I need tensor product of a free module and polynomial.
We have tensor product and polynomials so I just tried
to use them. But tensor product requires both arguments
to be free modules. Of course Polynomial(Integer)
is a free module over Integer. But it is not of
FreeModuleCategory(Integer, IndexedExponents(Symbol))
Now some questions and observations:
1) It is easy to implement tensor product of two modules when
just one of modules is free. Should we change tensor
product to allow this?
2) Actually, relatively easy implementation of tensor product
of A and B is possible if B is torsion-free and every
finitely generated submodule of A is contained in a
free module (and we can find this free module). This
is essentially what LinearlyExplicitRingOver gives,
except for that LinearlyExplicitRingOver requires
to have ring, while the property makes perfect sense
for modules.
3) Should we add FreeModuleCategory to polynomials and
related domains? Overhead in terms of implementation
is probably quite low. I am a bit concerned that
we add a lot of new signatures which make little
sense from point of view of naive users, but which
will complicate overload resolution (and make it
less predictable).
--
Waldek Hebisch
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