Notation

This page lists the notation used in this website.

N

The set of nonnegative integers.

Z, Q, R, C

The set of integers, rationals, reals, complexes.

i ∈ n

0 ≤ i < n (for n ∈ N).

[a .. b)

Half-open interval.

F_q

Finite field of order q. When q is a prime p, it's identified with the set p = {0, 1, ..., p−1} by modulo-p arithmetic.

Rⁿ

The set of n-dimensional vectors with components in R. Here n is used as the index set.

R^s×n

The set of (s×n)-matrices with components in R. Here s and n is used as the index set.

L

The function which maps a vector x ∈ F₂ⁿ to the rational number ∑_{j ∈ n} 2^−j−1x_j.

φ

The function which maps x ∈ F₂^s×n to a point in the hypercube ∏_{i ∈ s} [L(x_i) .. L(x_i)+2⁻ⁿ). We frequently use the point (L(x_i))_{i ∈ s} in theories, however in practical integration we use the center point of each cube.