A real polynomial system is an expression constructed with polynomial equations and inequalities combined using logical connectives and quantifiers and

ConstantArray[c, n] generates a list of n copies of the element c.ConstantArray[c, {n_1, n_2, ...}] generates an n_1*n_2*... array of nested lists containing copies of the ...

A Diophantine polynomial system is an expression constructed with polynomial equations and inequalities combined using logical connectives and quantifiers where the variables ...

Numerical root finding. NSolve gives you numerical approximations to all the roots of a polynomial equation. You can also use NSolve to solve sets of simultaneous equations ...

Counting roots of polynomials. CountRoots accepts polynomials with Gaussian rational coefficients. The root count includes multiplicities. This gives the number of real roots ...

Structural operations on polynomials. Here is a polynomial in one variable. Expand expands out products and powers, writing the polynomial as a simple sum of terms.

Orthogonal polynomials. Legendre polynomials LegendreP[n,x] arise in studies of systems with three-dimensional spherical symmetry. They satisfy the differential equation ...

For many kinds of practical calculations, the only operations you will need to perform on polynomials are essentially structural ones. If you do more advanced algebra with ...

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. ...

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 ...