Module hypercube 

Multilinear tensor expansions, generic over the hypercube the coefficients are indexed by.

An n-variate multilinear is stored as 2^n coefficients. The basis those coefficients are taken against factors as a tensor product over the variables. Every variable contributes the same two-element basis (b_0, b_1) of linear polynomials. That single choice fixes the cube, and with it what each coefficient means:

basis (1 - X, X)    vertices {0, 1}      coefficients are evaluations
basis (1, X)        vertices {0, inf}    coefficients are monomial coefficients

The object built over a cube again and again is the equality indicator. Written eq(X, Y), it extends the predicate X == Y multilinearly over the cube. Fixing one operand to a point leaves 2^n coefficients, called the expansion of that point.

Every routine here is generic over the cube. The Boolean-cube specializations live beside them, in the sibling equality indicator module.

Structs

InfCube

The infinity cube {0, inf}^n, whose per-variable basis is (1, X).

OneCube

The Boolean cube {0, 1}^n, whose per-variable basis is (1 - X, X).

Traits

Hypercube

A hypercube of coefficients for multilinear polynomials.

Functions

eq_ind

Evaluates the equality indicator multilinear at a pair of points.

eq_ind_partial_eval

Computes the partial evaluation of the equality indicator polynomial.

eq_ind_partial_eval_in

Builds the equality indicator expansion of a point into a buffer drawn from an allocator.

eq_ind_partial_eval_scalars

Computes the partial evaluation of the equality indicator polynomial, returning scalars.

eq_ind_truncate_low_inplace

Truncates a built equality indicator expansion to its low indexed variables.

eq_ind_zero

Evaluates the equality indicator multilinear with one operand fixed to all zeros.

scaled_eq_ind_partial_eval

Computes the partial evaluation of the equality indicator polynomial, scaled by a constant.

scaled_eq_ind_partial_eval_into

Builds the scaled equality indicator expansion of a point in a caller-supplied store.

scaled_eq_ind_partial_eval_scalars

Computes the scaled partial evaluation of the equality indicator, returning scalars.

tensor_prod_eq_ind

Tensor of values with the equality indicator evaluated at extra coordinates.