Creates a polynomial $f(x)$ over $\mathrm{GF}(p^m)$.

The polynomial $f(x)=a_d{x}^d+a_{d-1}{x}^{d-1}+\cdots +a_{1}x+a_0$ 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 an Array, 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 using galois.GF2(coeffs).

• Array subclass: The coefficients are explicitly converted to this Galois field using field(coeffs).

order: 'desc' | 'asc' = 'desc'¶

The interpretation of the coefficient degrees.

• "desc" (default): The first element of coeffs is the highest degree coefficient, i.e. $\{a_d,a_{d-1},\dots ,a_1,a_0\}$.

• "asc": The first element of coeffs is the lowest degree coefficient, i.e. $\{a_0,a_1,\dots ,a_{d-1},a_d\}$.