3. Semilocalizations of the Integers
  
  This package implements residue class unions of the semilocalizations Z_(pi)
  of  the ring of integers. It also provides the underlying GAP implementation
  of these rings themselves.
  
  
  3.1 Entering semilocalizations of the integers
  
  3.1-1 Z_pi
  
  > Z_pi( pi ) _______________________________________________________function
  > Z_pi( p ) ________________________________________________________function
  Returns:  The ring Z_(pi) or the ring Z_(p), respectively.
  
  The  returned  ring  has  the  property  IsZ_pi. The set pi of noninvertible
  primes can be retrieved by the operation NoninvertiblePrimes.
  
  ---------------------------  Example  ----------------------------
    
    gap> R := Z_pi(2);
    Z_( 2 )
    gap> S := Z_pi([2,5,7]);
    Z_( 2, 5, 7 )
    
  ------------------------------------------------------------------
  
  
  3.2 Methods for semilocalizations of the integers
  
  There   are   methods   for   the  operations  in,  Intersection,  IsSubset,
  StandardAssociate,    Gcd,   Lcm,   Factors   and   IsUnit   available   for
  semilocalizations   of   the   integers.  For  the  documentation  of  these
  operations,  see  the  GAP  reference  manual.  The standard associate of an
  element  of  a  ring  Z_(pi)  is defined by the product of the noninvertible
  prime factors of its numerator.
  
  ---------------------------  Example  ----------------------------
    
    gap> 4/7 in R; 3/2 in R;
    true
    false
    gap> Intersection(R,Z_pi([3,11])); IsSubset(R,S);
    Z_( 2, 3, 11 )
    true
    
  ------------------------------------------------------------------
  
  ---------------------------  Example  ----------------------------
    
    gap> StandardAssociate(R,-6/7);
    2
    gap> Gcd(S,90/3,60/17,120/33);
    10
    gap> Lcm(S,90/3,60/17,120/33);
    40
    gap> Factors(R,840);
    [ 105, 2, 2, 2 ]
    gap> Factors(R,-2/3);
    [ -1/3, 2 ]
    gap> IsUnit(S,3/11);
    true
    
  ------------------------------------------------------------------