Our implementation is slightly more general than primitive patchworking; it covers what is sometimes is called "combinatorial patchworking" in the literature. This means, we require that the lattice points (@my_monomials in your case) correspond to the entire set of monomials in, say, n va...

We did make changes concerning threejs in order to obtain correct visualization for https://www.matchthenet.de/xmas. And I can confirm your problem.

Requires an investigation. Stay tuned.

That does not have unique solutions. Instead the set of such solutions forms a polyhedron in the parameter space (= coefficients of the linear combinations).

Sorry, I don't understand the question.

Is it that P_2 is a subpolytope of P_1, and you want to find those vcertices of P_1 which are not vertices of P_2?

Your command sequence > $p = cube(3); > print($p->VERTICES); > save_data($p->VERTICES, "my_vertices.txt"); is perfectly OK; the result is a JSON file (format defined by polymake) which contains just one matrix plus a bit of metadata. If you want the matrix (coefficients separated by blanks...

Your example has a lineality space of positive dimension. polytope > $p = new Polytope(INEQUALITIES=>[[13,-6,0,-7,0,-9,0],[11,0,-8,0,-5,0,-6]],EQUATIONS=>[[-1,1,1,0,0,0,0],[-1,0,0,1,1,0,0],[-1,0,0,0,0,1,1]]); polytope > print $p->VERTICES; 1 -1/4 5/4 1 0 5/6 1/6 0 1 -1 0 0 -2/3 2/3 0 1 -1 0 0 -4/3 4...

You can specify polyhedra in terms of INEQUALITIES and EQUATIONS.
Asking for VERTICES then triggers a dual convex hull computation.

Please see tutorial.

The web version of polymake runs in a sandbox. So, by design, you cannot read from or write to files.

polymake uses the normalized volume convention for mixed volumes (i.e., counting solutions of polynomial systems directly, as in the BKK theorem). You can see this, e.g., from polytope > print mixed_volume(cube(2,0),cube(2,0)); 2 The mixed volume of a polygon with itself equals the volume (i.e., are...

Well, Vector and Array are random access data structures, i.e., you can use indices. And Set is not random access; pretty much as the error message says. These different data structures exist because they help make several kinds of functions fast: While vector and Array allow to access an element at...

Internally, polymake will always use indices starting at zero. matroid > $F = fano_matroid; matroid > print $F->CIRCUITS; {0 1 6} {0 2 5} {0 3 4} {1 2 3} {1 4 5} {2 4 6} {3 5 6} {0 1 2 4} {0 1 3 5} {0 2 3 6} {0 4 5 6} {1 2 5 6} {1 3 4 6} {2 3 4 5} But you can use LABELS to make things look different...