Can you, please, explain:
how to construct recursively the domains R for which Axiom has the
`factor' operation in R[x1..xn] == MPOLY([x1..xn], R)
?
More definitely, denote this class FF and consider the following
constructors.
(1) INT and Q = Fraction INT belong to FF, as I recall.
(2) PF p = PrimeField p, for a prime p: INT belongs FF, as I recall.
From what package to call `factor' for PF(p)[x1..xn] ?
(3) Let a field K be Q or PF(p).
Consider AE = AlgebraicExtension(K, [a1..am], [g1..gn])
-- the algebraic extension K by the elements a1..am, with the
equations g1..gn <- K[a1..am] for them
(may be, it is sufficient n = m = 1).
Simple example: AE := Q(squareRoot(5), cubicRoot(2)).
How AE(K, [a], [g]) is expressed in Axiom? Is it by ResidueRing?
Does AE(K, [a], [g]) belong to FF ?
If it does, from what package to call `factor' for
AE(K, [a], [g])[y1..yn] ?
(4) Let R : IntegralDomain belong to FF.
In what case Axiom provides `factor' for Fraction(R)[x1..xn] ?
For example, can Axiom factor in
(Fraction INT[x1..xn])[y1..yn] ?
If yes, then what is the package?
Thanks,
------
Sergei
[email protected]
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