E12D

Degree-12 extension field element (generic coefficients).

Represents an element of the extension field F_{q^12} modeled as the quotient ring F_qw/p(w), where p(w) is an irreducible polynomial of degree 12. Canonical polynomial form:

w0 + w1*w + w2*w^2 + w3*w^3 + w4*w^4 + w5*w^5
+ w6*w^6 + w7*w^7 + w8*w^8 + w9*w^9 + w10*w^10 + w11*w^11

Coefficients w0 … w11 are of type T.

When T is a limb-based integer type used in this codebase:

T = [u384] (4 x u96 limbs) or T = [u288] (3 x u96 limbs). Helpers below serialize/deserialize to a flat Array<felt252> (12x4 for u384, 12x3 for u288).
num::traits::One is implemented for E12D<u384> and E12D<u288>; the multiplicative identity is w0 = 1 and all other coefficients are zero.

Example: create the multiplicative identity for u288 coefficients.

let one: E12D<u288> = E12D {
    w0: U288One::one(),
    w1: U288Zero::zero(),
    w2: U288Zero::zero(),
    w3: U288Zero::zero(),
    w4: U288Zero::zero(),
    w5: U288Zero::zero(),
    w6: U288Zero::zero(),
    w7: U288Zero::zero(),
    w8: U288Zero::zero(),
    w9: U288Zero::zero(),
    w10: U288Zero::zero(),
    w11: U288Zero::zero(),
};

Fully qualified path: garaga::definitions::structs::fields::E12D

[derive(Copy, Drop, Debug, PartialEq)]
pub struct E12D<T> {
    pub w0: T,
    pub w1: T,
    pub w2: T,
    pub w3: T,
    pub w4: T,
    pub w5: T,
    pub w6: T,
    pub w7: T,
    pub w8: T,
    pub w9: T,
    pub w10: T,
    pub w11: T,
}