Crate binius_math

Mathematical primitives used in Binius, built atop the binius_field crate.

This crate provides a variety of mathematical primitives used in Binius, including:

• Multilinear polynomials
• Univariate polynomials
• Matrix operations
• Arithmetic expressions and evaluators

This crate is a dependency of binius_hal. When modules in binius_core need to be abstracted behind the HAL, this is one of the places they are often moved in order to avoid crate dependency cycles.

Structs

• BinarySubspace
  An $F_2$-linear subspace of a binary field.
• DefaultEvaluationDomainFactory
• EvaluationDomain
  A domain that univariate polynomials may be evaluated on.
• InterpolationDomain
  An extended version of EvaluationDomain that supports interpolation to monomial form. Takes longer to construct due to Vandermonde inversion, which has cubic complexity.
• IsomorphicEvaluationDomainFactory
• MLEDirectAdapter
  An adapter for MultilinearExtension that implements MultilinearPoly over the same packed field that the MultilinearExtension stores evaluations in.
• MLEEmbeddingAdapter
  An adapter for MultilinearExtension that implements MultilinearPoly over a packed extension field.
• Matrix
  A matrix over a field.
• MultilinearExtension
  A multilinear polynomial represented by its evaluations over the boolean hypercube.
• MultilinearQuery
  Tensor product expansion of sumcheck round challenges.
• MultilinearQueryRef
  Wraps MultilinearQuery to hide Data from the users.
• PackingDeref
  A wrapper for containers of underlier types that dereferences as packed field slices.

Enums

• ArithExpr
  Arithmetic expressions that can be evaluated symbolically.
• Error

Traits

• CompositionPoly
  A generic version of the CompositionPolyOS trait that is not object-safe.
• CompositionPolyOS
  A multivariate polynomial that is used as a composition of several multilinear polynomials.
• EvaluationDomainFactory
  Wraps type information to enable instantiating EvaluationDomains.
• MultilinearPoly
  Represents a multilinear polynomial.

Functions

• deinterleave
  Given a slice of packed fields representing 2^log_scalar_count scalars, returns an iterator that yields pairs of packed fields that can be unzipped into a deinterleaved representation of the slice.
• eq_ind_partial_eval
  Computes the partial evaluation of the equality indicator polynomial.
• evaluate_piecewise_multilinear
  Evaluate a piecewise multilinear polynomial at a point, given the evaluations of the pieces.
• evaluate_univariate
  Evaluate a univariate polynomial specified by its monomial coefficients.
• extrapolate_line
  Extrapolates lines through a pair of packed fields at a single point from a subfield.
• extrapolate_line_scalar
  Similar methods, but for scalar fields.
• extrapolate_lines
  Extrapolates lines through a pair of packed fields at a packed vector of points.
• fold
  Execute the fold operation.
• tensor_prod_eq_ind
  Tensor Product expansion of values with partial eq indicator evaluated at extra_query_coordinates

Type Aliases

• MultilinearExtensionBorrowed
  Type alias for the common pattern of a MultilinearExtension backed by borrowed data.