Accelerating the pace of engineering and science

# Documentation Center

• Trial Software

# numlib::sqrt2cfrac

Continued fraction expansion of square roots

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```numlib::sqrt2cfrac(a)
```

## Description

numlib::sqrt2cfrac(a) returns the continued fraction expansion of the square root of a as a sequence of two lists: the first one contains the non-periodic (integer) part, the second one contains the periodic part of the expansion.

## Examples

### Example 1

The square root of 87 can be written as 9 + q, where q is a number satisfying :

`numlib::sqrt2cfrac(87)`

### Example 2

Since 81 is a perfect square, there is no periodic part in the continued fraction expansion of its square root:

`numlib::sqrt2cfrac(81)`

## Parameters

 a A positive integer

## Return Values

If a is a perfect square, numlib::sqrt2cfrac returns a list with one entry; otherwise numlib::sqrt2cfrac returns a sequence of two lists, the first consisting of one integer, the second consisting of one or more integers.