# TensorPowerCategory(n, R, M)ΒΆ

- n: NonNegativeInteger
- R: CommutativeRing
- M: Module R

Category of tensor powers of modules over commutative rings.

- 0: %
- from AbelianMonoid
- 1: % if M has Algebra R
- from MagmaWithUnit
- *: (%, %) -> % if M has Algebra R
- from Magma
- *: (%, R) -> %
- from RightModule R
- *: (Integer, %) -> %
- from AbelianGroup
- *: (NonNegativeInteger, %) -> %
- from AbelianMonoid
- *: (PositiveInteger, %) -> %
- from AbelianSemiGroup
- *: (R, %) -> %
- from LeftModule R
- +: (%, %) -> %
- from AbelianSemiGroup
- -: % -> %
- from AbelianGroup
- -: (%, %) -> %
- from AbelianGroup
- =: (%, %) -> Boolean
- from BasicType
- ^: (%, NonNegativeInteger) -> % if M has Algebra R
- from MagmaWithUnit
- ^: (%, PositiveInteger) -> % if M has Algebra R
- from Magma
- ~=: (%, %) -> Boolean
- from BasicType
- annihilate?: (%, %) -> Boolean if M has Algebra R
- from Rng
- antiCommutator: (%, %) -> % if M has Algebra R
- from NonAssociativeSemiRng
- associator: (%, %, %) -> % if M has Algebra R
- from NonAssociativeRng
- characteristic: () -> NonNegativeInteger if M has Algebra R
- from NonAssociativeRing
- coerce: % -> OutputForm
- from CoercibleTo OutputForm
- coerce: Integer -> % if M has Algebra R
- from NonAssociativeRing
- coerce: R -> % if M has Algebra R
- from Algebra R
- commutator: (%, %) -> % if M has Algebra R
- from NonAssociativeRng
- hash: % -> SingleInteger
- from SetCategory
- hashUpdate!: (HashState, %) -> HashState
- from SetCategory
- latex: % -> String
- from SetCategory
- leftPower: (%, NonNegativeInteger) -> % if M has Algebra R
- from MagmaWithUnit
- leftPower: (%, PositiveInteger) -> % if M has Algebra R
- from Magma
- leftRecip: % -> Union(%, failed) if M has Algebra R
- from MagmaWithUnit
- one?: % -> Boolean if M has Algebra R
- from MagmaWithUnit
- opposite?: (%, %) -> Boolean
- from AbelianMonoid
- recip: % -> Union(%, failed) if M has Algebra R
- from MagmaWithUnit
- rightPower: (%, NonNegativeInteger) -> % if M has Algebra R
- from MagmaWithUnit
- rightPower: (%, PositiveInteger) -> % if M has Algebra R
- from Magma
- rightRecip: % -> Union(%, failed) if M has Algebra R
- from MagmaWithUnit
- sample: %
- from AbelianMonoid
- subtractIfCan: (%, %) -> Union(%, failed)
- from CancellationAbelianMonoid
- tensor: (M, M) -> %
- from TensorProductCategory(R, M, M)

- tensor: List M -> %
`tensor([x1, x2, ..., xn])`

constructs the tensor product of`x1, x2, ..., xn`

.- zero?: % -> Boolean
- from AbelianMonoid

BiModule(%, %) if M has Algebra R

BiModule(R, R)

LeftModule % if M has Algebra R

MagmaWithUnit if M has Algebra R

Module R

NonAssociativeRing if M has Algebra R

NonAssociativeRng if M has Algebra R

NonAssociativeSemiRing if M has Algebra R

NonAssociativeSemiRng if M has Algebra R

RightModule % if M has Algebra R

TensorProductCategory(R, M, M)

unitsKnown if M has Algebra R