LocalAlgebra(A, R)

fraction.spad line 55 [edit on github]

• A: Algebra R

• R: CommutativeRing

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.

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

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)

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

NonAssociativeAlgebra R

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