The first monomials in the GUV interpolation argument

The exponent vector of monomial j consists of its first m base-h digits. The range j < K ≤ h^m indexes precisely the first K monomials, allowing the interpolation argument to retain the actual source-set size. Products suffice to evaluate these monomials without a separate multivariate polynomial representation.

def Algebraic.Cutwidth.Extractor.monomialDigit (h j : ℕ) {m : ℕ} (i : Fin m) : ℕ

Digit i of j in base h, beginning with the units digit.

Equations

• Algebraic.Cutwidth.Extractor.monomialDigit h j i = j / h ^ ↑i % h

def Algebraic.Cutwidth.Extractor.digitMonomial {R : Type u_1} [CommMonoid R] {m : ℕ} (h j : ℕ) (z : Fin m → R) : R

Evaluate the monomial whose exponents are the first base-h digits of j.

Equations

• Algebraic.Cutwidth.Extractor.digitMonomial h j z = ∏ i : Fin m, z i ^ Algebraic.Cutwidth.Extractor.monomialDigit h j i