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A separable extension K of a field F is one in which every element's algebraic number minimal polynomial does not have multiple roots. In other words, the minimal polynomial ...

Borwein et al. (2004, pp. 4 and 44) term the expression of the integrals I_1 = int_0^1x^xdx (1) = 0.783430510... (2) I_2 = int_0^1(dx)/(x^x) (3) = 1.291285997... (4) (OEIS ...

Squarefree factorization is a first step in many factoring algorithms. It factors nonsquarefree polynomials in terms of squarefree factors that are relatively prime. It can ...

Let G be a permutation group on a set Omega and x be an element of Omega. Then G_x={g in G:g(x)=x} (1) is called the stabilizer of x and consists of all the permutations of G ...

The first Strehl identity is the binomial sum identity sum_(k=0)^n(n; k)^3=sum_(k=0)^n(n; k)^2(2k; n), (Strehl 1993, 1994; Koepf 1998, p. 55), which are the so-called Franel ...

A subset of an algebraic variety which is itself a variety. Every variety is a subvariety of itself; other subvarieties are called proper subvarieties. A sphere of the ...

Symmetry operations include the improper rotation, inversion operation, mirror plane, and rotation. Together, these operations create 32 crystal classes corresponding to the ...

A continuous group G which has the topology of a T2-space is a topological group. The simplest example is the group of real numbers under addition. The homeomorphism group of ...

Let m_1, m_2, ..., m_n be distinct primitive elements of a two-dimensional lattice M such that det(m_i,m_(i+1))>0 for i=1, ..., n-1. Each collection Gamma={m_1,m_2,...,m_n} ...

The transcendence degree of Q(pi), sometimes called the transcendental degree, is one because it is generated by one extra element. In contrast, Q(pi,pi^2) (which is the same ...