GeneralQuaternion(R, p, q)ΒΆ
quat.spad line 174 [edit on github]
p: R
q: R
GeneralQuaternion implements general quaternions over a commutative ring. The main constructor function is quatern which takes 4 arguments: the real part, the i imaginary part, the j imaginary part and the k imaginary part.
- 0: %
from AbelianMonoid
- 1: %
from MagmaWithUnit
- *: (%, %) -> %
from Magma
- *: (%, Fraction Integer) -> % if R has Field
from RightModule Fraction Integer
- *: (%, Integer) -> % if R has LinearlyExplicitOver Integer
from RightModule Integer
- *: (%, R) -> %
from RightModule R
- *: (Fraction Integer, %) -> % if R has Field
from LeftModule Fraction Integer
- *: (Integer, %) -> %
from AbelianGroup
- *: (NonNegativeInteger, %) -> %
from AbelianMonoid
- *: (PositiveInteger, %) -> %
from AbelianSemiGroup
- *: (R, %) -> %
from LeftModule R
- +: (%, %) -> %
from AbelianSemiGroup
- -: % -> %
from AbelianGroup
- -: (%, %) -> %
from AbelianGroup
- <=: (%, %) -> Boolean if R has OrderedSet
from PartialOrder
- <: (%, %) -> Boolean if R has OrderedSet
from PartialOrder
- >=: (%, %) -> Boolean if R has OrderedSet
from PartialOrder
- >: (%, %) -> Boolean if R has OrderedSet
from PartialOrder
- ^: (%, Integer) -> % if R has Field
from DivisionRing
- ^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- ^: (%, PositiveInteger) -> %
from Magma
- abs: % -> R if R has RealNumberSystem
from QuaternionCategory R
- annihilate?: (%, %) -> Boolean
from Rng
- antiCommutator: (%, %) -> %
- associates?: (%, %) -> Boolean if R has EntireRing
from EntireRing
- associator: (%, %, %) -> %
from NonAssociativeRng
- characteristic: () -> NonNegativeInteger
from NonAssociativeRing
- charthRoot: % -> Union(%, failed) if R has CharacteristicNonZero
- coerce: % -> OutputForm
from CoercibleTo OutputForm
- coerce: Fraction Integer -> % if R has Field or R has RetractableTo Fraction Integer
- coerce: Integer -> %
from NonAssociativeRing
- coerce: R -> %
from Algebra R
- commutator: (%, %) -> %
from NonAssociativeRng
- conjugate: % -> %
from QuaternionCategory R
- convert: % -> InputForm if R has ConvertibleTo InputForm
from ConvertibleTo InputForm
- D: % -> % if R has DifferentialRing
from DifferentialRing
- D: (%, List Symbol) -> % if R has PartialDifferentialRing Symbol
- D: (%, List Symbol, List NonNegativeInteger) -> % if R has PartialDifferentialRing Symbol
- D: (%, NonNegativeInteger) -> % if R has DifferentialRing
from DifferentialRing
- D: (%, R -> R) -> %
from DifferentialExtension R
- D: (%, R -> R, NonNegativeInteger) -> %
from DifferentialExtension R
- D: (%, Symbol) -> % if R has PartialDifferentialRing Symbol
- D: (%, Symbol, NonNegativeInteger) -> % if R has PartialDifferentialRing Symbol
- differentiate: % -> % if R has DifferentialRing
from DifferentialRing
- differentiate: (%, List Symbol) -> % if R has PartialDifferentialRing Symbol
- differentiate: (%, List Symbol, List NonNegativeInteger) -> % if R has PartialDifferentialRing Symbol
- differentiate: (%, NonNegativeInteger) -> % if R has DifferentialRing
from DifferentialRing
- differentiate: (%, R -> R) -> %
from DifferentialExtension R
- differentiate: (%, R -> R, NonNegativeInteger) -> %
from DifferentialExtension R
- differentiate: (%, Symbol) -> % if R has PartialDifferentialRing Symbol
- differentiate: (%, Symbol, NonNegativeInteger) -> % if R has PartialDifferentialRing Symbol
- eval: (%, Equation R) -> % if R has Evalable R
from Evalable R
- eval: (%, List Equation R) -> % if R has Evalable R
from Evalable R
- eval: (%, List R, List R) -> % if R has Evalable R
from InnerEvalable(R, R)
- eval: (%, List Symbol, List R) -> % if R has InnerEvalable(Symbol, R)
from InnerEvalable(Symbol, R)
- eval: (%, R, R) -> % if R has Evalable R
from InnerEvalable(R, R)
- eval: (%, Symbol, R) -> % if R has InnerEvalable(Symbol, R)
from InnerEvalable(Symbol, R)
- exquo: (%, %) -> Union(%, failed) if R has EntireRing
from EntireRing
- imagI: % -> R
