I am in need of free software that will work with polynomials over the
Tropical semiring.  I was unable to find anything suitable, so I
thought I would take a stab at implementing them in sage.  I have just
barely found sage though, so I don't yet understand it entirely.  This
list seemed very friendly so I thought I would ask a few questions:

1. Is this already implemented under a different name (it's also
called min-plus algebra), or someplace that I overlooked?

2. Is it reasonable to implement in sage?  In particular one thing
that I think may be difficult is that the polynomial 'x+3' is really
'0*x+3' since 0 is the multiplicative identity (infinity is the
additive identity).

3. Where is the best place to go to find out how to develop a sage
package etc.  Also good tutorials for python would be appreciated,
since I have never done any python development.  I do have experience
in a variety of other languages.

4. Would this be better to implement in something like GAP (so that
GAP users can take advantage of it as well) and then access it through
sage?

Thanks for your comments,
Ivan Andrus

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