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An ordered vector basisv_1,...,v_n for a finite-dimensional vector space V defines an orientation. Another basis w_i=Av_i gives the same orientation if the matrix A has a ...

The versine, also known as the "versed sine," is a little-used trigonometric function defined by versin(z) = 2sin^2(1/2z) (1) = 1-cosz, (2) where sinz is the sine and cosz is ...

A W^*-algebra is a C-*-algebra A for which there is a Banach space A_* such that its dual is A. Then the space A_* is uniquely defined and is called the pre-dual of A. Every ...

The Weierstrass constant is defined as the value sigma(1|1,i)/2, where sigma(z|omega_1,omega_2) is the Weierstrass sigma function with half-periods omega_1 and omega_2. ...

A variant of the Pollard p-1 method which uses Lucas sequences to achieve rapid factorization if some factor p of N has a decomposition of p+1 in small prime factors.

The identity element of an additive monoid or group or of any other algebraic structure (e.g., ring, module, abstract vector space, algebra) equipped with an addition. It is ...

D_q=1/(1-q)lim_(epsilon->0)(lnI(q,epsilon))/(ln(1/epsilon),) (1) where I(q,epsilon)=sum_(i=1)^Nmu_i^q, (2) epsilon is the box size, and mu_i is the natural measure. The ...

A definite integral is an integral int_a^bf(x)dx (1) with upper and lower limits. If x is restricted to lie on the real line, the definite integral is known as a Riemann ...

In general, an integer n is divisible by d iff the digit sum s_(d+1)(n) is divisible by d. Write a positive decimal integer a out digit by digit in the form ...

The hyperbolic functions sinhz, coshz, tanhz, cschz, sechz, cothz (hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cosecant, hyperbolic secant, and ...