DOCUMENTATION CENTER SEARCH

Mathematica > Mathematics and Algorithms > Formula Manipulation > Algebraic Transformations > Algebraic Numbers >

Mathematica > Mathematics and Algorithms > Number Theory > Algebraic Number Theory > Algebraic Numbers >

Mathematica > Mathematics and Algorithms > Mathematical Functions > Number Theoretic Functions > Algebraic Number Theory > Algebraic Numbers >

Built-in Mathematica Symbol

See Also »|More About »

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.

MORE INFORMATION

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.

Basic Examples (2)

Find a quadratic approximation to

:

Find algebraic approximants of any order:

Applications (2)

Properties & Relations (3)

Possible Issues (1)

Rationalize LatticeReduce Root FindSequenceFunction

New in 6 | Last modified in 7

Ask a question about this page | Suggest an improvement | Leave a message for the team