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Math::BigRat(3pm)      Perl Programmers Reference Guide      Math::BigRat(3pm)




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:

               $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 = (0, 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 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()
               my $h = Math::BigRat->from_hex('0x10');

           Create a BigRat from a hexadecimal number in string form.

       from_oct()
               my $o = Math::BigRat->from_oct('020');

           Create a BigRat from an octal number in string form.

       from_bin()
               my $b = Math::BigRat->from_bin('0b10000000');

           Create a BigRat from an binary number in string form.

       bnan()
               $x = Math::BigRat->bnan();

           Creates a new BigRat object representing NaN (Not A Number).  If
           used on an object, it will set it to NaN:

               $x->bnan();

       bzero()
               $x = Math::BigRat->bzero();

           Creates a new BigRat object representing zero.  If used on an
           object, it will set it to zero:

               $x->bzero();

       binf()
               $x = Math::BigRat->binf($sign);

           Creates a new BigRat object representing infinity. The optional
           argument is either '-' or '+', indicating whether you want infinity
           or minus infinity.  If used on an object, it will set it to
           infinity:

               $x->binf();
               $x->binf('-');

       bone()
               $x = Math::BigRat->bone($sign);

           Creates a new BigRat object representing one. The optional argument
           is either '-' or '+', indicating whether you want one or minus one.
           If used on an object, it will set it to one:

               $x->bone();                 # +1
               $x->bone('-');              # -1

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

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

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

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

           Returns $x modulo $y. When $x is finite, and $y is finite and non-
           zero, the result is identical to the remainder after floored
           division (F-division). If, in addition, both $x and $y are
           integers, the result is identical to the result from Perl's %
           operator.

       bmodinv()
               $x->bmodinv($mod);          # modular multiplicative inverse

           Returns the multiplicative inverse of $x modulo $mod. If

               $y = $x -> copy() -> bmodinv($mod)

           then $y is the number closest to zero, and with the same sign as
           $mod, satisfying

               ($x * $y) % $mod = 1 % $mod

           If $x and $y are non-zero, they must be relative primes, i.e.,
           "bgcd($y, $mod)==1". '"NaN"' is returned when no modular
           multiplicative inverse exists.

       bmodpow()
               $num->bmodpow($exp,$mod);           # modular exponentiation
                                                   # ($num**$exp % $mod)

           Returns the value of $num taken to the power $exp in the modulus
           $mod using binary exponentiation.  "bmodpow" is far superior to
           writing

               $num ** $exp % $mod

           because it is much faster - it reduces internal variables into the
           modulus whenever possible, so it operates on smaller numbers.

           "bmodpow" also supports negative exponents.

               bmodpow($num, -1, $mod)

           is exactly equivalent to

               bmodinv($num, $mod)

       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()".

       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.

       bint()
               $x->bint();

           Round $x towards zero.

       bsqrt()
               $x->bsqrt();

           Calculate the square root of $x.

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

           Calculate the N'th root of $x.

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

           Adds $y to $x and returns the result.

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

           Multiplies $y to $x and returns the result.

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

           Subtracts $y from $x and returns the result.

       bdiv()
               $q = $x->bdiv($y);
               ($q, $r) = $x->bdiv($y);

           In scalar context, divides $x by $y and returns the result. In list
           context, does floored division (F-division), returning an integer
           $q and a remainder $r so that $x = $q * $y + $r. The remainer
           (modulo) is equal to what is returned by "$x-"bmod($y)>.

       bdec()
               $x->bdec();

           Decrements $x by 1 and returns the result.

       binc()
               $x->binc();

           Increments $x by 1 and returns the result.

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

           Makes a deep copy of the object.

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

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

           Return a string representing this object.

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

           Compares $x with $y and takes the sign into account.  Returns -1,
           0, 1 or undef.

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

           Compares $x with $y while ignoring their sign. Returns -1, 0, 1 or
           undef.

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

           Returns true if and only if $x is equal to $y, and false otherwise.

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

           Returns true if and only if $x is not equal to $y, and false
           otherwise.

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

           Returns true if and only if $x is equal to $y, and false otherwise.

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

           Returns true if and only if $x is less than or equal to $y, and
           false otherwise.

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

           Returns true if and only if $x is greater than $y, and false
           otherwise.

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

           Returns true if and only if $x is greater than or equal to $y, and
           false otherwise.

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

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

       band()
               $x->band($y);               # bitwise and

       bior()
               $x->bior($y);               # bitwise inclusive or

       bxor()
               $x->bxor($y);               # bitwise exclusive or

       bnot()
               $x->bnot();                 # bitwise not (two's complement)

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

           Compute $x ** $y.

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

       blog()
               $x->blog($base, $accuracy);         # logarithm of x to the base $base

           If $base is not defined, Euler's number (e) is used:

               print $x->blog(undef, 100);         # log(x) to 100 digits

       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;

               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.


BUGS

       Please report any bugs or feature requests to "bug-math-bigrat at
       rt.cpan.org", or through the web interface at
       <https://rt.cpan.org/Ticket/Create.html?Queue=Math-BigRat> (requires
       login).  We will be notified, and then you'll automatically be notified
       of progress on your bug as I make changes.


SUPPORT

       You can find documentation for this module with the perldoc command.

           perldoc Math::BigRat

       You can also look for information at:

       o   RT: CPAN's request tracker

           <https://rt.cpan.org/Public/Dist/Display.html?Name=Math-BigRat>

       o   AnnoCPAN: Annotated CPAN documentation

           <http://annocpan.org/dist/Math-BigRat>

       o   CPAN Ratings

           <http://cpanratings.perl.org/dist/Math-BigRat>

       o   Search CPAN

           <http://search.cpan.org/dist/Math-BigRat/>

       o   CPAN Testers Matrix

           <http://matrix.cpantesters.org/?dist=Math-BigRat>

       o   The Bignum mailing list

           o   Post to mailing list

               "bignum at lists.scsys.co.uk"

           o   View mailing list

               <http://lists.scsys.co.uk/pipermail/bignum/>

           o   Subscribe/Unsubscribe

               <http://lists.scsys.co.uk/cgi-bin/mailman/listinfo/bignum>


LICENSE

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


SEE ALSO

       bigrat(3), Math::BigFloat(3) and Math::BigInt(3) as well as the
       backends Math::BigInt::FastCalc(3), Math::BigInt::GMP(3), and 
       Math::BigInt::Pari(3).


AUTHORS

       (C) by Tels <http://bloodgate.com/> 2001 - 2009.

       o   Maintained by Peter John Acklam <pjacklam@online.no> 2011-



perl v5.26.1                      2017-07-18                 Math::BigRat(3pm)

perl 5.26.1 - Generated Sun Nov 5 18:37:59 CST 2017
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