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