Hi Volker,

The first version (already documented and doctested) of toric lattices
is on trac:
http://trac.sagemath.org/sage_trac/ticket/9062
so you can take a look and comment if something is very bad. It is not
quite ready for review yet, but I don't anticipate changing existing
code - only adding some more.

These lattices allow creation and printing as "N(1,2,3)" and do not
allow mixing of wrong lattices for a given operation, as you wanted.
They behave "like ZZ^n", as I wanted. Elements are implemented in
Cython and as I was working on them, I was trying to make sure that
there are no big performance hits compared to just integer vectors. I
still have to work on matrix operations and support for morphisms, but
I don't anticipate any problems (everything is already in the Sage
structure files, I just need to make sure that all the types are in
agreement in necessary places). Then I will change cones and fans to
use these lattices by default instead of ZZ^n.

I wanted to have an option of suppressing lattice names in elements
output, but so far I have found your idea of having them extremely
convenient for debugging ;-) So instead of writing functions to get
rid of the names now, I put it on my todo list for the future since
there are more urgent things to do.

Thank you,
Andrey

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