TensorName

symbolica.community.spenso Class

TensorName(name: str, is_symmetric: Optional[bool] = None, is_antisymmetric: Optional[bool] = None, is_cyclesymmetric: Optional[bool] = None, is_linear: Optional[bool] = None, custom_normalization: Optional[Transformer] = None)

A symbolic name for tensor functions and structures.

TensorName represents named tensor functions that can be called with indices and arguments to create tensor structures. Names can have various mathematical properties like symmetry, antisymmetry, and custom normalization or printing behavior.

Examples

from symbolica.community.spenso import TensorName, Slot, Representation
T = TensorName("T")
symmetric_T = TensorName("S", is_symmetric=True)
antisymmetric_T = TensorName("A", is_antisymmetric=True)
rep = Representation.cof(3)
mu = rep('mu')
nu = rep('nu')
tensor_structure = T(mu, nu)

Constructor

Create a new tensor name with optional mathematical properties.

Returns

TensorName

A new TensorName with the specified properties

Examples

from symbolica.community.spenso import TensorName
T = TensorName("T")
g = TensorName("g", is_symmetric=True)
F = TensorName("F", is_antisymmetric=True)
D = TensorName("D", is_linear=True)

Parameters

Name	Type	Default	Description
`name`	`str`	`—`	The string name for the tensor function
`is_symmetric`	`Optional[bool]`	`None`	If True, tensor is symmetric under index permutation
`is_antisymmetric`	`Optional[bool]`	`None`	If True, tensor is antisymmetric under index permutation
`is_cyclesymmetric`	`Optional[bool]`	`None`	If True, tensor is symmetric under cyclic permutations
`is_linear`	`Optional[bool]`	`None`	If True, tensor is linear in its arguments
`custom_normalization`	`Optional[Transformer]`	`None`	Custom normalization function (advanced)

Member details

`repr`

Method

__repr__() -> str

No description is available for this member.

`str`

Method

__str__() -> str

No description is available for this member.

`to_expression`

Method

to_expression() -> Expression

Convert the tensor name to a symbolic expression.

Returns

Expression

A symbolic Expression representing this tensor name

Examples

T = TensorName("T")
expr = T.to_expression()

`g`

Static method

g() -> TensorName

Predefined metric tensor name.

`flat`

Static method

flat() -> TensorName

Predefined musical isomorphism tensor name. This enables dualizing self dual indices.

`gamma`

Static method

gamma() -> TensorName

Predefined gamma matrix name.

`gamma5`

Static method

gamma5() -> TensorName

Predefined gamma5 matrix name.

`projm`

Static method

projm() -> TensorName

Predefined left chiral projector name.

`projp`

Static method

projp() -> TensorName

Predefined right chiral projector name.

`sigma`

Static method

sigma() -> TensorName

Predefined sigma matrix name.

`f`

Static method

f() -> TensorName

Predefined color structure constant name.

`t`

Static method

t() -> TensorName

Predefined color generator name.

`call`

Method

Overloads

Overload 1 #

__call__(*args: Slot | Expression | int | str | float | complex) -> TensorIndices

Call the tensor name with arguments to create tensor structures.

Accepts a mix of slots and symbolic expressions (for additional arguments).

Returns

TensorIndices

A new TensorIndices object

Examples

from symbolica.community.spenso import TensorName, Slot, Representation
import symbolica as sp
T = TensorName("T")
rep = Representation.euc(3)
mu = rep("mu")
nu = rep("nu")
indexed_tensor = T(mu, nu)

Parameters

Name	Type	Default	Description
`args`	`Slot \| Expression \| int \| str \| float \| complex`	`—`	—

Overload 2 #

__call__(*args: Representation | Expression) -> TensorStructure

Call the tensor name with arguments to create a TensorStructure.

Accepts a mix of representations and symbolic expressions (for additional arguments).

Returns

TensorStructure

A new TensorStructure object

Examples

from symbolica.community.spenso import TensorName, Slot, Representation
import symbolica as sp
T = TensorName("T")
rep = Representation.euc(3)
structure_tensor = T(rep, rep)

Parameters

Name	Type	Default	Description
`args`	`Representation \| Expression`	`—`	—

View generated signature source: docs/api/python/spynso3.pyi:1285