Algebra(R)
catdef.spad line 105
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The category of associative algebras (modules which are themselves rings).
- * : (%, %) -> %
- 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
- 0 : () -> %
- from AbelianMonoid
- 1 : () -> %
- from MagmaWithUnit
- = : (%, %) -> Boolean
- from BasicType
- ^ : (%, NonNegativeInteger) -> %
- from MagmaWithUnit
- ^ : (%, PositiveInteger) -> %
- from Magma
- annihilate? : (%, %) -> Boolean
- from Rng
- antiCommutator : (%, %) -> %
- from NonAssociativeSemiRng
- associator : (%, %, %) -> %
- from NonAssociativeRng
- characteristic : () -> NonNegativeInteger
- from NonAssociativeRing
- coerce : R -> %
coerce(r) maps the ring element r to a member of the algebra.
- 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
- one? : % -> Boolean
- from MagmaWithUnit
- opposite? : (%, %) -> Boolean
- from AbelianMonoid
- plenaryPower : (%, PositiveInteger) -> %
- from NonAssociativeAlgebra(R)
- 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
- zero? : % -> Boolean
- from AbelianMonoid
- ~= : (%, %) -> Boolean
- from BasicType
RightModule(%)
Rng
Monoid
NonAssociativeAlgebra(R)
Ring
SemiGroup
CancellationAbelianMonoid
LeftModule(%)
BasicType
unitsKnown
NonAssociativeRing
Magma
NonAssociativeSemiRng
SemiRing
LeftModule(R)
Module(R)
AbelianGroup
NonAssociativeSemiRing
SetCategory
AbelianSemiGroup
BiModule(R, R)
AbelianMonoid
BiModule(%, %)
NonAssociativeRng
MagmaWithUnit
RightModule(R)
CoercibleTo(OutputForm)
SemiRng