OrderedRing

catdef.spad line 1055 [edit on github]

Ordered sets which are also rings, that is, domains where the ring operations are compatible with the ordering.

* : (%, %) -> %

from Magma

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

0 : () -> %

from AbelianMonoid

1 : () -> %

from MagmaWithUnit

< : (%, %) -> Boolean

from PartialOrder

<= : (%, %) -> Boolean

from PartialOrder

= : (%, %) -> Boolean

from BasicType

> : (%, %) -> Boolean

from PartialOrder

>= : (%, %) -> Boolean

from PartialOrder

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

abs : % -> %

abs(x) returns the absolute value of x.

annihilate? : (%, %) -> Boolean

from Rng

antiCommutator : (%, %) -> %

from NonAssociativeSemiRng

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

from NonAssociativeRng

characteristic : () -> NonNegativeInteger

from NonAssociativeRing

coerce : Integer -> %

from NonAssociativeRing

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

commutator : (%, %) -> %

from NonAssociativeRng

latex : % -> String

from SetCategory

leftPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower : (%, PositiveInteger) -> %

from Magma

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

from MagmaWithUnit

max : (%, %) -> %

from OrderedSet

min : (%, %) -> %

from OrderedSet

negative? : % -> Boolean

negative?(x) tests whether x is strictly less than 0.

one? : % -> Boolean

from MagmaWithUnit

opposite? : (%, %) -> Boolean

from AbelianMonoid

positive? : % -> Boolean

positive?(x) tests whether x is strictly greater than 0.

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

from MagmaWithUnit

rightPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower : (%, PositiveInteger) -> %

from Magma

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

from MagmaWithUnit

sample : () -> %

from AbelianMonoid

sign : % -> Integer

sign(x) is 1 if x is positive, -1 if x is negative, 0 if x equals 0.

smaller? : (%, %) -> Boolean

from Comparable

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

from CancellationAbelianMonoid

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

Rng

Monoid

MagmaWithUnit

CharacteristicZero

OrderedCancellationAbelianMonoid

CancellationAbelianMonoid

LeftModule(%)

OrderedAbelianSemiGroup

Ring

unitsKnown

RightModule(%)

SemiRing

NonAssociativeRing

CoercibleTo(OutputForm)

OrderedSet

AbelianGroup

AbelianSemiGroup

SetCategory

Comparable

SemiGroup

AbelianMonoid

OrderedAbelianMonoid

NonAssociativeSemiRng

PartialOrder

BasicType

BiModule(%, %)

NonAssociativeSemiRing

Magma

SemiRng

NonAssociativeRng

OrderedAbelianGroup