CancellationAbelianMonoidΒΆ

catdef.spad line 165

This is an AbelianMonoid with the cancellation property, i.e. `` a+b = a+c => b=c ``. This is formalised by the partial subtraction operator, which satisfies the axioms listed below:

0: %
from AbelianMonoid
*: (NonNegativeInteger, %) -> %
from AbelianMonoid
*: (PositiveInteger, %) -> %
from AbelianSemiGroup
+: (%, %) -> %
from AbelianSemiGroup
=: (%, %) -> Boolean
from BasicType
~=: (%, %) -> Boolean
from BasicType
coerce: % -> OutputForm
from CoercibleTo OutputForm
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
latex: % -> String
from SetCategory
opposite?: (%, %) -> Boolean
from AbelianMonoid
sample: %
from AbelianMonoid
subtractIfCan: (%, %) -> Union(%, failed)
subtractIfCan(x, y) returns an element z such that z+y=x or “failed” if no such element exists.
zero?: % -> Boolean
from AbelianMonoid

AbelianMonoid

AbelianSemiGroup

BasicType

CoercibleTo OutputForm

SetCategory