index.KAF

2012                
(|AbelianMonoid|)
|category|
(((|AbelianMonoid|) (|Category|)) (T |AbelianMonoid|))
(T)
(|Join| (|AbelianSemiGroup|)
        (CATEGORY |domain| (SIGNATURE |Zero| ($) |constant|)
         (SIGNATURE |sample| ($) |constant|)
         (SIGNATURE |zero?| ((|Boolean|) $))
         (SIGNATURE * ($ (|NonNegativeInteger|) $))
         (SIGNATURE |opposite?| ((|Boolean|) $ $))))
"catdef.spad"
((|Zero| (*1 *1) (|ofCategory| *1 (|AbelianMonoid|)))
 (|sample| (*1 *1) (|ofCategory| *1 (|AbelianMonoid|)))
 (|zero?| (*1 *2 *1)
  (AND (|ofCategory| *1 (|AbelianMonoid|)) (|isDomain| *2 (|Boolean|))))
 (* (*1 *1 *2 *1)
    (AND (|ofCategory| *1 (|AbelianMonoid|))
         (|isDomain| *2 (|NonNegativeInteger|))))
 (|opposite?| (*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|AbelianMonoid|)) (|isDomain| *2 (|Boolean|)))))
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| (((|Boolean|) $) 22 T ELT))
 (|sample| (($) 23 T CONST)) (|opposite?| (((|Boolean|) $ $) 20 T ELT))
 (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT))
 (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT))
 (|Zero| (($) 24 T CONST)) (= (#1# 8 T ELT)) (+ (($ $ $) 18 T ELT))
 (* (($ (|PositiveInteger|) $) 17 T ELT)
    (($ (|NonNegativeInteger|) $) 21 T ELT)))
ABELMON
(((|AbelianSemiGroup|) . T))
(((|AbelianSemiGroup|) . T) ((|BasicType|) . T)
 ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T) ((|Type|) . T))
((|constructor|
  (NIL
   "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with an additive identity element. \\blankline"))
 (|opposite?|
  (((|Boolean|) $ $)
   "\\spad{opposite?(x,y)} holds if the sum of \\spad{x} and \\spad{y} is \\spad{0}."))
 (*
  (($ (|NonNegativeInteger|) $)
   "\\spad{n * x} is left-multiplication by a non negative integer"))
 (|zero?|
  (((|Boolean|) $) "\\spad{zero?(x)} tests if \\spad{x} is equal to 0."))
 (|sample| (($) "\\spad{sample yields} a value of type \\%"))
 (|Zero| (($) "0 is the additive identity element.")))
(("documentation" 0 1436) ("ancestors" 0 1312) ("parents" 0 1283)
 ("abbreviation" 0 1275) ("predicates" 0 NIL) ("attributes" 0 NIL)
 ("signaturesAndLocals" 0 NIL) ("superDomain" 0 NIL) ("operationAlist" 0 827)
 ("modemaps" 0 408) ("sourceFile" 0 394) ("constructorCategory" 0 109)
 ("dualSignature" 0 105) ("constructorModemap" 0 50) ("constructorKind" 0 39)
 ("constructorForm" 0 21))