# LocalAlgebra(A, R)ΒΆ

LocalAlgebra produces the localization of an algebra, i.e. fractions whose numerators come from some `R` algebra.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from LeftModule %

*: (%, R) -> %

from RightModule R

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

*: (R, %) -> %

from LeftModule R

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, R) -> %

`x / d` divides the element `x` by `d`.

/: (A, R) -> %

`a / d` divides the element `a` by `d`.

<=: (%, %) -> Boolean if A has OrderedRing

from PartialOrder

<: (%, %) -> Boolean if A has OrderedRing

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean if A has OrderedRing

from PartialOrder

>: (%, %) -> Boolean if A has OrderedRing

from PartialOrder

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

abs: % -> % if A has OrderedRing

from OrderedRing

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %
associator: (%, %, %) -> %
characteristic: () -> NonNegativeInteger
coerce: % -> OutputForm
coerce: Integer -> %
coerce: R -> %

from Algebra R

commutator: (%, %) -> %
denom: % -> R

`denom x` returns the denominator of `x`.

latex: % -> String

from SetCategory

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

max: (%, %) -> % if A has OrderedRing

from OrderedSet

min: (%, %) -> % if A has OrderedRing

from OrderedSet

negative?: % -> Boolean if A has OrderedRing

from OrderedRing

numer: % -> A

`numer x` returns the numerator of `x`.

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

plenaryPower: (%, PositiveInteger) -> %
positive?: % -> Boolean if A has OrderedRing

from OrderedRing

recip: % -> Union(%, failed)

from MagmaWithUnit

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sign: % -> Integer if A has OrderedRing

from OrderedRing

smaller?: (%, %) -> Boolean if A has OrderedRing

from Comparable

subtractIfCan: (%, %) -> Union(%, failed)
zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(%, %)

BiModule(R, R)

CancellationAbelianMonoid

CharacteristicZero if A has OrderedRing

Comparable if A has OrderedRing

Magma

MagmaWithUnit

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

OrderedAbelianGroup if A has OrderedRing

OrderedAbelianMonoid if A has OrderedRing

OrderedRing if A has OrderedRing

OrderedSet if A has OrderedRing

PartialOrder if A has OrderedRing

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown