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A Gröbner basis G for a system of polynomials A is an equivalence system that possesses useful properties, for example, that another polynomial f is a combination of those in ...

The characteristic polynomial is the polynomial left-hand side of the characteristic equation det(A-lambdaI)=0, (1) where A is a square matrix and I is the identity matrix of ...

The complex conjugate of a complex number z=a+bi is defined to be z^_=a-bi. (1) The conjugate matrix of a matrix A=(a_(ij)) is the matrix obtained by replacing each element ...

Experimental mathematics is a type of mathematical investigation in which computation is used to investigate mathematical structures and identify their fundamental properties ...

An additive group is a group where the operation is called addition and is denoted +. In an additive group, the identity element is called zero, and the inverse of the ...

Adomian polynomials decompose a function u(x,t) into a sum of components u(x,t)=sum_(n=0)^inftyu_n(x,t) (1) for a nonlinear operator F as F(u(x,t))=sum_(n=0)^inftyA_n. (2) ...

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 ...

The minimal polynomial of an algebraic number zeta is the unique irreducible monic polynomial of smallest degree p(x) with rational coefficients such that p(zeta)=0 and whose ...

A classic arithmetical problem probably first posed by Euclid and investigated by various authors in the Middle Ages. The problem is formulated as a dialogue between the two ...

Bézout's theorem for curves states that, in general, two algebraic curves of degrees m and n intersect in m·n points and cannot meet in more than m·n points unless they have ...