Implement Minkowski decomposition of polytopes

[sagetrac-etzanaki]

I plan to add code for Minkowski Decomposition of Polytopes
based on the algorithm in "On the space of Minkowski summands of a convex polytope" http://www.eurocg2016.usi.ch/sites/default/files/paper_76.pdf (which appeared in the conference EuroCG 2016, Lugano, Switzerland, March 30-April 1, 2016)

For special cases such as associahedra, specialized algorithms are available - e.g., C. Lange, Discrete & Computational Geometry volume 50, pages 903–939 (2013) https://link.springer.com/article/10.1007/s00454-013-9546-5

Also G. Fourier, Marked poset polytopes: Minkowski sums, indecomposables, and unimodular equivalence, https://www.sciencedirect.com/science/article/abs/pii/S0022404915001942

J. Ivanović, GEOMETRICAL REALISATIONS OF THE SIMPLE PERMUTOASSOCIAHEDRON BY MINKOWSKI SUMS, https://www.jstor.org/stable/26964946

T. Michiels and R. Cools. Decomposing the secondary
Cayley polytope. Discr. Comput. Geometry,
23:367–380, 2000.

CC: @VivianePons @mkoeppe @jplab @mo271

Component: geometry

Keywords: polytope, Minkowski sum, Minkowski decomposition, days82

Issue created by migration from https://trac.sagemath.org/ticket/22181

[videlec]

comment:2

Note that polymake already has a C++ implementation following Fukada's "From the zonotope construction to the Minkowski addition of convex polytopes" (2004).

[mkoeppe]

comment:4

accessing polymake is now easy with #22683: backend_polymake for Polyhedron

[mkoeppe]

comment:7

@sagetrac-etzanaki - has anything been implemented?