Module extension

Structs§

Binomial: Marker for the binomial reducer X^D - W (degree-generic).
CubicTrinomial: Marker for the trinomial reducer X^3 - X - 1.
ExtField: Unified extension-field representation.
PackedExtField: Unified packed extension-field representation (SIMD-lane parallel).
QuinticTrinomial: Marker for the trinomial reducer X^5 + X^2 - 1.

BinomiallyExtendable: Trait for fields that support binomial extension of the form F[X]/(X^D - W).
ComplexExtendable: A field for which p = 3 (mod 4). Equivalently, -1 is not a square, so the complex extension can be defined F[i] = F[X]/(X^2+1).
CubicTrinomialExtendable: Trait for fields that support a degree-3 extension using the trinomial X^3 - X - 1.
ExtensionAlgebra: Algebra over F that supports degree-D extension arithmetic with a given reducer Shape.
ExtensionShape: Sealed marker for the reducing polynomial shape of an extension field.
HasComplexBinomialExtension: The complex extension of this field has a binomial extension.
HasFrobenius: Trait for extension fields that support Frobenius automorphisms.
HasTwoAdicBinomialExtension: Trait for binomial extensions that support a two-adic subgroup generator.
HasTwoAdicComplexBinomialExtension: The complex extension of this field has a two-adic binomial extension.
HasTwoAdicCubicExtension: Trait for cubic trinomial extensions that expose two-adic subgroup generators.
HasTwoAdicQuinticExtension: Trait for quintic extensions that support two-adic subgroup generators.
QuinticTrinomialExtendable: Trait for fields that support a degree-5 extension using the trinomial X^5 + X^2 - 1.

binomial_mul: Multiply two vectors representing elements in a binomial extension.
binomial_square: Square a vector representing an element in a binomial extension.
cubic_square
octic_mul: Multiplication in an octic binomial extension field.
quartic_mul: Multiplication in a quartic binomial extension field.
quintic_mul: Multiplication in a quintic binomial extension field.
quintic_square: Square an element in the quintic extension field.
trinomial_cubic_mul: Multiply in R[X]/(X^3 - X - 1).
trinomial_quintic_mul: Multiply two elements in the quintic trinomial extension field (X^5 + X^2 - 1).
vector_add: Add two vectors element wise.
vector_sub: Subtract two vectors element wise.

BinomialExtensionField: Binomial extension field F[X] / (X^D - W).
Complex
CubicTrinomialExtensionField: A degree-3 extension field using X^3 - X - 1.
PackedBinomialExtensionField: Packed binomial extension field F[X] / (X^D - W), one element per SIMD lane.
PackedCubicTrinomialExtensionField: Packed cubic extension field, one element per SIMD lane.
PackedQuinticTrinomialExtensionField: Packed quintic extension field, one element per SIMD lane.
QuinticTrinomialExtensionField: A degree-5 extension field using the trinomial X^5 + X^2 - 1.