On Aug 11, 12:57 pm, Ralf Hemmecke <[email protected]> wrote:
> > existed), whereas Ralph's
>
> I prefer my name to be spelled correctly. ;-)
Oops, sorry about that.
> > was to nudge FriCAS into creating an
> > equation between polynomials over the extension field and then let
> > FriCAS automatically lift the given polynomial over the extension
> > field.
>
> No. Look closer to how I've defined p.
>
> p:P := x^2 + 1
Yes, you're right. I didn't realize P was the type of polynomials over
the *extension* field.
But I've just tried it here with p a polynomial over the *base* field
and it still works:
-- TRANSCRIPT --
(1) -> gf2 := PrimeField 2
(1) PrimeField(2)
Type: Type
(2) -> gf16 := FiniteFieldExtensionByPolynomial(gf2,x**4+x+1)
(2) FiniteFieldExtensionByPolynomial(PrimeField(2),?^4+?+1)
Type: Type
(3) -> p : POLY gf2 := x**2 + 1
2
(3) x + 1
Type:
Polynomial(PrimeField(2))
(4) -> alpha := primitiveElement()$gf16
(4) %A
Type: FiniteFieldExtensionByPolynomial(PrimeField(2),?
^4+?+1)
(5) -> eval(p, x::POLY gf16 = alpha)
2
(5) %A + 1
Type: Polynomial(FiniteFieldExtensionByPolynomial(PrimeField(2),?
^4+?+1))
-- TRANSCRIPT --
So here I think alpha is first coerced from a gf16 to a POLY gf16 then
p is lifted from a POLY gf2 to a POLY gf16.
>
... lots of useful stuff snipped ...
>
> Untyped expressions are perhaps easy to work with, but with typed
> expressions, you have more information at hand when you need it and thus
> it's less risky to do something wrong by accident.
Yes, that's what attracts me to FriCAS/Axiom: being less likely to get
undetected bogus results.
Thanks for your help,
Paul
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