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 ...

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.

Packing a large number of sophisticated algorithms—many recent and original—into a powerful collection of functions, Mathematica draws on almost every major result in number ...

Mathematica contains the world's largest collection of number theoretic functions, many based on specially developed algorithms.

Throughout Mathematica there is support not only for approximate real numbers, but also for exact numbers represented in algebraic or symbolic form. Functions like Floor, ...

 

AlgebraicNumber[\[Theta], {c_0, c_1, ..., c_n}] represents the algebraic number in the field \[DoubleStruckCapitalQ][\[Theta]] given by c_0 + c_1 \[Theta] + ... + c_n ...

PowersRepresentations[n, k, p] gives the distinct representations of the integer n as a sum of k non-negative p\[Null]^th integer powers.

For ordinary polynomials, Factor and Expand give the most important forms. For rational expressions, there are many different forms that can be useful. Different kinds of ...

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 ...