GaussianIntegers is an option for FactorInteger, PrimeQ, Factor, and related functions that specifies whether factorization should be done over Gaussian integers.

RootOfUnityQ[a] yields True if a is a root of unity, and yields False otherwise.

Modulus -> n is an option that can be given in certain algebraic functions to specify that integers should be treated modulo n.

Pattern matching makes possible some of the most succinct and elegant programs in the Mathematica language—immediately compressing large numbers of conditional cases into ...

Decompose[poly, x] decomposes a polynomial, if possible, into a composition of simpler polynomials.

When you do symbolic calculations, it is quite easy to end up with extremely complicated expressions. Often, you will not even want to see the complete result of a ...

NumberFieldSignature[a] gives the signature of the field \[DoubleStruckCapitalQ][a] generated by the algebraic number a.

The flexibility of Mathematica's symbolic architecture is reflected in its rich collection of carefully defined constructs for localization and modularization. The use of ...

Element[x, dom] or x \[Element] dom asserts that x is an element of the domain dom. Element[{x_1, x_2, ...}, dom] asserts that all the x_i are elements of dom. Element[patt, ...

Mathematica's symbolic character allows a powerful unification of the notion of conditionals in programming and in mathematics.