A core activity in exploratory experimental mathematics is recognition of numbers: going backward from a number to find out how it can be generated. The Wolfram Language provides tools for recognizing many classes of numbers, including a number of original algorithms.

Primes  ▪  Algebraics  ▪  Rationals  ▪  Integers

Element — test whether a number is in a given class

Rationalize — find a rational approximation

ContinuedFraction  ▪  Convergents

RootApproximant — find an approximating algebraic number

ToRadicals  ▪  RootReduce  ▪  MinimalPolynomial

FindIntegerNullVector — find vector such that

LatticeReduce — find reduced basis vectors in a lattice

FunctionExpand — reduce an exact numeric expression to simpler functions

PrimeQ — recognize prime numbers

CompositeQ  ▪  SquareFreeQ  ▪  PrimePowerQ  ▪  AlgebraicIntegerQ

FindSequenceFunction — find functional forms for integer sequences