Localize(M, R)ΒΆ

fraction.spad line 1

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