Localize(M, R)

fraction.spad line 1 [edit on github]

• M : Module(R)
• R : CommutativeRing

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

* : (%, R) -> %

from RightModule(R)

* : (R, %) -> %

from LeftModule(R)

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

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.

0 : () -> %

from AbelianMonoid

< : (%, %) -> 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

coerce : % -> OutputForm

from CoercibleTo(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")

from CancellationAbelianMonoid

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

LeftModule(R)

BiModule(R, R)

PartialOrder

OrderedCancellationAbelianMonoid

CancellationAbelianMonoid

OrderedAbelianSemiGroup

CoercibleTo(OutputForm)

OrderedSet

Module(R)

AbelianGroup

AbelianSemiGroup

SetCategory

Comparable

AbelianMonoid

OrderedAbelianMonoid

BasicType

RightModule(R)

OrderedAbelianGroup