CancellationAbelianMonoid

catdef.spad line 166 [edit on github]

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:

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

0 : () -> %

from AbelianMonoid

= : (%, %) -> Boolean

from BasicType

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

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

~= : (%, %) -> Boolean

from BasicType

SetCategory

AbelianSemiGroup

BasicType

CoercibleTo(OutputForm)

AbelianMonoid