NonAssociativeRng

naalgc.spad line 142 [edit on github]

NonAssociativeRng is a basic ring-type structure, not necessarily commutative or associative, and not necessarily with unit. Axioms x*(y+z) = x*y + x*z (x+y)*z = x*z + y*z Common Additional Axioms noZeroDivisorsab = 0 => a=0 or b=0

* : (%, %) -> %

from Magma

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

0 : () -> %

from AbelianMonoid

= : (%, %) -> Boolean

from BasicType

^ : (%, PositiveInteger) -> %

from Magma

antiCommutator : (%, %) -> %

from NonAssociativeSemiRng

associator : (%, %, %) -> %

associator(a, b, c) returns (a*b)*c-a*(b*c).

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

commutator : (%, %) -> %

commutator(a, b) returns a*b-b*a.

latex : % -> String

from SetCategory

leftPower : (%, PositiveInteger) -> %

from Magma

opposite? : (%, %) -> Boolean

from AbelianMonoid

rightPower : (%, PositiveInteger) -> %

from Magma

sample : () -> %

from AbelianMonoid

subtractIfCan : (%, %) -> Union(%, "failed")

from CancellationAbelianMonoid

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

CancellationAbelianMonoid

CoercibleTo(OutputForm)

AbelianMonoid

AbelianGroup

AbelianSemiGroup

SetCategory

Magma

NonAssociativeSemiRng

BasicType