Math::NumSeq::SqrtEngel -- Engel expansion of a square root
use Math::NumSeq::SqrtEngel; my $seq = Math::NumSeq::SqrtEngel->new (sqrt => 2); my ($i, $value) = $seq->next;
This is terms in the Engel expansion of a square root. The Engel expansion approaches the root by a series
1 1 1 sqrt(S) = ---- + --------- + -------------- + ... a[1] a[1]*a[2] a[1]*a[2]*a[3]
where each a[i] is chosen to make the term as big as possible without the total exceeding the target sqrt(S).
The sequence values are each successive a[i]. For example sqrt(2)
1 1 1 1 1 sqrt(2) = --- + --- + ----- + ------- + ---------- + ... 1 1*3 1*3*5 1*3*5*5 1*3*5*5*16
is
1, 3, 5, 5, 16, etc starting i=1
For a perfect square the expansion is a finite sequence of 1s adding up to the root. This is unlikely to be interesting, but works as a $seq
sequence..
sqrt(perfect square) = 1/1 + 1/1 + ... + 1/1
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::SqrtEngel->new (sqrt => $integer)
Create and return a new sequence object giving the Engel expansion terms of sqrt($integer)
.
The current code requires Math::BigInt
sqrt()
, which may mean BigInt 1.60 or higher (which comes with Perl 5.8.0).
Math::NumSeq, Math::NumSeq::SqrtDigits
http://user42.tuxfamily.org/math-numseq/index.html
Copyright 2011, 2012, 2013, 2014 Kevin Ryde
Math-NumSeq is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.
Math-NumSeq is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.