On Mon, Jul 10, 2023 at 01:18:47AM +0200, Waldek Hebisch wrote:
> I wonder what to do with ModMonic? AFAICS there are at least
> 26 exported but unimplemented operations. In particular,
> ModMonic export UnivariatePolynomialCategory. This is
> mathematically incorrect because generator of univariate
> polynomials is transcendental over base ring, while in
> ModMonic generator is algebraic.
>
> ModMonic have limited use and we probably could give it
> a different type that exports less operations.
After little investigation it looks like most resonable
category could be Join(CommutativeRing, Algebra(R))
plus specific exports. Another possibility is
MonogenicAlgebra(R, Rep) with specific exports. The
first one requires removal of 3 operations, that is 'exquo',
'recip' and 'divide'. However those operations are exported
only because when R is a Field also MonogenicAlgebra(R, Rep)
claims to be a Field. And ModMonic is a field only if R is a
field and modulus polynomial is irreducible. ddfact.spad uses
ModMonic with polynomial which is _not_ irreducible,
so MonogenicAlgebra was too much.
When we declare type as Join(CommutativeRing, Algebra(R))
plus specific exports, and remove unimplemented 'An' from
specific exports there are only 3 undefined operations:
characteristic, index and lookup.
Both changes require little adjustment to 'ffdoms.spad'
and require R to be a CommutaiveRing.
--
Waldek Hebisch
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