Math::NumSeq::SqrtEngel(3pm)

1Math::NumSeq::SqrtEngelU(s3e)r Contributed Perl DocumentaMtaitohn::NumSeq::SqrtEngel(3)
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NAME

6       Math::NumSeq::SqrtEngel -- Engel expansion of a square root
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SYNOPSIS

9        use Math::NumSeq::SqrtEngel;
10        my $seq = Math::NumSeq::SqrtEngel->new (sqrt => 2);
11        my ($i, $value) = $seq->next;
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DESCRIPTION

14       This is terms in the Engel expansion of a square root.  The Engel
15       expansion approaches the root by a series
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17                     1         1              1
18          sqrt(S) = ---- + --------- + -------------- + ...
19                    a[1]   a[1]*a[2]   a[1]*a[2]*a[3]
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21       where each a[i] is chosen to make the term as big as possible without
22       the total exceeding the target sqrt(S).
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24       The sequence values are each successive a[i].  For example sqrt(2)
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26                     1     1      1        1          1
27          sqrt(2) = --- + --- + ----- + ------- + ---------- + ...
28                     1    1*3   1*3*5   1*3*5*5   1*3*5*5*16
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30       is
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32           1, 3, 5, 5, 16, etc
33           starting i=1
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35       For a perfect square the expansion is a finite sequence of 1s adding up
36       to the root.  This is unlikely to be interesting, but works as a $seq
37       sequence..
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39           sqrt(perfect square) = 1/1 + 1/1 + ... + 1/1
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FUNCTIONS

42       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
43       classes.
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45       "$seq = Math::NumSeq::SqrtEngel->new (sqrt => $integer)"
46           Create and return a new sequence object giving the Engel expansion
47           terms of "sqrt($integer)".
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BUGS

50       The current code requires "Math::BigInt" "sqrt()", which may mean
51       BigInt 1.60 or higher (which comes with Perl 5.8.0).
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HOME PAGE

57       <http://user42.tuxfamily.org/math-numseq/index.html>
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LICENSE

60       Copyright 2011, 2012, 2013, 2014, 2016, 2019 Kevin Ryde
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62       Math-NumSeq is free software; you can redistribute it and/or modify it
63       under the terms of the GNU General Public License as published by the
64       Free Software Foundation; either version 3, or (at your option) any
65       later version.
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67       Math-NumSeq is distributed in the hope that it will be useful, but
68       WITHOUT ANY WARRANTY; without even the implied warranty of
69       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
70       General Public License for more details.
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72       You should have received a copy of the GNU General Public License along
73       with Math-NumSeq.  If not, see <http://www.gnu.org/licenses/>.
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77perl v5.34.0                      2021-07-22        Math::NumSeq::SqrtEngel(3)