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The kth exterior power of an element alpha in an exterior algebra LambdaV is given by the wedge product of alpha with itself k times. Note that if alpha has odd degree, then ...

Let f be an integer polynomial. The f can be factored into a product of two polynomials of lower degree with rational coefficients iff it can be factored into a product of ...

The ring of integers of a number field K, denoted O_K, is the set of algebraic integers in K, which is a ring of dimension d over Z, where d is the extension degree of K over ...

Let K be a number field of extension degree d over Q. Then an order O of K is a subring of the ring of integers of K with d generators over Z, including 1. The ring of ...

A graph vertex in a graph is said to be an odd node if its vertex degree is odd.

A polynomial function is a function whose values can be expressed in terms of a defining polynomial. A polynomial function of maximum degree 0 is said to be a constant ...

For p(z)=a_nz^n+a_(n-1)z^(n-1)+...+a_0, (1) polynomial of degree n>=1, the Schur transform is defined by the (n-1)-degree polynomial Tp(z) = a^__0p(z)-a_np^*(z) (2) = ...

In an exterior algebra ^ V, a top-dimensional form has degree n where n=dimV. Any form of higher degree must be zero. For example, if V=R^4 then alpha=e_1 ^ e_2 ^ e_3 ^ e_4 ...

A group is called k-transitive group if there exists a set of elements on which the group acts faithfully and k-transitively. It should be noted that transitivity computed ...

If r is a root of the polynomial equation x^n+a_(n-1)x^(n-1)+...+a_1x+a_0=0, where the a_is are integers and r satisfies no similar equation of degree <n, then r is called an ...