NAME
Math::NumSeq::FractionDigits  the digits of a fraction p/q
SYNOPSIS
use Math::NumSeq::FractionDigits;
my $seq = Math::NumSeq::FractionDigits>new (fraction => '2/11');
my ($i, $value) = $seq>next;
DESCRIPTION
The sequence of digits which are a given fraction. For example 1/7 in decimal, being 0.14285714...
1, 4, 2, 8, 5, 7, 1, 4, etc
After any integer part, the fraction digits are a repeating sequence. If the fraction is num/den and is in least terms (num and den have no common factor) then the period is either den1 or some divisor of den1.
A particular a repeating sequence a,b,c,d,a,b,c,d,etc can be cooked up with fraction abcd/9999, the denominator being as many 9s as digits to repeat. For a base other than decimal the "9" is radix1.
FUNCTIONS
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::FractionDigits>new (fraction => $f)
$seq = Math::NumSeq::FractionDigits>new (fraction => $f, radix => $r)

Create and return a new sequence object giving the digits of
$f
.$f
is a string "num/den", or a decimal "xx.yy",2/29 29.125 1.5/3.25
The default sequence values are decimal digits, or the
radix
parameter can select another base. (But thefraction
parameter is still decimal.)If the numerator or denominator of the fraction is bigger than fits Perl integer calculations then
Math::BigInt
is used automatically.
Random Access
$value = $seq>ith($i)

Return the
$i
'th digit of the fraction.
FORMULAS
Next
For a given num/den, with num < den, the next digit below the radix point is formed by
num *= radix # now 0 <= num/den < radix
quot,rem = num divide den
digit = quot # 0 <= digit < radix
new num = rem
Ith
For an arbitrary digit i, the repeated num*=radix can be applied by a modular powering
rpower = radix^i mod den
num = num * rpower mod den
i here acts as a count of how many digits to skip. For example if i=0 then rpower=1 and doesn't change the numerator at all. With that big skip the digit is then the same as for "next" above,
num *= radix # now 0 <= num/den < radix
digit = floor(num/den) # 0 <= digit < radix
The usual modular powering techniques can be applied to calculate radix^i mod den. Math::BigInt
has a bmodpow which is used in the code if the inputs are big.
SEE ALSO
Math::NumSeq, Math::NumSeq::SqrtDigits
HOME PAGE
http://user42.tuxfamily.org/mathnumseq/index.html
LICENSE
Copyright 2010, 2011, 2012, 2013, 2014 Kevin Ryde
MathNumSeq 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.
MathNumSeq 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 MathNumSeq. If not, see <http://www.gnu.org/licenses/>.