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For elliptic curves over the rationals Q, the group of rational points is always finitely generated (i.e., there always exists a finite set of group generators). This theorem ...

The highest order power in a univariate polynomial is known as its order (or, more properly, its polynomial degree). For example, the polynomial ...

For a group G and a normal subgroup N of G, the quotient group of N in G, written G/N and read "G modulo N", is the set of cosets of N in G. Quotient groups are also called ...

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 ...

Differential Equations

Eigenvectors are a special set of vectors associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic vectors, ...

Differential evolution is a stochastic parallel direct search evolution strategy optimization method that is fairly fast and reasonably robust. Differential evolution is ...

The first example discovered of a map from a higher-dimensional sphere to a lower-dimensional sphere which is not null-homotopic. Its discovery was a shock to the ...

The icosahedral group I_h is the group of symmetries of the icosahedron and dodecahedron having order 120, equivalent to the group direct product A_5×Z_2 of the alternating ...

Lagrange's identity is the algebraic identity (sum_(k=1)^na_kb_k)^2=(sum_(k=1)^na_k^2)(sum_(k=1)^nb_k^2)-sum_(1<=k<j<=n)(a_kb_j-a_jb_k)^2 (1) (Mitrinović 1970, p. 41; Marsden ...