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 Topics FrontPage AboutAxiom AxiomDocumentation Axiom Algebra PositiveInteger <-- You are here. 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. CommutativeStar ++ CommutativeStar means multiplication is commutative : x*y = y*x == SubDomain(NonNegativeInteger,x+->(x > 0)) add x:% y:% spad Compiling FriCAS source code from file /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/2005619913106366479-25px001.spad using old system compiler. PI abbreviates domain PositiveInteger ------------------------------------------------------------------------ initializing NRLIB PI for PositiveInteger compiling into NRLIB PI ****** comp fails at level 1 with expression: ****** ((+-> |x| (> |x| 0))) ****** level 1 ****** $x:= (+-> x (> x (Zero)))$m:= (Boolean) \$f:= ((((|#1| #) (* #) (+ #) (< #) ...))) >> Apparent user error: compLambda: signature needed (+-> x (> x (Zero))) fricas)show PositiveInteger PositiveInteger is a domain constructor Abbreviation for PositiveInteger is PI This constructor is exposed in this frame. ------------------------------- Operations -------------------------------- ?*? : (%,%) -> % ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % ? Boolean ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean 1 : () -> % ?^? : (%,PositiveInteger) -> % coerce : % -> OutputForm gcd : (%,%) -> % hash : % -> SingleInteger latex : % -> String max : (%,%) -> % min : (%,%) -> % one? : % -> Boolean qcoerce : Integer -> % recip : % -> Union(%,"failed") sample : () -> % smaller? : (%,%) -> Boolean ?~=? : (%,%) -> Boolean ?^? : (%,NonNegativeInteger) -> % hashUpdate! : (HashState,%) -> HashState

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