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Fraction
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The Fraction domain implements quotients.  The elements must
belong to a domain of category IntegralDomain: multiplication
must be commutative and the product of two non-zero elements must not
be zero.  This allows you to make fractions of most things you would
think of, but don't expect to create a fraction of two matrices!  The
abbreviation for Fraction is FRAC. 

Use / to create a fraction. ::

  a := 11/12
    11
    --
    12
                   Type: Fraction Integer

  b := 23/24
    23
    --
    24
                   Type: Fraction Integer

The standard arithmetic operations are available. ::

  3 - a*b**2 + a + b/a
    313271
    ------
     76032
                   Type: Fraction Integer

Extract the numerator and denominator by using numer and denom,
respectively. ::

  numer(a)
    11
                   Type: PositiveInteger

  denom(b)
    24
                   Type: PositiveInteger

Operations like max, min, negative?, positive? and zero?
are all available if they are provided for the numerators and
denominators.  

Don't expect a useful answer from factor, gcd or lcm if you apply
them to fractions. ::

  r := (x**2 + 2*x + 1)/(x**2 - 2*x + 1)
     2
    x  + 2x + 1
    -----------
     2
    x  - 2x + 1
                  Type: Fraction Polynomial Integer

Since all non-zero fractions are invertible, these operations have trivial
definitions. ::

  factor(r)
     2
    x  + 2x + 1
    -----------
     2
    x  - 2x + 1
                  Type: Factored Fraction Polynomial Integer

Use map to apply factor to the numerator and denominator, which is
probably what you mean. ::

  map(factor,r)
           2
    (x + 1)
    --------
           2
    (x - 1)
                  Type: Fraction Factored Polynomial Integer

Other forms of fractions are available.  Use continuedFraction to
create a continued fraction. ::

  continuedFraction(7/12)
      1 |     1 |     1 |     1 |
    +---+ + +---+ + +---+ + +---+
    | 1     | 1     | 2     | 2
                  Type: ContinuedFraction Integer

Use partialFraction to create a partial fraction. ::

  partialFraction(7,12)
          3   1
     1 - -- + -
          2   3
         2
                  Type: PartialFraction Integer

Use conversion to create alternative views of fractions with objects
moved in and out of the numerator and denominator. ::

  g := 2/3 + 4/5*%i
     2   4
     - + - %i
     3   5
                  Type: Complex Fraction Integer

  g :: FRAC COMPLEX INT
    10 + 12%i
    ---------
        15
                  Type: Fraction Complex Integer

See Also: 

* ``)help ContinuedFraction``
* ``)help PartialFraction``
* ``)help Integer``
* ``)show Fraction``