TensorIndices

symbolica.community.spenso Class

TensorIndices(*slots: TensorIndices | list[Slot], name: TensorName | str | Expression | None = None)

A tensor structure with abstract indices for symbolic tensor operations.

TensorIndices represents the index structure of tensors with named abstract indices that can be contracted, manipulated symbolically, and converted to expressions. It maintains both the representation structure and index assignments.

Examples

from symbolica.community.spenso import TensorIndices, Representation, TensorName
rep = Representation.euc(3)
mu = rep('mu')
nu = rep('nu')
indices = TensorIndices(mu, nu)
T = TensorName("T")
named_indices = T(mu, nu)
expr = named_indices.to_expression()

Constructor

Create tensor structure from slots and optional arguments.

Returns

TensorIndices

A new TensorIndices object

Examples

from symbolica import S
from symbolica.community.spenso import TensorIndices, Representation, TensorName
rep = Representation.euc(3)
mu = rep('mu')
nu = rep('nu')
structure = TensorIndices(mu, nu)
x = S('x')
structure_with_args = TensorIndices(mu, nu, x)
T = TensorName("T")
named_structure = TensorIndices(mu, nu, name=T)

Parameters

Name	Type	Default	Description
`slots`	`TensorIndices \| list[Slot]`	`—`	—
`name`	`TensorName \| str \| Expression \| None`	`None`	Optional tensor name to assign to the structure

Member details

`set_name`

Method

set_name(name: TensorName | str | Expression) -> None

Set the tensor name for this structure.

Examples

from symbolica.community.spenso import TensorIndices, TensorName, Representation
rep = Representation.euc(3)
structure = TensorIndices(rep('mu'), rep('nu'))
T = TensorName("T")
structure.set_name(T)

Parameters

Name	Type	Default	Description
`name`	`TensorName \| str \| Expression`	`—`	The tensor name to assign

`get_name`

Method

get_name() -> Optional[TensorName]

Get the tensor name of this structure.

Returns

TensorName or None

The tensor name if set, None otherwise

Examples

name = structure.get_name()

`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 indices to a symbolic expression.

Creates a symbolic representation of the tensor with its indices that can be used in algebraic manipulations and pattern matching.

Returns

Expression

A symbolic Expression representing this indexed tensor

Raises

RuntimeError: If the tensor structure has no name

Examples

from symbolica.community.spenso import TensorName, Representation
T = TensorName("T")
rep = Representation.euc(3)
mu = rep('mu')
nu = rep('nu')
indices = T(mu, nu)
expr = indices.to_expression()

`len`

Method

__len__() -> int

No description is available for this member.

`add`

Method

__add__(rhs: Expression | int | str | float | complex | TensorIndices | Expression) -> Expression

Add this expression to other, returning the result.

Parameters

Name	Type	Default	Description
`rhs`	`Expression \| int \| str \| float \| complex \| TensorIndices \| Expression`	`—`	—

`radd`

Method

__radd__(rhs: Expression | int | str | float | complex | TensorIndices | Expression) -> Expression

Add this expression to other, returning the result.

Parameters

Name	Type	Default	Description
`rhs`	`Expression \| int \| str \| float \| complex \| TensorIndices \| Expression`	`—`	—

`sub`

Method

__sub__(rhs: Expression | int | str | float | complex | TensorIndices | Expression) -> Expression

Subtract other from this expression, returning the result.

Parameters

Name	Type	Default	Description
`rhs`	`Expression \| int \| str \| float \| complex \| TensorIndices \| Expression`	`—`	—

`rsub`

Method

__rsub__(rhs: Expression | int | str | float | complex | TensorIndices | Expression) -> Expression

Subtract this expression from other, returning the result.

Parameters

Name	Type	Default	Description
`rhs`	`Expression \| int \| str \| float \| complex \| TensorIndices \| Expression`	`—`	—

`mul`

Method

__mul__(rhs: Expression | int | str | float | complex | TensorIndices | Expression) -> Expression

Add this expression to other, returning the result.

Parameters

Name	Type	Default	Description
`rhs`	`Expression \| int \| str \| float \| complex \| TensorIndices \| Expression`	`—`	—

`rmul`

Method

__rmul__(rhs: Expression | int | str | float | complex | TensorIndices | Expression) -> Expression

Add this expression to other, returning the result.

Parameters

Name	Type	Default	Description
`rhs`	`Expression \| int \| str \| float \| complex \| TensorIndices \| Expression`	`—`	—

`getitem`

Method

Overloads

Overload 1 #

__getitem__(item: slice) -> list[Expression | complex | float]

Get expanded indices at the specified range of flattened indices.

Returns

list of list of int

List of expanded indices

Parameters

Name	Type	Default	Description
`item`	`slice`	`—`	Slice object defining the range of indices

Overload 2 #

__getitem__(item: Sequence[int]) -> Expression | complex | float

Get flattened index associated to this expanded index.

Returns

int

The flat index

Parameters

Name	Type	Default	Description
`item`	`Sequence[int]`	`—`	Multi-dimensional index coordinates

Overload 3 #

__getitem__(item: int) -> Expression | complex | float

Get expanded index associated to this flat index.

Returns

list of int

Multi-dimensional index coordinates

Parameters

Name	Type	Default	Description
`item`	`int`	`—`	Flat index into the tensor

View generated signature source: docs/api/python/spynso3.pyi:955