- Introduction
- Tensors
- Creating Tensors
- Black-box Tensors
- Tensors with Structure Constant Sequences
- Bilinear Tensors
- Tensors from Algebraic Objects
- Tensor(A): Alg -> TenSpcElt, Map
- Example Multilinear_D4LieAlgebra (H62E11)
- Tensor(Q) : RngUPolRes -> TenSpcElt, Map
- Example Multilinear_WittAlgebra (H62E12)
- CommutatorTensor(A) : Alg -> TenSpcElt, Map
- Example Multilinear_CommutatorFromAlgebra (H62E13)
- Example Multilinear_MatrixJordanAlgebra (H62E14)
- AssociatorTensor(A) : Alg -> TenSpcElt, Map
- Example Multilinear_AssociatorFromAlgebra (H62E15)
- pCentralTensor(G, p, s, t) : Grp, RngIntElt, RngIntElt, RngIntElt -> TenSpcElt, List
- Example Multilinear_TensorPGroup (H62E16)
- MatrixTensor(K, S) : Fld, [RngIntElt] -> TenSpcElt, List
- Polarisation(f) : MPolElt -> TenSpcElt, MPolElt
- Example Multilinear_TensorPolarization (H62E17)
- New Tensors from Old
- Operations with Tensors
- Elementary Operations
- General Properties
- Tensors As Multilinear Maps
- Operations with Bilinear Maps
- x * T : Any, TenSpcElt -> Any
- x * T : Any, TenSpc -> Any
- Example Multilinear_BimapInfix (H62E31)
- x * y : BmpUElt, BmpVElt -> Any
- LeftDomain(B) : TenSpcElt -> BmpU
- RightDomain(B) : TenSpcElt -> BmpV
- IsCoercible(U,x) : BmpU, Any -> BoolElt, BmpUElt
- Example Multilinear_BimapProduct (H62E32)
- Parent(x) : BmpUElt -> BmpU
- Parent(X) : BmpU -> TenSpcElt
- u1 eq u2 : BmpUElt, BmpUElt -> BoolElt
- v1 eq v2 : BmpUElt, BmpUElt -> BoolElt
- U1 eq U2 : BmpU, BmpU -> BoolElt
- V1 eq V2 : BmpV, BmpV -> BoolElt
- Example Multilinear_BimapProduct2 (H62E33)
- Manipulating Tensor Data
- Slice(T, grid) : TenSpcElt, [SetEnum] -> SeqEnum
- Example Multilinear_TensorSlicing (H62E34)
- SliceAsMatrices(T, grid, a, b) : TenSpcElt, [SetEnum], RngIntElt, RngIntElt -> SeqEnum
- Example Multilinear_SliceAsMatrices (H62E35)
- Foliation(T, i) : TenSpcElt, RngIntElt -> Mtrx
- Example Multilinear_ExfoliateFoliation (H62E36)
- AsTensorSpace(T, i) : TenSpcElt, RngIntElt -> TenSpc, Mtrx
- AsCotensorSpace(T) : TenSpcElt -> TenSpc, Mtrx
- Example Multilinear_TensorsToSpaces (H62E37)
- AsTensor(S) : TenSpc -> TenSpcElt
- Example Multilinear_SpacesToTensors (H62E38)
- Invariants of Tensors
- Exporting Tensors
- Tensor Spaces
- Constructions of Tensor and Cotensor Spaces
- Operations on Tensor Spaces
- Membership and Comparison with Tensor Spaces
- T in TS : TenSpcElt, TenSpc -> BoolElt
- TS ! T : TenSpc, TenSpcElt -> TenSpcElt
- TS ! S : TenSpc, SeqEnum -> TenSpcElt
- T ! n : TenSpc, RngIntElt -> TenSpcElt
- IsCoercible(TS, x) : TenSpc, Any -> BoolElt, TenSpcElt
- Example Multilinear_Coercion (H62E53)
- S eq T : TenSpc, TenSpc -> BoolElt
- S subset T : TenSpc, TenSpc -> BoolElt
- IsCoercible(T, S) : TenSpc, Any -> BoolElt
- Example Multilinear_TenSpcContainment (H62E54)
- Tensor Spaces as Modules
- Basis(T) : TenSpc -> SeqEnum
- T . i : TenSpc, RngIntElt -> TenSpcElt
- NumberOfGenerators(T) : TenSpc -> RngIntElt
- Dimension(T) : TenSpc -> RngIntElt
- # T : TenSpc -> RngIntElt
- Example Multilinear_BasicModule (H62E55)
- Random(T) : TenSpc -> TenSpcElt
- RandomTensor(R, S) : Rng, [RngIntElt] -> TenSpcElt
- Example Multilinear_RandomTensors (H62E56)
- RandomAlternatingTensor(R, d, n, c) : Rng, RngIntElt, RngIntElt, RngIntElt -> TenSpcElt
- RandomAntisymmetricTensor(R, d, n, c) : Rng, RngIntElt, RngIntElt, RngIntElt -> TenSpcElt
- RandomSymmetricTensor(R, d, n, c) : Rng, RngIntElt, RngIntElt, RngIntElt -> TenSpcElt
- Example Multilinear_RandomSymTen (H62E57)
- Properties of Tensor Spaces
- Tensor Categories
- Constructing Tensor Categories
- Operations on Tensor Categories
- Categorical Operations
- Categorical Operations on Tensors
- Subtensor(T, S) : TenSpcElt, List -> TenSpcElt
- Subtensor(T, D, C) : TenSpcElt, List, Any -> TenSpcElt
- IsSubtensor(T, S) : TenSpcElt, TenSpcElt -> BoolElt
- Example Multilinear_Subtensors (H62E64)
- LocalIdeal(T, S, I) : TenSpcElt, List, RngIntElt -> TenSpcElt
- LocalIdeal(T, D, C, I) : TenSpcElt, List, Any, RngIntElt -> TenSpcElt
- LocalIdeal(T, S, I) : TenSpcElt, TenSpcElt, RngIntElt -> TenSpcElt
- IsLocalIdeal(T, S, I) : TenSpcElt, TenSpcElt, RngIntElt -> BoolElt
- Example Multilinear_LocalIdeals (H62E65)
- Ideal(T, S) : TenSpcElt, List -> TenSpcElt
- Ideal(T, D, C) : TenSpcElt, List, Any -> TenSpcElt
- Ideal(T, S) : TenSpcElt, TenSpcElt -> TenSpcElt
- IsIdeal(T, S) : TenSpcElt, TenSpcElt -> BoolElt
- Example Multilinear_Ideals (H62E66)
- LocalQuotient(T, S, I : parameters) : TenSpcElt, TenSpcElt, RngIntElt -> TenSpcElt, Hmtp
- Quotient(T, S : parameters) : TenSpcElt, TenSpcElt -> TenSpcElt, Hmtp
- Example Multilinear_Quotients (H62E67)
- Categorical Operations on Tensor Spaces
- Homotopisms
- Constructions of Homotopisms
- Homotopism(T, S, M : parameters) : TenSpcElt, TenSpcElt, List -> Hmtp
- Homotopism(M, C) : List, TenCat -> Hmtp
- IsHomotopism(T, s, H) : TenSpcElt, TenSpcElt, Hmtp -> BoolElt
- Example Multilinear_HomotopismConst (H62E70)
- Example Multilinear_MixedHomotopisms (H62E71)
- Basic Operations with Homotopisms
- Basic Properties of Homotopisms
- Linear Invariants of Tensors
- Some Extended Examples
- Bibliography
V2.28, 13 July 2023