DivisionRing

catdef.spad line 312 [edit on github]

A division ring (sometimes called a skew field), i.e. a not necessarily commutative ring where all non-zero elements have multiplicative inverses.

* : (%, %) -> %

from Magma

* : (%, Fraction(Integer)) -> %

from RightModule(Fraction(Integer))

* : (Fraction(Integer), %) -> %

from LeftModule(Fraction(Integer))

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

0 : () -> %

from AbelianMonoid

1 : () -> %

from MagmaWithUnit

= : (%, %) -> Boolean

from BasicType

^ : (%, Integer) -> %

x^n returns x raised to the integer power n.

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

annihilate? : (%, %) -> Boolean

from Rng

antiCommutator : (%, %) -> %

from NonAssociativeSemiRng

associates? : (%, %) -> Boolean

from EntireRing

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

from NonAssociativeRng

characteristic : () -> NonNegativeInteger

from NonAssociativeRing

coerce : Fraction(Integer) -> %

from Algebra(Fraction(Integer))

coerce : Integer -> %

from NonAssociativeRing

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

commutator : (%, %) -> %

from NonAssociativeRng

exquo : (%, %) -> Union(%, "failed")

from EntireRing

inv : % -> %

inv x returns the multiplicative inverse of x. Error: if x is 0.

latex : % -> String

from SetCategory

leftPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower : (%, PositiveInteger) -> %

from Magma

leftRecip : % -> Union(%, "failed")

from MagmaWithUnit

one? : % -> Boolean

from MagmaWithUnit

opposite? : (%, %) -> Boolean

from AbelianMonoid

plenaryPower : (%, PositiveInteger) -> %

from NonAssociativeAlgebra(Fraction(Integer))

recip : % -> Union(%, "failed")

from MagmaWithUnit

rightPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower : (%, PositiveInteger) -> %

from Magma

rightRecip : % -> Union(%, "failed")

from MagmaWithUnit

sample : () -> %

from AbelianMonoid

subtractIfCan : (%, %) -> Union(%, "failed")

from CancellationAbelianMonoid

unit? : % -> Boolean

from EntireRing

unitCanonical : % -> %

from EntireRing

unitNormal : % -> Record(unit : %, canonical : %, associate : %)

from EntireRing

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

RightModule(%)

EntireRing

Monoid

noZeroDivisors

RightModule(Fraction(Integer))

CancellationAbelianMonoid

TwoSidedRecip

NonAssociativeRing

Ring

BasicType

unitsKnown

BiModule(Fraction(Integer), Fraction(Integer))

Rng

Magma

NonAssociativeSemiRng

SemiRing

LeftModule(Fraction(Integer))

Module(Fraction(Integer))

AbelianSemiGroup

SetCategory

Algebra(Fraction(Integer))

AbelianGroup

LeftModule(%)

SemiGroup

AbelianMonoid

BiModule(%, %)

NonAssociativeRng

NonAssociativeAlgebra(Fraction(Integer))

MagmaWithUnit

CoercibleTo(OutputForm)

SemiRng

NonAssociativeSemiRing