numlib::sqrt2cfrac --
continued fraction expansion of square roots
Introductionnumlib::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.
Call(s)numlib::sqrt2cfrac(a)
Parametersa |
- | a positive integer |
ReturnsIf 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.
Related
Functions
Example
1The square root of 87 can be written as 9+q, where q is a rational number satisfying q= 1/(3+1/(18+q)) :
>> numlib::sqrt2cfrac(87)
[9], [3, 18]
Example
2Since 81 is a perfect square, there is no periodic part in the continued fraction expansion of its square root:
>> numlib::sqrt2cfrac(81)
[9]