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by joswig
19 Nov 2019, 14:49
Forum: News
Topic: polymake 3.6 released
Replies: 0
Views: 4

polymake 3.6 released

This is to announce the release of polymake 3.6. This time we mainly focused on new mathematical concepts and algorithms. In particular we now have: compactifications of tropical hypersurfaces; see Kastner, Shaw and Winz, arXiv:1612.09526 (implementation by the authors) tropical Voronoi diagrams; se...
by joswig
29 Aug 2019, 10:32
Forum: News
Topic: polymake 3.5 released
Replies: 0
Views: 583

polymake 3.5 released

This is to announce the release of polymake 3.5 . Highlights include the following: Thanks to Lars' effort there is new big object type HyperplaneArrangement in application fan. Its key algorithm allows to compute the induced cell decomposition of the surrounding Euclidean space. Moreover, there are...
by joswig
29 Aug 2019, 10:23
Forum: Helpdesk
Topic: affine dependencies of a polytope
Replies: 1
Views: 193

Re: affine dependencies of a polytope

Yes, it works as follows. Let us take the standard square as an example. Your question is about the matroid generated by the vertices. polytope > $V=cube(2)->VERTICES; polytope > $M = new matroid::Matroid(VECTORS=>$V); polytope > print $M->BASES; {0 1 2} {0 1 3} {0 2 3} {1 2 3} Each line describes o...
by joswig
27 Aug 2019, 13:32
Forum: Helpdesk
Topic: Visualization using Ubuntu
Replies: 3
Views: 194

Re: Visualization using Ubuntu

From your description alone it is impossible to say what went wrong. Among other details, in particular, the polymake version number is missing. Most likely, however, it will be a java related issue. Maybe you can try > threejs(simplex(3)->VISUAL); which triggers basic visualization through your web...
by joswig
25 Aug 2019, 12:10
Forum: Helpdesk
Topic: Unexpected behavior when finding regular subdivisions
Replies: 1
Views: 113

Re: Unexpected behavior when finding regular subdivisions

The difference is that fan::SubdivisionOfPoints takes homogeneous coordinates, whereas topaz::GeometricSimplicialComplex does not.
by joswig
23 Aug 2019, 12:08
Forum: Helpdesk
Topic: polytope over quadratic number fields
Replies: 10
Views: 364

Re: polytope over quadratic number fields

Indeed, this is a gap in the documentation. Thanks for pointing this out. I just made an addition to https://polymake.org/doku.php/user_guide/tutorials/coordinates , which will become visible not before tomorrow (after the automated update). Here it comes. polymake has limited support for other orde...
by joswig
21 Aug 2019, 16:16
Forum: Helpdesk
Topic: polytope over quadratic number fields
Replies: 10
Views: 364

Re: polytope over quadratic number fields

A third source of error is that some of the Johnson solids are represented with float coordinates, i.e., coordinate-wise in an inexact way. E.g., polytope > $j = johnson_solid(9); $_=$j->description; chomp; print "$_: ", $j->F_VECTOR, " ", $j->type->full_name, "\n"; Johnson solid J9: Elongated penta...
by joswig
21 Aug 2019, 16:08
Forum: Helpdesk
Topic: polytope over quadratic number fields
Replies: 10
Views: 364

Re: polytope over quadratic number fields

A second potential source of error could be that there are competing conventions as far as names are concerned. Here is one line of polymake code which generates all Johnson solids and lists their names and f-vectors. polytope> for (my $k=1; $k<=92; ++$k) { $j = johnson_solid($k); $_=$j->description...
by joswig
21 Aug 2019, 15:56
Forum: Helpdesk
Topic: polytope over quadratic number fields
Replies: 10
Views: 364

Re: polytope over quadratic number fields

The following is computed with polymake 3.4 and confirmed with the brand new version 3.5: polytope > print rhombicosidodecahedron()->F_VECTOR; 60 120 62 polytope > print truncated_dodecahedron()->F_VECTOR; 60 90 32 At least these two seem to agree with yours. It also works with the Julia interface P...
by joswig
16 Jun 2019, 13:29
Forum: General Discussion
Topic: another questions re: vert(hom(p, q))
Replies: 1
Views: 9225

Re: another questions re: vert(hom(p, q))

Each point in the mapping polytope/Hom-polytope is encoded as the constant 1 (for homogenization) plus a matrix encoded as consecutive row vectors. That matrix encodes a projective transformation (yielding affine coordinates, however), such that it can be applied to points in the polytope correspond...

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