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An algorithm for determining the order of an elliptic curve E/F_p over the finite field F_p.

In order to find a root of a polynomial equation a_0x^n+a_1x^(n-1)+...+a_n=0, (1) consider the difference equation a_0y(t+n)+a_1y(t+n-1)+...+a_ny(t)=0, (2) which is known to ...

A standard form of the linear programming problem of maximizing a linear function over a convex polyhedron is to maximize c·x subject to mx<=b and x>=0, where m is a given ...

A very general theorem that allows the number of discrete combinatorial objects of a given type to be enumerated (counted) as a function of their "order." The most common ...

1. Find a complete system of invariants, or 2. Decide when two metrics differ only by a coordinate transformation. The most common statement of the problem is, "Given metrics ...

A map F from R^n to R^n is area-preserving if m(F^(-1)(A))=m(A) for every subregion A of R^n, where m(A) is the n-dimensional measure of A. A linear transformation is ...

If the abstract simplicial complex S is isomorphic with the vertex scheme of the simplicial complex K, then K is said to be a geometric realization of S, and is uniquely ...

A permutation group (G,X) is k-homogeneous if it is transitive on unordered k-subsets of X. The projective special linear group PSL(2,q) is 3-homogeneous if q=3 (mod 4).

The Jacobian group of a one-dimensional linear series is given by intersections of the base curve with the Jacobian curve of itself and two curves cutting the series.

Let V!=(0) be a finite dimensional vector space over the complex numbers, and let A be a linear operator on V. Then V can be expressed as a direct sum of cyclic subspaces.