But it works.
(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) -> a := index(2)$gf16
(3) %A
Type: FiniteFieldExtensionByPolynomial(PrimeField(2),?^4+?+1)
(4) -> P := Polynomial(gf16)
(4) Polynomial(FiniteFieldExtensionByPolynomial(PrimeField(2),?^4+?+1))
Type: Type
(5) -> p:P := x^2 + 1
2
(5) x + 1
Type:
Polynomial(FiniteFieldExtensionByPolynomial(PrimeField(2),?^4+?+1))
(6) -> eval(p, x::P=a)
2
(6) %A + 1
Type:
Polynomial(FiniteFieldExtensionByPolynomial(PrimeField(2),?^4+?+1))
The problem is rather that eval requires an element of type Equation(%)
as the second argument.
(7) -> )sh P
[-- snip --]
eval : (%,List(Equation(%))) -> %
eval :
(%,List(Symbol),List(FiniteFieldExtensionByPolynomial(PrimeField(2),?^4+?+1)))
-> %
eval : (%,List(Symbol),List(%)) -> %
eval : (%,List(%),List(%)) -> %
eval :
(%,Symbol,FiniteFieldExtensionByPolynomial(PrimeField(2),?^4+?+1)) -> %
[-- snap --]
Obviously, if one works over Integer, the FriCAS interpreter is able to
lift, But not in the case of gf16.
(7) -> x=1
(7) x= 1
Type: Equation(Polynomial(Integer))
(8) -> x=a
There are 3 exposed and 0 unexposed library operations named
equation having 2 argument(s) but none was determined to be
applicable. Use HyperDoc Browse, or issue
)display op equation
to learn more about the available operations. Perhaps
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.
Cannot find a definition or applicable library operation named
equation with argument type(s)
Variable(x)
FiniteFieldExtensionByPolynomial(PrimeField(2),?^4+?+1)
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.
Some experiments brought me to the conclusion that the x is the problem.
But, in fact, both work
(8) -> x=a::P
(8) x= %A
Type:
Equation(Polynomial(FiniteFieldExtensionByPolynomial(PrimeField(2),?^4+?+1)))
(9) -> x::P=a
(9) x= %A
Type:
Equation(Polynomial(FiniteFieldExtensionByPolynomial(PrimeField(2),?^4+?+1
The 3-argument eval is different. It wants a symbol as the second
parameter and explicitly an element of gf16 as the third argument (see
last eval signature above). Still the result will live in P not gf16, so
Bill's coerce is necessary depending on what result type Paul actually
wants.
Ralf
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