darijgr
commented
11 years ago Description changed:
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+++
@@ -1 +1,11 @@
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.
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:
While the integer 2 doesn't canonically act on the tropical semiring, the nonnegative integer 2 should.
Depends on #14507
CC: @tscrim @sagetrac-sage-combinat @maxale
Component: combinatorics
Issue created by migration from https://trac.sagemath.org/ticket/14797