See also NonNegativeInteger

spad
)abbrev domain PI PositiveInteger
++ Author:
++ Date Created:
++ Change History:
++ Basic Operations:
++ Related Constructors:
++ Keywords: positive integer
++ Description: \spadtype{PositiveInteger} provides functions for
++   positive integers.
PositiveInteger: Join(AbelianSemiGroup,OrderedSet,Monoid) with
            gcd: (%,%) -> %
              ++ gcd(a,b) computes the greatest common divisor of two
              ++ positive integers \spad{a} and b.
            commutative("*")
              ++ commutative("*") means multiplication is commutative : x*y = y*x
 == SubDomain(NonNegativeInteger,#1 > 0) add
   x:%
   y:%

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/8833918516811102525-25px001.spad using 
      old system compiler.
   PI abbreviates domain PositiveInteger 
------------------------------------------------------------------------
   initializing NRLIB PI for PositiveInteger 
   compiling into NRLIB PI 
(time taken in buildFunctor:  0)

;;;     ***       |PositiveInteger| REDEFINED

;;;     ***       |PositiveInteger| REDEFINED
Time: 0.07 SEC.

   Cumulative Statistics for Constructor PositiveInteger
      Time: 0.07 seconds

--------------non extending category----------------------
.. PositiveInteger of cat 
(|Join| (|AbelianSemiGroup|) (|OrderedSet|) (|Monoid|)
        (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $))
            (ATTRIBUTE (|commutative| "*"))))   has no 
(|OrderedAbelianMonoidSup|)    finalizing NRLIB PI 
   Processing PositiveInteger for Browser database:
--------(gcd (% % %))---------
--------(commutative (attribute *))---------
--------constructor---------
------------------------------------------------------------------------
   PositiveInteger is now explicitly exposed in frame initial 
   PositiveInteger will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/PI.NRLIB/code

axiom
)show PositiveInteger

 PositiveInteger  is a domain constructor
 Abbreviation for PositiveInteger is PI
 This constructor is exposed in this frame.
 Issue )edit /var/zope2/var/LatexWiki/8833918516811102525-25px001.spad to see algebra source
code for PI 

------------------------------- Operations --------------------------------
 ?*? : (%,%) -> %                      ?*? : (PositiveInteger,%) -> %
 ?**? : (%,PositiveInteger) -> %       ?+? : (%,%) -> %
 ?<? : (%,%) -> Boolean                ?<=? : (%,%) -> Boolean
 ?=? : (%,%) -> Boolean                ?>? : (%,%) -> Boolean
 ?>=? : (%,%) -> Boolean               1 : () -> %
 ?^? : (%,PositiveInteger) -> %        coerce : % -> OutputForm
 gcd : (%,%) -> %                      hash : % -> SingleInteger
 latex : % -> String                   max : (%,%) -> %
 min : (%,%) -> %                      one? : % -> Boolean
 recip : % -> Union(%,"failed")        sample : () -> %
 ?~=? : (%,%) -> Boolean
 ?**? : (%,NonNegativeInteger) -> %
 ?^? : (%,NonNegativeInteger) -> %