Research proof index

splitNth is the left inverse of the n-way recombination: splitting the polynomial ∑ j, X^j * (u j)(X^n) recovers u i for each component i.

If G is a polynomial generator, then G is zero-evading with error the maximum of the total degrees of the individual polynomials divided by the size of the smallest evaluation sets S i. Remark 3.20, the version of the statement in the brackets [BCGM25]. Note: Remark 3.20 provides two ways of viewing a polynomial generator as a zero-evading generator...

If g is continuous on (0, ∞), positive for t ≥ t₀, and has strictly negative derivative at any zero in (0, t₀), then g is positive on all of (0, ∞).

The partial trace (left) of a positive definite matrix is positive definite.

Relate stepsV and steps

A positivity lemma for self-difference-convolutions. If $f=g\mathbin{\circleddash}g$ and the nonnegative weight $\nu$ has a factorization $\nu=h\mathbin{\circleddash}h$, then every natural power of $f$ has nonnegative weighted inner product with $\nu$: $\langle f^k,\nu\rangle\ge0$ for every $k\in\mathbb N$.