Search Results for ""

An algebraic expression in variables {x_1,...,x_n} is an expression constructed with the variables and algebraic numbers using addition, multiplication, and rational powers.

Regular expressions define formal languages as sets of strings over a finite alphabet. Let sigma denote a selected alphabet. Then emptyset is a regular expression that ...

Algebraic geometry is the study of geometries that come from algebra, in particular, from rings. In classical algebraic geometry, the algebra is the ring of polynomials, and ...

The use of techniques from algebra, topology, and geometry in the solution of combinatorial problems, or the use of combinatorial methods to attack problems in these areas ...

In algebra, a period is a number that can be written an integral of an algebraic function over an algebraic domain. More specifically, a period is a real number ...

An algebraic equation in n variables is an polynomial equation of the form f(x_1,x_2,...,x_n)=sum_(e_1,...,e_n)c_(e_1,e_2,...,e_n)x_1^(e_1)x_2^(e_2)...x_n^(e_n)=0, where the ...

An algebraic set is the locus of zeros of a collection of polynomials. For example, the circle is the set of zeros of x^2+y^2-1 and the point at (0,0) is the set of zeros of ...

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 ...

If r is a root of a nonzero polynomial equation a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0=0, (1) where the a_is are integers (or equivalently, rational numbers) and r satisfies no ...

A congruence of the form f(x)=0 (mod n) where f(x) is an integer polynomial (Nagell 1951, p. 73).