BUILT-IN MATHEMATICA SYMBOL

RootApproximant

RootApproximant[x]
converts the number x to one of the "simplest" algebraic numbers that approximates it well.

RootApproximant[x, n]
finds an algebraic number of degree at most n that approximates x.

Details and Options Details and Options

For degrees above 2, RootApproximant generates Root objects.
RootApproximant[x] effectively tests the total number of bits in the description of x by successively higher-degree algebraic numbers, and returns the first case for which the number of bits is small.
Results from RootApproximant may not be unique.
MinimalPolynomial yields the minimal polynomial for the result of RootApproximant.
The option Method->{"DegreeCost"->p} specifies an additional cost p to be used for each successively higher power in determining the "simplest" approximation.