from QuaternionCategory R
- imagJ: % -> R
from QuaternionCategory R
- imagK: % -> R
from QuaternionCategory R
- inv: % -> % if R has Field
from DivisionRing
- latex: % -> String
from SetCategory
- leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- leftPower: (%, PositiveInteger) -> %
from Magma
- leftRecip: % -> Union(%, failed)
from MagmaWithUnit
- map: (R -> R, %) -> %
from FullyEvalableOver R
- max: (%, %) -> % if R has OrderedSet
from OrderedSet
- min: (%, %) -> % if R has OrderedSet
from OrderedSet
- norm: % -> R
from QuaternionCategory R
- one?: % -> Boolean
from MagmaWithUnit
- opposite?: (%, %) -> Boolean
from AbelianMonoid
- plenaryPower: (%, PositiveInteger) -> %
from NonAssociativeAlgebra R
- quatern: (R, R, R, R) -> %
from QuaternionCategory R
- rational?: % -> Boolean if R has IntegerNumberSystem
from QuaternionCategory R
- rational: % -> Fraction Integer if R has IntegerNumberSystem
from QuaternionCategory R
- rationalIfCan: % -> Union(Fraction Integer, failed) if R has IntegerNumberSystem
from QuaternionCategory R
- real: % -> R
from QuaternionCategory R
- recip: % -> Union(%, failed)
from MagmaWithUnit
- reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix Integer, vec: Vector Integer) if R has LinearlyExplicitOver Integer
- reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix R, vec: Vector R)
from LinearlyExplicitOver R
- reducedSystem: Matrix % -> Matrix Integer if R has LinearlyExplicitOver Integer
- reducedSystem: Matrix % -> Matrix R
from LinearlyExplicitOver R
- retract: % -> Fraction Integer if R has RetractableTo Fraction Integer
from RetractableTo Fraction Integer
- retract: % -> Integer if R has RetractableTo Integer
from RetractableTo Integer
- retract: % -> R
from RetractableTo R
- retractIfCan: % -> Union(Fraction Integer, failed) if R has RetractableTo Fraction Integer
from RetractableTo Fraction Integer
- retractIfCan: % -> Union(Integer, failed) if R has RetractableTo Integer
from RetractableTo Integer
- retractIfCan: % -> Union(R, failed)
from RetractableTo R
- rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- rightPower: (%, PositiveInteger) -> %
from Magma
- rightRecip: % -> Union(%, failed)
from MagmaWithUnit
- sample: %
from AbelianMonoid
- smaller?: (%, %) -> Boolean if R has OrderedSet
from Comparable
- subtractIfCan: (%, %) -> Union(%, failed)
- unit?: % -> Boolean if R has EntireRing
from EntireRing
- unitCanonical: % -> % if R has EntireRing
from EntireRing
- unitNormal: % -> Record(unit: %, canonical: %, associate: %) if R has EntireRing
from EntireRing
- zero?: % -> Boolean
from AbelianMonoid
Algebra Fraction Integer if R has Field
Algebra R
BiModule(%, %)
BiModule(Fraction Integer, Fraction Integer) if R has Field
BiModule(R, R)
CharacteristicNonZero if R has CharacteristicNonZero
CharacteristicZero if R has CharacteristicZero
CoercibleFrom Fraction Integer if R has RetractableTo Fraction Integer
CoercibleFrom Integer if R has RetractableTo Integer
Comparable if R has OrderedSet
ConvertibleTo InputForm if R has ConvertibleTo InputForm
DifferentialRing if R has DifferentialRing
DivisionRing if R has Field
Eltable(R, %) if R has Eltable(R, R)
EntireRing if R has EntireRing
Evalable R if R has Evalable R
InnerEvalable(R, R) if R has Evalable R
InnerEvalable(Symbol, R) if R has InnerEvalable(Symbol, R)
LeftModule Fraction Integer if R has Field
LinearlyExplicitOver Integer if R has LinearlyExplicitOver Integer
Module Fraction Integer if R has Field
Module R
NonAssociativeAlgebra Fraction Integer if R has Field
noZeroDivisors if R has EntireRing
OrderedSet if R has OrderedSet
PartialDifferentialRing Symbol if R has PartialDifferentialRing Symbol
PartialOrder if R has OrderedSet
RetractableTo Fraction Integer if R has RetractableTo Fraction Integer
RetractableTo Integer if R has RetractableTo Integer
RightModule Fraction Integer if R has Field
RightModule Integer if R has LinearlyExplicitOver Integer
TwoSidedRecip if R has Field