Mathematica can work with polynomials whose coefficients are in the finite field Z_p of integers modulo a prime p. Functions for manipulating polynomials over finite fields. ...

Solve[expr, vars] attempts to solve the system expr of equations or inequalities for the variables vars. Solve[expr, vars, dom] solves over the domain dom. Common choices of ...

Cyclotomic[n, x] gives the n\[Null]^th cyclotomic polynomial in x.

Resultant[poly_1, poly_2, var] computes the resultant of the polynomials poly_1 and poly_2 with respect to the variable var. Resultant[poly_1, poly_2, var, Modulus -> p] ...

ToRadicals[expr] attempts to express all Root objects in expr in terms of radicals.

Subresultants[poly_1, poly_2, var] generates a list of the principal subresultant coefficients of the polynomials poly_1 and poly_2 with respect to the variable var.

A symmetric polynomial in variables x_1,…,x_n is a polynomial that is invariant under arbitrary permutations of x_1,…,x_n. Polynomials are called elementary symmetric ...

Built into Mathematica is the world's largest collection of both numerical and symbolic equation solving capabilities—with many original algorithms, all automatically ...

SymmetricReduction[f, {x_1, ..., x_n}] gives a pair of polynomials {p, q} in x_1, ..., x_n such that f == p + q, where p is the symmetric part and q is the ...

PowerExpand[expr] expands all powers of products and powers. PowerExpand[expr, {x_1, x_2, ...}] expands only with respect to the variables x_i.