TensorPower(n, R, B, M)

tensor.spad line 310 [edit on github]

• n : NonNegativeInteger
• R : CommutativeRing
• B : OrderedSet
• M : FreeModuleCategory(R, B)

Tensor powers of a free module over a commutative ring. It is represented as a free module over the cartesian power of the basis.

* : (%, %) -> % 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

coefficient : (%, Vector(B)) -> R

from FreeModuleCategory(R, Vector(B))

coefficients : % -> List(R)

from FreeModuleCategory(R, Vector(B))

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

construct : List(Record(k : Vector(B), c : R)) -> %

from IndexedProductCategory(R, Vector(B))

constructOrdered : List(Record(k : Vector(B), c : R)) -> % if Vector(B) has Comparable

from IndexedProductCategory(R, Vector(B))

latex : % -> String

from SetCategory

leadingCoefficient : % -> R if Vector(B) has Comparable

from IndexedProductCategory(R, Vector(B))

leadingMonomial : % -> % if Vector(B) has Comparable

from IndexedProductCategory(R, Vector(B))

leadingSupport : % -> Vector(B) if Vector(B) has Comparable

from IndexedProductCategory(R, Vector(B))

leadingTerm : % -> Record(k : Vector(B), c : R) if Vector(B) has Comparable

from IndexedProductCategory(R, Vector(B))

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

linearExtend : (Mapping(R, Vector(B)), %) -> R

from FreeModuleCategory(R, Vector(B))

listOfTerms : % -> List(Record(k : Vector(B), c : R))

from IndexedDirectProductCategory(R, Vector(B))

map : (Mapping(R, R), %) -> %

from IndexedProductCategory(R, Vector(B))

monomial : (R, Vector(B)) -> %

from IndexedProductCategory(R, Vector(B))

monomial? : % -> Boolean

from IndexedProductCategory(R, Vector(B))

monomials : % -> List(%)

from FreeModuleCategory(R, Vector(B))

numberOfMonomials : % -> NonNegativeInteger

from IndexedDirectProductCategory(R, Vector(B))

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

reductum : % -> % if Vector(B) has Comparable

from IndexedProductCategory(R, Vector(B))

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

smaller? : (%, %) -> Boolean if R has Comparable and Vector(B) has Comparable

from Comparable

subtractIfCan : (%, %) -> Union(%, "failed")

from CancellationAbelianMonoid

support : % -> List(Vector(B))

from FreeModuleCategory(R, Vector(B))

tensor : (M, M) -> %

from TensorProductCategory(R, M, M)

tensor : List(B) -> %

tensor : List(M) -> %

from TensorPowerCategory(n, R, M)

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

Comparable

Algebra(R)

RightModule(%)

Monoid

IndexedProductCategory(R, Vector(B))

AbelianMonoid

BiModule(R, R)

NonAssociativeAlgebra(R)

CancellationAbelianMonoid

MagmaWithUnit

NonAssociativeRing

AbelianGroup

BiModule(%, %)

LeftModule(%)

LeftModule(R)

SetCategory

CoercibleTo(OutputForm)

TensorPowerCategory(n, R, M)

Rng

SemiGroup

Magma

FreeModuleCategory(R, Vector(B))

unitsKnown

AbelianSemiGroup

IndexedDirectProductCategory(R, Vector(B))

NonAssociativeSemiRing

AbelianProductCategory(R)

Module(R)

TensorProductCategory(R, M, M)

RightModule(R)

NonAssociativeRng

Ring

SemiRng

NonAssociativeSemiRng

BasicType

SemiRing