There are efficient algorithms for testing polynomial irreducibility and factoring polynomials over finite field. This is a polynomial ring in the "n" elementary symmetric polynomials for . Originally, algebraic geometry was the study of common zeros of sets of multivariate polynomials. The study of the sets of zeros of polynomials is the object of algebraic geometry. Many computer algebra systems have a built in function to compute the cyclotomic polynomials. Projective varieties were subsets defined by a set of homogeneous polynomials. The total number of roots of these monic irreducible polynomials is . Monomial degree is fundamental to the theory of univariate and multivariate polynomials. Both and form a sequence of orthogonal polynomials. One of the methods is based on the permutation polynomials. This results from the fact that the Galois groups of the cyclotomic polynomials are cyclic. These conventions are useful when defining Euclidean division of polynomials. It follows that they are roots of irreducible polynomials of degree over . See in particular the orthogonal polynomials. Similarly, the rational expressions are the field of fractions of polynomials.