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An abstract vector space of dimension n over a field k is the set of all formal expressions a_1v_1+a_2v_2+...+a_nv_n, (1) where {v_1,v_2,...,v_n} is a given set of n objects ...

The successive square method is an algorithm to compute a^b in a finite field GF(p). The first step is to decompose b in successive powers of two, b=sum_(i)delta_i2^i, (1) ...

An operator defined on a set S which takes two elements from S as inputs and returns a single element of S. Binary operators are called compositions by Rosenfeld (1968). Sets ...

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 ...

The Grassmann graph J_q(n,k) is defined such that the vertices are the k-dimensional subspaces of an n-dimensional finite field of order q and edges correspond to pairs of ...

A computation is an operation that begins with some initial conditions and gives an output which follows from a definite set of rules. The most common example are ...

Consider h_+(d) proper equivalence classes of forms with discriminant d equal to the field discriminant, then they can be subdivided equally into 2^(r-1) genera of ...

A commutative Noetherian unit ring having only finitely many maximal ideals. A ring having the same properties except Noetherianity is called quasilocal. If K is a field, the ...

The semigroup algebra K[S], where K is a field and S a semigroup, is formally defined in the same way as the group algebra K[G]. Similarly, a semigroup ring R[S] is a ...

There are (at least) two mathematical objects known as Weierstrass forms. The first is a general form into which an elliptic curve over any field K can be transformed, given ...