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...
Indeed, the triangulation (induced by MONOMIALS and COEFFICIENTS) is the same. Yet your code already exploits this automatically. The property PATCHWORK is declared multiple (see apps/tropical/rules/patchwork.rules) which means that all the patchworks for all your choices of signs will be kept. Prob...
A polytope in 70 dimensions with 200 inequalities may have as many as 983858800923516812309510979394668240 vertices (by McMullen's upper bound theorem). Of course that number can also be much smaller. In general, there is no good way to tell ahead of time if such a computation is possible and how lo...
All known algorithms for computing the mixed volume are exponential in the dimension. Since even computing the volume is known to be #P-hard there is no hope for any improvement.
One comment: to run polymake code on a pure Windows machine you could employ some live version of Linux, e.g., Ubuntu . And a question: which computation do you want to do with CPLEX? polymake is capable of solving (mixed integer) linear programs exactly. Of course, CPLEX is much faster (as it uses ...
