


Math::BigRat(3p) Perl Programmers Reference GuideMath::BigRat(3p)


NAME
       Math::BigRat - Arbitrary big rational numbers

SYNOPSIS
               use Math::BigRat;

               my $x = Math::BigRat->new('3/7'); $x += '5/9';

               print $x->bstr(),"\n";
               print $x ** 2,"\n";

               my $y = Math::BigRat->new('inf');
               print "$y ", ($y->is_inf ? 'is' : 'is not') , " infinity\n";

               my $z = Math::BigRat->new(144); $z->bsqrt();

DESCRIPTION
       Math::BigRat complements Math::BigInt and Math::BigFloat
       by providing support for arbitrary big rational numbers.

   MATH LIBRARY
       You can change the underlying module that does the low-
       level math operations by using:

               use Math::BigRat try => 'GMP';

       Note: This needs Math::BigInt::GMP installed.

       The following would first try to find Math::BigInt::Foo,
       then Math::BigInt::Bar, and when this also fails, revert
       to Math::BigInt::Calc:

               use Math::BigRat try => 'Foo,Math::BigInt::Bar';

       If you want to get warned when the fallback occurs,
       replace "try" with "lib":

               use Math::BigRat lib => 'Foo,Math::BigInt::Bar';

       If you want the code to die instead, replace "try" with
       "only":

               use Math::BigRat only => 'Foo,Math::BigInt::Bar';

METHODS
       Any methods not listed here are derived from
       Math::BigFloat (or Math::BigInt), so make sure you check
       these two modules for further information.

   new()
               $x = Math::BigRat->new('1/3');

       Create a new Math::BigRat object. Input can come in
       various forms:



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               $x = Math::BigRat->new(123);                            # scalars
               $x = Math::BigRat->new('inf');                          # infinity
               $x = Math::BigRat->new('123.3');                        # float
               $x = Math::BigRat->new('1/3');                          # simple string
               $x = Math::BigRat->new('1 / 3');                        # spaced
               $x = Math::BigRat->new('1 / 0.1');                      # w/ floats
               $x = Math::BigRat->new(Math::BigInt->new(3));           # BigInt
               $x = Math::BigRat->new(Math::BigFloat->new('3.1'));     # BigFloat
               $x = Math::BigRat->new(Math::BigInt::Lite->new('2'));   # BigLite

               # You can also give D and N as different objects:
               $x = Math::BigRat->new(
                       Math::BigInt->new(-123),
                       Math::BigInt->new(7),
                       );                      # => -123/7

   numerator()
               $n = $x->numerator();

       Returns a copy of the numerator (the part above the line)
       as signed BigInt.

   denominator()
               $d = $x->denominator();

       Returns a copy of the denominator (the part under the
       line) as positive BigInt.

   parts()
               ($n,$d) = $x->parts();

       Return a list consisting of (signed) numerator and
       (unsigned) denominator as BigInts.

   numify()
               my $y = $x->numify();

       Returns the object as a scalar. This will lose some data
       if the object cannot be represented by a normal Perl
       scalar (integer or float), so use as_int() or as_float()
       instead.

       This routine is automatically used whenever a scalar is
       required:

               my $x = Math::BigRat->new('3/1');
               @array = (1,2,3);
               $y = $array[$x];                # set $y to 3

   as_int()/as_number()
               $x = Math::BigRat->new('13/7');
               print $x->as_int(),"\n";                # '1'

       Returns a copy of the object as BigInt, truncated to an



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       integer.

       "as_number()" is an alias for "as_int()".

   as_float()
               $x = Math::BigRat->new('13/7');
               print $x->as_float(),"\n";              # '1'

               $x = Math::BigRat->new('2/3');
               print $x->as_float(5),"\n";             # '0.66667'

       Returns a copy of the object as BigFloat, preserving the
       accuracy as wanted, or the default of 40 digits.

       This method was added in v0.22 of Math::BigRat (April
       2008).

   as_hex()
               $x = Math::BigRat->new('13');
               print $x->as_hex(),"\n";                # '0xd'

       Returns the BigRat as hexadecimal string. Works only for
       integers.

   as_bin()
               $x = Math::BigRat->new('13');
               print $x->as_bin(),"\n";                # '0x1101'

       Returns the BigRat as binary string. Works only for
       integers.

   as_oct()
               $x = Math::BigRat->new('13');
               print $x->as_oct(),"\n";                # '015'

       Returns the BigRat as octal string. Works only for
       integers.

   from_hex()/from_bin()/from_oct()
               my $h = Math::BigRat->from_hex('0x10');
               my $b = Math::BigRat->from_bin('0b10000000');
               my $o = Math::BigRat->from_oct('020');

       Create a BigRat from an hexadecimal, binary or octal
       number in string form.

   length()
               $len = $x->length();

       Return the length of $x in digitis for integer values.

   digit()
               print Math::BigRat->new('123/1')->digit(1);     # 1
               print Math::BigRat->new('123/1')->digit(-1);    # 3



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       Return the N'ths digit from X when X is an integer value.

   bnorm()
               $x->bnorm();

       Reduce the number to the shortest form. This routine is
       called automatically whenever it is needed.

   bfac()
               $x->bfac();

       Calculates the factorial of $x. For instance:

               print Math::BigRat->new('3/1')->bfac(),"\n";    # 1*2*3
               print Math::BigRat->new('5/1')->bfac(),"\n";    # 1*2*3*4*5

       Works currently only for integers.

   bround()/round()/bfround()
       Are not yet implemented.

   bmod()
               use Math::BigRat;
               my $x = Math::BigRat->new('7/4');
               my $y = Math::BigRat->new('4/3');
               print $x->bmod($y);

       Set $x to the remainder of the division of $x by $y.

   bneg()
               $x->bneg();

       Used to negate the object in-place.

   is_one()
               print "$x is 1\n" if $x->is_one();

       Return true if $x is exactly one, otherwise false.

   is_zero()
               print "$x is 0\n" if $x->is_zero();

       Return true if $x is exactly zero, otherwise false.

   is_pos()/is_positive()
               print "$x is >= 0\n" if $x->is_positive();

       Return true if $x is positive (greater than or equal to
       zero), otherwise false. Please note that '+inf' is also
       positive, while 'NaN' and '-inf' aren't.

