# 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 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.

# Examples

open allclose all

## Basic Examples(2)

Find a quadratic approximation to :

 In[1]:=
 Out[1]=
 In[2]:=
 Out[2]=

Find algebraic approximants of any order:

 In[1]:=
 Out[1]=
 In[2]:=
 Out[2]=
 In[3]:=
 Out[3]=

# See Also

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