numlib::sqrt2cfrac
--
continued fraction expansion of square rootsnumlib::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.
numlib::sqrt2cfrac(a)
a |
- | a positive integer |
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.
The 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]
Since 81 is a perfect square, there is no periodic part in the continued fraction expansion of its square root:
>> numlib::sqrt2cfrac(81)
[9]