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,...

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...

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...

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...

A google search for "polymake" and "newton polytope" reveals:
https://polymake.org/doku.php/user_guid ... s_tutorial

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).

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...

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...

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...

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...