Mathematica's symbolic character allows it to provide deep integrated support for algebraic numbers. At the core are Root objects, which provide exact implicit ...
Quartics is an option for functions that involve solving algebraic equations that specifies whether explicit forms for solutions to quartic equations should be given.
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 ...
Functions like Factor usually assume that all coefficients in the polynomials they produce must involve only rational numbers. But by setting the option Extension you can ...
Orthogonal polynomials. Legendre polynomials LegendreP[n,x] arise in studies of systems with three-dimensional spherical symmetry. They satisfy the differential equation ...
The representation of algebraic numbers. When you enter a Root object, the polynomial that appears in it is automatically reduced to a minimal form. This extracts the pure ...
An expression like x^2+2x-7==0 represents an equation in Mathematica. You will often need to solve equations like this, to find out for what values of x they are true. This ...
With its convenient symbolic representation of algebraic numbers, Mathematica's state-of-the-art algebraic number theory capabilities provide a concrete implementation of one ...
PolynomialGCD[poly_1, poly_2, ...] gives the greatest common divisor of the polynomials poly_i. PolynomialGCD[poly_1, poly_2, ..., Modulus -> p] evaluates the GCD modulo the ...
NumberFieldRootsOfUnity[a] gives the roots of unity for the field \[DoubleStruckCapitalQ][a] generated by the algebraic number a.