Mathematica provides representation of algebraic numbers as Root objects. A Root object contains the minimal polynomial of the algebraic number and the root number—an integer ...

Based on original algorithms developed at Wolfram Research, Mathematica's core randomness generation is both highly efficient and of exceptional quality. Mathematica can ...

The ability to generate pseudorandom numbers is important for simulating events, estimating probabilities and other quantities, making randomized assignments or selections, ...

NumberFieldDiscriminant[a] gives the discriminant of the field \[DoubleStruckCapitalQ][a] generated by the algebraic number a.

NumberFieldRegulator[a] gives the regulator of the field \[DoubleStruckCapitalQ][a] generated by the algebraic number a.

NumberFieldFundamentalUnits[a] gives a list of fundamental units for the field \[DoubleStruckCapitalQ][a] generated by the algebraic number a.

ToNumberField[a, \[Theta]] expresses the algebraic number a in the number field generated by \[Theta]. ToNumberField[{a_1, a_2, ...}, \[Theta]] expresses the a_i in the field ...

A core activity in exploratory experimental mathematics is recognition of numbers: going backward from a number to find out how it can be generated. Mathematica provides ...

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 includes functions for performing a variety of specific algebraic transformations. Some are algorithmically straightforward; others include highly sophisticated ...