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In a monoid or multiplicative group where the operation is a product ·, the multiplicative inverse of any element g is the element g^(-1) such that g·g^(-1)=g^(-1)·g=1, with ...

The word "normal form" is used in a variety of different ways in mathematics. In general, it refers to a way of representing objects so that, although each may have many ...

Simplemindedly, a number theoretic transform is a generalization of a fast Fourier transform obtained by replacing e^(-2piik/N) with an nth primitive root of unity. This ...

Let (A,<=) and (B,<=) be disjoint totally ordered sets with order types alpha and beta. Then the ordinal sum is defined at set (C=A union B,<=) where, if c_1 and c_2 are both ...

Given any set B, the associated pair groupoid is the set B×B with the maps alpha(a,b)=a and beta(a,b)=b, and multiplication (a,b)·(b,c)=(a,c). The inverse is ...

A convex figure constructed by iteratively halving the base of an equilateral triangle and then sliding adjacent triangles so that they slightly overlap. Combining several ...

The representation, beloved of engineers and physicists, of a complex number in terms of a complex exponential x+iy=|z|e^(iphi), (1) where i (called j by engineers) is the ...

An algorithm is said to be solvable in polynomial time if the number of steps required to complete the algorithm for a given input is O(n^k) for some nonnegative integer k, ...

Consider the expression 3×7+2^2. This expression has value (3×7)+(2^2)=25 due to what is called operator precedence (or "order of operations"). Precedence of common operators ...

Typesetting "errors" in which exponents or multiplication signs are omitted but the resulting expression is equivalent to the original one. Examples include 2^59^2=2592 (1) ...