To show the regular icosahedron you can just use icosahedron()->VISUAL; or icosahedron()->VISUAL_GRAPH; if you only want to see the vertices and the edges. What you will get exactly will depend on the configuration of your setup, the default backend being threejs. To show the four planes additionall...
03 Apr 2024, 11:35
Forum: Helpdesk
Topic: "ERROR: Cannot draw zero cycle at ... "
Replies: 4
Views: 4410

### Re: "ERROR: Cannot draw zero cycle at ... "

Sorry, the correct homogenization of your example is the following. $quadric = toTropicalPolynomial("max(2*x,1+x+y,2+2*y,1+y+z,2*z,4+2*w)");$TQuadric = new Hypersurface<Max>(POLYNOMIAL=>$quadric);$TQuadric->VISUAL; My previous explanation is valid: the input needs to be homogeneous, i.e....
24 Mar 2024, 12:15
Forum: Helpdesk
Topic: "ERROR: Cannot draw zero cycle at ... "
Replies: 4
Views: 4410

### Re: "ERROR: Cannot draw zero cycle at ... "

polymake uses homogeneous polynomials throughout. Please replace the first line of your code by

Code: Select all

$quadric = toTropicalPolynomial("max(2*x,w+x+y,2*w+2*y,w+y+z,2*z,4*w)");  See this tutorial and these jupyter notebooks for more examples. 18 Oct 2023, 15:53 Forum: Helpdesk Topic: Recognizing the topology of surfaces Replies: 8 Views: 15789 ### Re: Recognizing the topology of surfaces 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: 16028

### 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: 16028

### 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: 14409

### 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: 11503

### 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: 11503

### 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...