# Localize(M, R)ΒΆ

Localize(`M`, `R`) produces fractions with numerators from an `R` module `M` and denominators being the nonzero elements of `R`.

0: %

from AbelianMonoid

*: (%, 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`.

/: (M, R) -> %

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

<=: (%, %) -> Boolean if M has OrderedAbelianGroup

from PartialOrder

<: (%, %) -> Boolean if M has OrderedAbelianGroup

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean if M has OrderedAbelianGroup

from PartialOrder

>: (%, %) -> Boolean if M has OrderedAbelianGroup

from PartialOrder

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm
denom: % -> R

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

latex: % -> String

from SetCategory

max: (%, %) -> % if M has OrderedAbelianGroup

from OrderedSet

min: (%, %) -> % if M has OrderedAbelianGroup

from OrderedSet

numer: % -> M

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

opposite?: (%, %) -> Boolean

from AbelianMonoid

sample: %

from AbelianMonoid

smaller?: (%, %) -> Boolean if M has OrderedAbelianGroup

from Comparable

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

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(R, R)

CancellationAbelianMonoid

Comparable if M has OrderedAbelianGroup

OrderedSet if M has OrderedAbelianGroup

PartialOrder if M has OrderedAbelianGroup

SetCategory