ContinuedFraction

ContinuedFraction(number)

the complete continued fraction representation for a rational or quadradic irrational number.

ContinuedFraction(number, n)

generate the first n terms in the continued fraction representation of number.

See:

• Wikipedia - Continued fraction

Examples

>> FromContinuedFraction({2,3,4,5})
157/68

>> ContinuedFraction(157/68)
{2,3,4,5}

>> ContinuedFraction(45/16)
{2,1,4,3}

For square roots of non-negative integer arguments ContinuedFraction determines the periodic part:

>> ContinuedFraction(Sqrt(13))
{3,{1,1,1,1,6}}

>> ContinuedFraction(Sqrt(919))
{30,{3,5,1,2,1,2,1,1,1,2,3,1,19,2,3,1,1,4,9,1,7,1,3,6,2,11,1,1,1,29,1,1,1,11,2,6,3,1,7,1,9,4,1,1,3,2,19,1,3,2,1,1,1,2,1,2,1,5,3,60}}

Related terms

FromContinuedFraction, QuadraticIrrationalQ

Implementation status

• ✅ - full supported

Github

• Implementation of ContinuedFraction