Localize(M, R)ΒΆ

fraction.spad line 1 [edit on github]

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

from CoercibleTo OutputForm

denom: % -> R

denom x returns the denominator of x.

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

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

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(R, R)

CancellationAbelianMonoid

CoercibleTo OutputForm

Comparable if M has OrderedAbelianGroup

LeftModule R

Module R

OrderedAbelianGroup if M has OrderedAbelianGroup

OrderedAbelianMonoid if M has OrderedAbelianGroup

OrderedAbelianSemiGroup if M has OrderedAbelianGroup

OrderedCancellationAbelianMonoid if M has OrderedAbelianGroup

OrderedSet if M has OrderedAbelianGroup

PartialOrder if M has OrderedAbelianGroup

RightModule R

SetCategory