LocalAlgebra(A, R)ΒΆ
fraction.spad line 55 [edit on github]
A: Algebra R
LocalAlgebra produces the localization of an algebra, i.e. fractions whose numerators come from some R
algebra.
- 0: %
from AbelianMonoid
- 1: %
from MagmaWithUnit
- *: (%, %) -> %
from LeftModule %
- *: (%, 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 elementx
byd
.
- /: (A, R) -> %
a / d
divides the elementa
byd
.
- <=: (%, %) -> Boolean if A has OrderedRing
from PartialOrder
- <: (%, %) -> Boolean if A has OrderedRing
from PartialOrder
- >=: (%, %) -> Boolean if A has OrderedRing
from PartialOrder
- >: (%, %) -> Boolean if A has OrderedRing
from PartialOrder
- ^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- ^: (%, PositiveInteger) -> %
from Magma
- abs: % -> % if A has OrderedRing
from OrderedRing
- annihilate?: (%, %) -> Boolean
from Rng
- antiCommutator: (%, %) -> %
- 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 ofx
.
- 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 ofx
.
- one?: % -> Boolean
from MagmaWithUnit
- opposite?: (%, %) -> Boolean
from AbelianMonoid
- plenaryPower: (%, PositiveInteger) -> %
from NonAssociativeAlgebra R
- 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)
- zero?: % -> Boolean
from AbelianMonoid
Algebra R
BiModule(%, %)
BiModule(R, R)
CharacteristicZero if A has OrderedRing
Comparable if A has OrderedRing
Module R
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