-
galois.Poly(coeffs: ArrayLike, field: type[Array] | None =
None
, order: 'desc' | 'asc' ='desc'
) Creates a polynomial \(f(x)\) over \(\mathrm{GF}(p^m)\).
The polynomial \(f(x) = a_d x^d + a_{d-1} x^{d-1} + \dots + a_1 x + a_0\) with degree \(d\) has coefficients \(\{a_{d}, a_{d-1}, \dots, a_1, a_0\}\) in \(\mathrm{GF}(p^m)\).
- Parameters¶
- coeffs: ArrayLike¶
The polynomial coefficients \(\{a_d, a_{d-1}, \dots, a_1, a_0\}\).
- field: type[Array] | None =
None
¶ The Galois field \(\mathrm{GF}(p^m)\) the polynomial is over.
None
(default): If the coefficients are anArray
, they won’t be modified. If the coefficients are not explicitly in a Galois field, they are assumed to be from \(\mathrm{GF}(2)\) and are converted usinggalois.GF2(coeffs)
.Array
subclass: The coefficients are explicitly converted to this Galois field usingfield(coeffs)
.
- order: 'desc' | 'asc' =
'desc'
¶ The interpretation of the coefficient degrees.
"desc"
(default): The first element ofcoeffs
is the highest degree coefficient, i.e. \(\{a_d, a_{d-1}, \dots, a_1, a_0\}\)."asc"
: The first element ofcoeffs
is the lowest degree coefficient, i.e. \(\{a_0, a_1, \dots, a_{d-1}, a_d\}\).