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The number of real roots of an algebraic equation with real coefficients whose real roots are simple over an interval, the endpoints of which are not roots, is equal to the ...

An element of an extension field of a field F which is not algebraic over F. A transcendental number is a complex number which is transcendental over the field Q of rational ...

A function f:{0,1}^(l(n))×{0,1}^n->{0,1}^(m(n)) is a trapdoor one-way hash function if f is a trapdoor one-way function and is also a one-way hash function, i.e., if, ...

Johnson solid J_(61).

Trigonometric functions of pi/p for p prime have an especially complicated Galois-minimal representation. In particular, the case cos(pi/23) requires approximately 500 MB of ...

A polynomial is called unimodal if the sequence of its coefficients is unimodal. If P(x) is log-convex and Q(x) is unimodal, then P(x)Q(x) is unimodal.

A unimodal sequence is a finite sequence that first increases and then decreases. A sequence {s_1,s_2,...,s_n} is unimodal if there exists a t such that s_1<=s_2<=...<=s_t ...

Let alpha, -beta, and -gamma^(-1) be the roots of the cubic equation t^3+2t^2-t-1=0, (1) then the Rogers L-function satisfies L(alpha)-L(alpha^2) = 1/7 (2) ...

The zero product property asserts that, for elements a and b, ab=0=>a=0 or b=0. This property is especially relevant when considering algebraic structures because, e.g., ...

The smallest positive composite number and the first even perfect square. Four is the smallest even number appearing in a Pythagorean triple: 3, 4, 5. In the numerology of ...