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Number Recognition
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 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
RootApproximant find an approximating algebraic number
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
FindSequenceFunction find functional forms for integer sequences