TensorPowerCategory(n, R, M)

tensor.spad line 275 [edit on github]

Category of tensor powers of modules over commutative rings.

* : (%, %) -> % if M has Algebra(R)
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 : () -> % if M has Algebra(R)
from MagmaWithUnit
= : (%, %) -> Boolean
from BasicType
^ : (%, 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)
from NonAssociativeSemiRng
associator : (%, %, %) -> % if M has Algebra(R)
from NonAssociativeRng
characteristic : () -> NonNegativeInteger if M has Algebra(R)
from NonAssociativeRing
coerce : R -> % if M has Algebra(R)
from Algebra(R)
coerce : Integer -> % if M has Algebra(R)
from NonAssociativeRing
coerce : % -> OutputForm
from CoercibleTo(OutputForm)
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
~= : (%, %) -> Boolean
from BasicType

RightModule(%)

Rng

Monoid

NonAssociativeAlgebra(R)

TensorProductCategory(R, M, M)

SemiGroup

CancellationAbelianMonoid

LeftModule(%)

Algebra(R)

BasicType

unitsKnown

NonAssociativeRing

Magma

NonAssociativeSemiRng

SemiRing

Module(R)

AbelianGroup

NonAssociativeSemiRing

SetCategory

AbelianSemiGroup

BiModule(R, R)

AbelianMonoid

BiModule(%, %)

NonAssociativeRng

LeftModule(R)

MagmaWithUnit

RightModule(R)

CoercibleTo(OutputForm)

SemiRng

Ring