I have the following problem when I try to evaluate a polynomial in a
finite-field extension:
-- START OF TRANSCRIPT --
gf2 := PrimeField 2 -- the base field
(1) PrimeField(2)
Type: Type
gf16 := FiniteFieldExtensionByPolynomial(gf2, x**4 + x + 1) -- the
extension field
(2) FiniteFieldExtensionByPolynomial(PrimeField(2),?^4+?+1)
Type: Type
a := index(2)$gf16 -- a primitive element of the extension field
(3) %A
Type: FiniteFieldExtensionByPolynomial(PrimeField(2),?
^4+?+1)
order a -- check primitiveness
(4) 15
Type:
PositiveInteger
p := x**2 + 1 :: POLY gf2 -- a polynomial over the base field
2
(5) x + 1
Type:
Polynomial(PrimeField(2))
eval(p, x=a)
There are 3 exposed and 0 unexposed library operations named
equation having 2 argument(s) but none was determined to be
applicable. Use HyperDoc Browse, or issue
)display op equation
to learn more about the available operations. Perhaps
package-calling the operation or using coercions on the
arguments
will allow you to apply the operation.
Cannot find a definition or applicable library operation named
equation with argument type(s)
Variable(x)
FiniteFieldExtensionByPolynomial(PrimeField(2),?^4+?+1)
Perhaps you should use "@" to indicate the required return
type,
or "$" to specify which version of the function you need.
-- END OF TRANSCRIPT --
where I expect
eval(p,x=a)
to give the same result as
a**2 + 1
which does indeed work, as follows:
-- START OF TRANSCRIPT --
(6) -> a**2 + 1
2
(6) %A + 1
Type: FiniteFieldExtensionByPolynomial(PrimeField(2),?
^4+?+1)
-- END OF TRANSCRIPT --
Any idea what I'm doing wrong?
Thanks,
Paul
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