TensorPowerCategory(n, R, M)ΒΆ

tensor.spad line 275 [edit on github]

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

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)

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

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra R if M has Algebra R

BasicType

BiModule(%, %) if M has Algebra R

BiModule(R, R)

CancellationAbelianMonoid

CoercibleTo OutputForm

LeftModule % if M has Algebra R

LeftModule R

Magma if M has Algebra R

MagmaWithUnit if M has Algebra R

Module R

Monoid if M has Algebra 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

RightModule R

Ring if M has Algebra R

Rng if M has Algebra R

SemiGroup if M has Algebra R

SemiRing if M has Algebra R

SemiRng if M has Algebra R

SetCategory

TensorProductCategory(R, M, M)

unitsKnown if M has Algebra R