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Let E be an elliptic curve defined over the field of rationals Q(sqrt(-d)) having equation y^2=x^3+ax+b with a and b integers. Let P be a point on E with integer coordinates ...

A rational homomorphism phi:G->G^' defined over a field is called an isogeny when dimG=dimG^'. Two groups G and G^' are then called isogenous if there exists a third group ...

An extremum is a maximum or minimum. An extremum may be local (a.k.a. a relative extremum; an extremum in a given region which is not the overall maximum or minimum) or ...

An algebraically soluble equation of odd prime degree which is irreducible in the natural field possesses either 1. Only a single real root, or 2. All real roots.

The Chern number is defined in terms of the Chern class of a manifold as follows. For any collection Chern classes such that their cup product has the same dimension as the ...

The Pontryagin number is defined in terms of the Pontryagin class of a manifold as follows. For any collection of Pontryagin classes such that their cup product has the same ...

The zonal polynomials are a class of orthogonal polynomials. They are a special case of the Jack polynomials corresponding to the case alpha=2.

The tabulation of raw data obtained by dividing it into classes of some size and computing the number of data elements (or their fraction out of the total) falling within ...

The definition of a set by enumerating its members. An extensional definition can always be reduced to an intentional one. An extension field is sometimes also called simply ...

The group of all nonsingular n×n stochastic matrices over a field F. It is denoted S(n,F). If p is prime and F is the finite field of order q=p^m, S(n,q) is written instead ...