# TensorPowerCategory(n, R, M)ΒΆ

tensor.spad line 275 [edit on github]

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

- ^: (%, NonNegativeInteger) -> % if M has Algebra R
from MagmaWithUnit

- ^: (%, PositiveInteger) -> % if M has Algebra R
from Magma

- annihilate?: (%, %) -> Boolean if M has Algebra R
from Rng

- antiCommutator: (%, %) -> % if M has Algebra R

- 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

- 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

- plenaryPower: (%, PositiveInteger) -> % if M has Algebra R
from NonAssociativeAlgebra R

- 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)

- 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

NonAssociativeAlgebra R if M has Algebra 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