TensorProduct(R, B1, B2, M1, M2)

tensor.spad line 76 [edit on github]

• R : CommutativeRing
• B1 : OrderedSet
• B2 : OrderedSet
• M1 : FreeModuleCategory(R, B1)
• M2 : FreeModuleCategory(R, B2)

Tensor product of free modules over a commutative ring. It is represented as a free module over the direct product of the respective bases. The factor domains must provide operations listOfTerms, whose result is assumed to be stored in reverse order.

* : (%, %) -> % if M1 has Algebra(R) and M2 has Algebra(R) or M2 has NonAssociativeAlgebra(R) and M1 has NonAssociativeAlgebra(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 M1 has Algebra(R) and M2 has Algebra(R) or M2 has CommutativeRing and M2 has NonAssociativeAlgebra(R) and M1 has CommutativeRing and M1 has NonAssociativeAlgebra(R)

from MagmaWithUnit

= : (%, %) -> Boolean

from BasicType

^ : (%, NonNegativeInteger) -> % if M1 has Algebra(R) and M2 has Algebra(R) or M2 has CommutativeRing and M2 has NonAssociativeAlgebra(R) and M1 has CommutativeRing and M1 has NonAssociativeAlgebra(R)

from MagmaWithUnit

^ : (%, PositiveInteger) -> % if M1 has Algebra(R) and M2 has Algebra(R) or M2 has NonAssociativeAlgebra(R) and M1 has NonAssociativeAlgebra(R)

from Magma

annihilate? : (%, %) -> Boolean if M1 has Algebra(R) and M2 has Algebra(R) or M2 has CommutativeRing and M2 has NonAssociativeAlgebra(R) and M1 has CommutativeRing and M1 has NonAssociativeAlgebra(R)

from Rng

antiCommutator : (%, %) -> % if M1 has Algebra(R) and M2 has Algebra(R) or M2 has NonAssociativeAlgebra(R) and M1 has NonAssociativeAlgebra(R)

from NonAssociativeSemiRng

associator : (%, %, %) -> % if M1 has Algebra(R) and M2 has Algebra(R) or M2 has NonAssociativeAlgebra(R) and M1 has NonAssociativeAlgebra(R)

from NonAssociativeRng

characteristic : () -> NonNegativeInteger if M1 has Algebra(R) and M2 has Algebra(R) or M2 has CommutativeRing and M2 has NonAssociativeAlgebra(R) and M1 has CommutativeRing and M1 has NonAssociativeAlgebra(R)

from NonAssociativeRing

coefficient : (%, Product(B1, B2)) -> R

from FreeModuleCategory(R, Product(B1, B2))

coefficients : % -> List(R)

from FreeModuleCategory(R, Product(B1, B2))

coerce : % -> % if M2 has CommutativeRing and M2 has NonAssociativeAlgebra(R) and M1 has CommutativeRing and M1 has NonAssociativeAlgebra(R)

from Algebra(%)

coerce : R -> % if M1 has Algebra(R) and M2 has Algebra(R)

from Algebra(R)

coerce : Integer -> % if M1 has Algebra(R) and M2 has Algebra(R) or M2 has CommutativeRing and M2 has NonAssociativeAlgebra(R) and M1 has CommutativeRing and M1 has NonAssociativeAlgebra(R)

from NonAssociativeRing

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

commutator : (%, %) -> % if M1 has Algebra(R) and M2 has Algebra(R) or M2 has NonAssociativeAlgebra(R) and M1 has NonAssociativeAlgebra(R)

from NonAssociativeRng

construct : List(Record(k : Product(B1, B2), c : R)) -> %

from IndexedProductCategory(R, Product(B1, B2))

constructOrdered : List(Record(k : Product(B1, B2), c : R)) -> % if Product(B1, B2) has Comparable

from IndexedProductCategory(R, Product(B1, B2))

latex : % -> String

from SetCategory

leadingCoefficient : % -> R if Product(B1, B2) has Comparable

from IndexedProductCategory(R, Product(B1, B2))

leadingMonomial : % -> % if Product(B1, B2) has Comparable

from IndexedProductCategory(R, Product(B1, B2))

leadingSupport : % -> Product(B1, B2) if Product(B1, B2) has Comparable

from IndexedProductCategory(R, Product(B1, B2))

leadingTerm : % -> Record(k : Product(B1, B2), c : R) if Product(B1, B2) has Comparable

from IndexedProductCategory(R, Product(B1, B2))

leftPower : (%, NonNegativeInteger) -> % if M1 has Algebra(R) and M2 has Algebra(R) or M2 has CommutativeRing and M2 has NonAssociativeAlgebra(R) and M1 has CommutativeRing and M1 has NonAssociativeAlgebra(R)

