TensorPowerCategory(n, R, M)ΒΆ

tensor.spad line 267

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

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

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