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.

* : (%, %) -> %

from Magma

* : (%, R) -> %

from RightModule(R)

* : (R, %) -> %

from LeftModule(R)

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

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.

0 : () -> %

from AbelianMonoid

1 : () -> %

from MagmaWithUnit

< : (%, %) -> 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

abs : % -> % if A has OrderedRing

from OrderedRing

annihilate? : (%, %) -> Boolean

from Rng

antiCommutator : (%, %) -> %

from NonAssociativeSemiRng

associator : (%, %, %) -> %

from NonAssociativeRng

characteristic : () -> NonNegativeInteger

from NonAssociativeRing

coerce : R -> %

from Algebra(R)

coerce : Integer -> %

from NonAssociativeRing

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

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

~= : (%, %) -> Boolean

from BasicType

Comparable

OrderedAbelianSemiGroup

RightModule(%)

Monoid

Algebra(R)

AbelianMonoid

BiModule(R, R)

NonAssociativeAlgebra(R)

CancellationAbelianMonoid

OrderedSet

MagmaWithUnit

NonAssociativeRing

AbelianGroup

LeftModule(R)

LeftModule(%)

SetCategory

Rng

AbelianSemiGroup

Magma

SemiGroup

OrderedAbelianMonoid

PartialOrder

BiModule(%, %)

unitsKnown

CoercibleTo(OutputForm)

OrderedCancellationAbelianMonoid

NonAssociativeSemiRing

RightModule(R)

OrderedAbelianGroup

OrderedRing

Module(R)

NonAssociativeRng

Ring

SemiRng

NonAssociativeSemiRng

CharacteristicZero

BasicType

SemiRing