       "is_positive()" is an alias for "is_pos()".





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   is_neg()/is_negative()
               print "$x is < 0\n" if $x->is_negative();

       Return true if $x is negative (smaller than zero),
       otherwise false. Please note that '-inf' is also negative,
       while 'NaN' and '+inf' aren't.

       "is_negative()" is an alias for "is_neg()".

   is_int()
               print "$x is an integer\n" if $x->is_int();

       Return true if $x has a denominator of 1 (e.g. no fraction
       parts), otherwise false. Please note that '-inf', 'inf'
       and 'NaN' aren't integer.

   is_odd()
               print "$x is odd\n" if $x->is_odd();

       Return true if $x is odd, otherwise false.

   is_even()
               print "$x is even\n" if $x->is_even();

       Return true if $x is even, otherwise false.

   bceil()
               $x->bceil();

       Set $x to the next bigger integer value (e.g. truncate the
       number to integer and then increment it by one).

   bfloor()
               $x->bfloor();

       Truncate $x to an integer value.

   bsqrt()
               $x->bsqrt();

       Calculate the square root of $x.

   broot()
               $x->broot($n);

       Calculate the N'th root of $x.

   badd()/bmul()/bsub()/bdiv()/bdec()/binc()
       Please see the documentation in Math::BigInt.

   copy()
               my $z = $x->copy();

       Makes a deep copy of the object.



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       Please see the documentation in Math::BigInt for further
       details.

   bstr()/bsstr()
               my $x = Math::BigInt->new('8/4');
               print $x->bstr(),"\n";                  # prints 1/2
               print $x->bsstr(),"\n";                 # prints 1/2

       Return a string representating this object.

   bacmp()/bcmp()
       Used to compare numbers.

       Please see the documentation in Math::BigInt for further
       details.

   blsft()/brsft()
       Used to shift numbers left/right.

       Please see the documentation in Math::BigInt for further
       details.

   bpow()
               $x->bpow($y);

       Compute $x ** $y.

       Please see the documentation in Math::BigInt for further
       details.

   bexp()
               $x->bexp($accuracy);            # calculate e ** X

       Calculates two integers A and B so that A/B is equal to "e
       ** $x", where "e" is Euler's number.

       This method was added in v0.20 of Math::BigRat (May 2007).

       See also blog().

   bnok()
               $x->bnok($y);              # x over y (binomial coefficient n over k)

       Calculates the binomial coefficient n over k, also called
       the "choose" function. The result is equivalent to:

               ( n )      n!
               | - |  = -------
               ( k )    k!(n-k)!

       This method was added in v0.20 of Math::BigRat (May 2007).

   config()
               use Data::Dumper;



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               print Dumper ( Math::BigRat->config() );
               print Math::BigRat->config()->{lib},"\n";

       Returns a hash containing the configuration, e.g. the
       version number, lib loaded etc. The following hash keys
       are currently filled in with the appropriate information.

               key             RO/RW   Description
                                       Example
               ============================================================
               lib             RO      Name of the Math library
                                       Math::BigInt::Calc
               lib_version     RO      Version of 'lib'
                                       0.30
               class           RO      The class of config you just called
                                       Math::BigRat
               version         RO      version number of the class you used
                                       0.10
               upgrade         RW      To which class numbers are upgraded
                                       undef
               downgrade       RW      To which class numbers are downgraded
                                       undef
               precision       RW      Global precision
                                       undef
               accuracy        RW      Global accuracy
                                       undef
               round_mode      RW      Global round mode
                                       even
               div_scale       RW      Fallback accuracy for div
                                       40
               trap_nan        RW      Trap creation of NaN (undef = no)
                                       undef
               trap_inf        RW      Trap creation of +inf/-inf (undef = no)
                                       undef

       By passing a reference to a hash you may set the
       configuration values. This works only for values that a
       marked with a "RW" above, anything else is read-only.

   objectify()
       This is an internal routine that turns scalars into
       objects.

BUGS
       Some things are not yet implemented, or only implemented
       half-way:

       inf handling (partial)
       NaN handling (partial)
       rounding (not implemented except for bceil/bfloor)
       $x ** $y where $y is not an integer
       bmod(), blog(), bmodinv() and bmodpow() (partial)




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LICENSE
       This program is free software; you may redistribute it
       and/or modify it under the same terms as Perl itself.

SEE ALSO
       Math::BigFloat and Math::Big as well as
       Math::BigInt::BitVect, Math::BigInt::Pari and
       Math::BigInt::GMP.

       See <http://search.cpan.org/search?dist=bignum> for a way
       to use Math::BigRat.

       The package at
       <http://search.cpan.org/search?dist=Math%3A%3ABigRat> may
       contain more documentation and examples as well as
       testcases.

AUTHORS
       (C) by Tels <http://bloodgate.com/> 2001 - 2008.






































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