#14797: Polynomials over semirings
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Reporter: darij | Owner: sage-combinat
Type: task | Status: new
Priority: major | Milestone: sage-5.12
Component: combinatorics | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: #14507 | Stopgaps:
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Description changed by darij:
Old description:
> With semirings implemented (#14507), it seems not too wide a stretch to
> ask for algebraic constructions involving them, such as (semi)algebras
> over semirings, and polynomials over semirings acting on such
> semialgebras. This would allow to reuse lots of code written for rings in
> a semiring context provided there are no minus signs appearing; right now
> I see two cases where I could use such a thing.
New description:
With semirings implemented (#14507), it seems not too wide a stretch to
ask for algebraic constructions involving them, such as (semi)algebras
over semirings, and polynomials over semirings acting on such
semialgebras. This would allow to reuse lots of code written for rings in
a semiring context provided there are no minus signs appearing; right now
I see two cases where I could use such a thing.
In particular, this should work rather than throwing an ArithmeticError:
{{{
sage: NN = NonNegativeIntegers()
sage: T = TropicalSemiring(QQ)
sage: NN(2) * T(3)
}}}
While the *integer* 2 doesn't canonically act on the tropical semiring,
the *nonnegative integer* 2 should.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14797#comment:1>
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