from MagmaWithUnit

leftPower : (%, PositiveInteger) -> % if M1 has Algebra(R) and M2 has Algebra(R) or M2 has NonAssociativeAlgebra(R) and M1 has NonAssociativeAlgebra(R)

from Magma

leftRecip : % -> Union(%, "failed") if M1 has Algebra(R) and M2 has Algebra(R) or M2 has CommutativeRing and M2 has NonAssociativeAlgebra(R) and M1 has CommutativeRing and M1 has NonAssociativeAlgebra(R)

from MagmaWithUnit

linearExtend : (Mapping(R, Product(B1, B2)), %) -> R

from FreeModuleCategory(R, Product(B1, B2))

listOfTerms : % -> List(Record(k : Product(B1, B2), c : R))

from IndexedDirectProductCategory(R, Product(B1, B2))

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

from IndexedProductCategory(R, Product(B1, B2))

monomial : (R, Product(B1, B2)) -> %

from IndexedProductCategory(R, Product(B1, B2))

monomial? : % -> Boolean

from IndexedProductCategory(R, Product(B1, B2))

monomials : % -> List(%)

from FreeModuleCategory(R, Product(B1, B2))

numberOfMonomials : % -> NonNegativeInteger

from IndexedDirectProductCategory(R, Product(B1, B2))

one? : % -> Boolean if M1 has Algebra(R) and M2 has Algebra(R) or M2 has CommutativeRing and M2 has NonAssociativeAlgebra(R) and M1 has CommutativeRing and M1 has NonAssociativeAlgebra(R)

from MagmaWithUnit

opposite? : (%, %) -> Boolean

from AbelianMonoid

plenaryPower : (%, PositiveInteger) -> % if M1 has Algebra(R) and M2 has Algebra(R) or M2 has NonAssociativeAlgebra(R) and M1 has NonAssociativeAlgebra(R)

from NonAssociativeAlgebra(R)

recip : % -> Union(%, "failed") if M1 has Algebra(R) and M2 has Algebra(R) or M2 has CommutativeRing and M2 has NonAssociativeAlgebra(R) and M1 has CommutativeRing and M1 has NonAssociativeAlgebra(R)

from MagmaWithUnit

reductum : % -> % if Product(B1, B2) has Comparable

from IndexedProductCategory(R, Product(B1, B2))

rightPower : (%, NonNegativeInteger) -> % if M1 has Algebra(R) and M2 has Algebra(R) or M2 has CommutativeRing and M2 has NonAssociativeAlgebra(R) and M1 has CommutativeRing and M1 has NonAssociativeAlgebra(R)

from MagmaWithUnit

rightPower : (%, PositiveInteger) -> % if M1 has Algebra(R) and M2 has Algebra(R) or M2 has NonAssociativeAlgebra(R) and M1 has NonAssociativeAlgebra(R)

from Magma

rightRecip : % -> Union(%, "failed") if M1 has Algebra(R) and M2 has Algebra(R) or M2 has CommutativeRing and M2 has NonAssociativeAlgebra(R) and M1 has CommutativeRing and M1 has NonAssociativeAlgebra(R)

from MagmaWithUnit

sample : () -> %

from AbelianMonoid

smaller? : (%, %) -> Boolean if Product(B1, B2) has Comparable and R has Comparable

from Comparable

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

from CancellationAbelianMonoid

support : % -> List(Product(B1, B2))

from FreeModuleCategory(R, Product(B1, B2))

tensor : (M1, M2) -> %

from TensorProductCategory(R, M1, M2)

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

Comparable

Algebra(R)

RightModule(%)

Monoid

Algebra(%)

AbelianMonoid

BiModule(R, R)

NonAssociativeAlgebra(R)

CancellationAbelianMonoid

FreeModuleCategory(R, Product(B1, B2))

MagmaWithUnit

NonAssociativeRing

AbelianGroup

LeftModule(%)

IndexedDirectProductCategory(R, Product(B1, B2))

LeftModule(R)

CommutativeStar

Module(%)

TensorProductCategory(R, M1, M2)

SetCategory

Rng

IndexedProductCategory(R, Product(B1, B2))

CommutativeRing

TwoSidedRecip

Magma

SemiGroup

BiModule(%, %)

unitsKnown

CoercibleTo(OutputForm)

AbelianSemiGroup

NonAssociativeSemiRing

AbelianProductCategory(R)

NonAssociativeAlgebra(%)

Module(R)

RightModule(R)

NonAssociativeRng

Ring

SemiRng

NonAssociativeSemiRng

BasicType

SemiRing