ContinuedFraction

Usage

• ContinuedFraction[x, n] generates a list of the first n terms in the continued fraction representation of x.
• ContinuedFraction[x] generates a list of all terms that can be obtained given the precision of x.

Notes

• The continued fraction representation {

, ... } corresponds to the expression

• x can be either an exact or an inexact number.

• Example: ContinuedFraction[Pi, 4]

• For exact numbers, ContinuedFraction[x] can be used if x is rational, or is a quadratic irrational.

• For quadratic irrationals, ContinuedFraction[x] returns a result of the form {

, ... , {

, ... }}, corresponding to an infinite sequence of terms, starting with the

, and followed by cyclic repetitions of the

• Since the continued fraction representation for a rational number has only a limited number of terms, ContinuedFraction[x, n] may yield a list with less than n elements in this case.

• For terminating continued fractions, {... , k} is always equivalent to { ... , k-1, 1}; ContinuedFraction returns the first of these forms.

• FromContinuedFraction[list] reconstructs a number from the result of ContinuedFraction.

• See Section 3.2.5.

• Implementation notes: see Section A.9.4.

• New in Version 4.

Further Examples