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

  • 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.

Examples

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Basic Examples  (2)

Find a quadratic approximation to :

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Find algebraic approximants of any order:

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Scope  (4)

Options  (1)

Applications  (2)

Properties & Relations  (3)

Possible Issues  (1)

See Also

Rationalize  LatticeReduce  Root  FindSequenceFunction  MinimalPolynomial

Introduced in 2007
(6.0)
| Updated in 2008
(7.0)