BUILT-IN MATHEMATICA SYMBOL

# RootApproximant

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 OptionsDetails and Options

• For degrees above 2, RootApproximant generates Root objects.
• 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.

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Find a quadratic approximation to :

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Find algebraic approximants of any order:

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