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A homogeneous space M is a space with a transitive group action by a Lie group. Because a transitive group action implies that there is only one group orbit, M is isomorphic ...

A rule for polynomial computation which both reduces the number of necessary multiplications and results in less numerical instability due to potential subtraction of one ...

Horowitz reduction is used in indefinite integration to reduce a rational function into polynomial and logarithmic parts. The polynomial part is then trivially integrated, ...

The extension of a, an ideal in commutative ring A, in a ring B, is the ideal generated by its image f(a) under a ring homomorphism f. Explicitly, it is any finite sum of the ...

The radical of an ideal a in a ring R is the ideal which is the intersection of all prime ideals containing a. Note that any ideal is contained in a maximal ideal, which is ...

At the age of 17, Bernard Mares proposed the definite integral (Borwein and Bailey 2003, p. 26; Bailey et al. 2006) C_2 = int_0^inftycos(2x)product_(n=1)^(infty)cos(x/n)dx ...

Let Q(x)=Q(x_1,x_2,...,x_n) be an integer-valued n-ary quadratic form, i.e., a polynomial with integer coefficients which satisfies Q(x)>0 for real x!=0. Then Q(x) can be ...

A polynomial of the form f(x)=a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0 having coefficients a_i that are all integers. An integer polynomial gives integer values for all integer ...

A differential ideal is an ideal I in the ring of smooth forms on a manifold M. That is, it is closed under addition, scalar multiplication, and wedge product with an ...

Let X be an infinite set of urelements, and let V(^*X) be an enlargement of the superstructure V(X). Let A,B in V(X) be finitary algebras with finitely many operations, and ...