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A short exact sequence of groups A, B, and C is given by two maps alpha:A->B and beta:B->C and is written 0->A->B->C->0. (1) Because it is an exact sequence, alpha is ...

Let theta be an irrational number, define S(theta)={c+dtheta:c,d in N}, and let c_n(theta)+thetad_n(theta) be the sequence obtained by arranging the elements of S(theta) in ...

A matrix for which horizontal and vertical dimensions are the same (i.e., an n×n matrix). A matrix m may be tested to determine if it is square in Wolfram Language using ...

Squarefree factorization is a first step in many factoring algorithms. It factors nonsquarefree polynomials in terms of squarefree factors that are relatively prime. It can ...

For two random variates X and Y, the correlation is defined bY cor(X,Y)=(cov(X,Y))/(sigma_Xsigma_Y), (1) where sigma_X denotes standard deviation and cov(X,Y) is the ...

Subresultants can be viewed as a generalization of resultants, which are the product of the pairwise differences of the roots of polynomials. Subresultants are the most ...

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 ...

Let A denote an R-algebra, so that A is a vector space over R and A×A->A (1) (x,y)|->x·y, (2) where x·y is vector multiplication which is assumed to be bilinear. Now define ...

A unit vector is a vector of length 1, sometimes also called a direction vector (Jeffreys and Jeffreys 1988). The unit vector v^^ having the same direction as a given ...

The equation of motion for a membrane shaped as a right isosceles triangle of length c on a side and with the sides oriented along the positive x and y axes is given by where ...