LocalAlgebra(A, R)ΒΆ

fraction.spad line 62

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

0: %
from AbelianMonoid
1: %
from MagmaWithUnit
*: (%, %) -> %
from Magma
*: (%, 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: (%, %) -> %
from NonAssociativeSemiRng
associator: (%, %, %) -> %
from NonAssociativeRng
characteristic: () -> NonNegativeInteger
from NonAssociativeRing
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: Integer -> %
from NonAssociativeRing
coerce: R -> %
from Algebra R
commutator: (%, %) -> %
from NonAssociativeRng
denom: % -> R
denom x returns the denominator of x.
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
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
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)
from CancellationAbelianMonoid
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra R

BasicType

BiModule(%, %)

BiModule(R, R)

CancellationAbelianMonoid

CharacteristicZero if A has OrderedRing

CoercibleTo OutputForm

Comparable if A has OrderedRing

LeftModule %

LeftModule R

Magma

MagmaWithUnit

Module R

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

OrderedAbelianGroup if A has OrderedRing

OrderedAbelianMonoid if A has OrderedRing

OrderedAbelianSemiGroup if A has OrderedRing

OrderedCancellationAbelianMonoid if A has OrderedRing

OrderedRing if A has OrderedRing

OrderedSet if A has OrderedRing

PartialOrder if A has OrderedRing

RightModule %

RightModule R

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown