To add to the previous post, my future plans are:

- Make sure that faces enumeration is the same everywhere, especially
for vertices and facets. This is relevant for lattice polytopes,
polyhedra, cones, and fans. We have had recently to fix some doctests
in Polyhedra because of random sorting and I have had to fix some of
the new doctests when I switched from 4.4 to 4.4.2.rc0.

- Write good plotting functions. For Fano toric varieties they must be
well-coordinated with lattice polytopes and I want to make the latter
ones more convenient and flexible.

- Improve morphisms and their doctests in schemes in general. My first
attack on documenting/improving schemes.generic.homset&morphism was
not very succesful, but I am going to continue. TestSuite(s).run()
should eventually work for schemes and ambient spaces! While it may
seem reasonable to first fix these issues and then add new classes, I
think that it is also good to have more "generic" ambient spaces for
testing purposes. Besides, with toric varieties merged I will
definitely understand at least some modules in schemes ;-)

- Implement classes to be used for lattices of cones/fans/lattice
polytopes.Ironically, lattice polytopes don't support lattices! For
cones and fans providing "lattice=" argument should "just work".

- While some of my "old" code got incorporated into the posted
patches, I still have quite a bit of written code which I hope to
convert into this framework.

- Quoting Volker: "implement everything that is known!"

Andrey

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