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A root of a polynomial P(z) is a number z_i such that P(z_i)=0. The fundamental theorem of algebra states that a polynomial P(z) of degree n has n roots, some of which may be ...

The Chebotarev density theorem is a complicated theorem in algebraic number theory which yields an asymptotic formula for the density of prime ideals of a number field K that ...

A cubic curve is an algebraic curve of curve order 3. An algebraic curve over a field K is an equation f(X,Y)=0, where f(X,Y) is a polynomial in X and Y with coefficients in ...

One would think that by analogy with the matching-generating polynomial, independence polynomial, etc., a cycle polynomial whose coefficients are the numbers of cycles of ...

A hexahedron is a polyhedron with six faces. The figure above shows a number of named hexahedra, in particular the acute golden rhombohedron, cube, cuboid, hemicube, ...

Abstractly, a spatial configuration F is said to possess rotational symmetry if F remains invariant under the group C=C(F). Here, C(F) denotes the group of rotations of F and ...

Transitivity is a result of the symmetry in the group. A group G is called transitive if its group action (understood to be a subgroup of a permutation group on a set Omega) ...

A leaf of an unrooted tree is a node of vertex degree 1. Note that for a rooted or planted tree, the root vertex is generally not considered a leaf node, whereas all other ...

An Abelian integral, are also called a hyperelliptic integral, is an integral of the form int_0^x(dt)/(sqrt(R(t))), where R(t) is a polynomial of degree >4.

The degree to which a given quantity is correct and free from error. For example, a quantity specified as 100+/-1 has an (absolute) accuracy of +/-1 (meaning its true value ...