OrderedIntegralDomainΒΆ
catdef.spad line 1021 [edit on github]
The category of ordered commutative integral domains, where ordering and the arithmetic operations are compatible.
- 0: %
from AbelianMonoid
- 1: %
from MagmaWithUnit
- *: (%, %) -> %
from Magma
- *: (Integer, %) -> %
from AbelianGroup
- *: (NonNegativeInteger, %) -> %
from AbelianMonoid
- *: (PositiveInteger, %) -> %
from AbelianSemiGroup
- +: (%, %) -> %
from AbelianSemiGroup
- -: % -> %
from AbelianGroup
- -: (%, %) -> %
from AbelianGroup
- <=: (%, %) -> Boolean
from PartialOrder
- <: (%, %) -> Boolean
from PartialOrder
- >=: (%, %) -> Boolean
from PartialOrder
- >: (%, %) -> Boolean
from PartialOrder
- ^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- ^: (%, PositiveInteger) -> %
from Magma
- abs: % -> %
from OrderedRing
- annihilate?: (%, %) -> Boolean
from Rng
- antiCommutator: (%, %) -> %
- associates?: (%, %) -> Boolean
from EntireRing
- associator: (%, %, %) -> %
from NonAssociativeRng
- characteristic: () -> NonNegativeInteger
from NonAssociativeRing
- coerce: % -> %
from Algebra %
- coerce: % -> OutputForm
from CoercibleTo OutputForm
- coerce: Integer -> %
from NonAssociativeRing
- commutator: (%, %) -> %
from NonAssociativeRng
- exquo: (%, %) -> Union(%, failed)
from EntireRing
- 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
from OrderedRing
- one?: % -> Boolean
from MagmaWithUnit
- opposite?: (%, %) -> Boolean
from AbelianMonoid
- plenaryPower: (%, PositiveInteger) -> %
from NonAssociativeAlgebra %
- positive?: % -> Boolean
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
from OrderedRing
- smaller?: (%, %) -> Boolean
from Comparable
- subtractIfCan: (%, %) -> Union(%, failed)
- unit?: % -> Boolean
from EntireRing
- unitCanonical: % -> %
from EntireRing
- unitNormal: % -> Record(unit: %, canonical: %, associate: %)
from EntireRing
- zero?: % -> Boolean
from AbelianMonoid
Algebra %
BiModule(%, %)
Module %