TensorIndices

TensorIndices

TensorIndices()

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()

Methods

Name Description
__add__ Add this expression to other, returning the result.
__getitem__ Get expanded indices at the specified range of flattened indices.
__len__
__mul__ Add this expression to other, returning the result.
__new__ Create tensor structure from slots and optional arguments.
__radd__ Add this expression to other, returning the result.
__repr__
__rmul__ Add this expression to other, returning the result.
__rsub__ Subtract this expression from other, returning the result.
__str__
__sub__ Subtract other from this expression, returning the result.
get_name Get the tensor name of this structure.
set_name Set the tensor name for this structure.
to_expression Convert the tensor indices to a symbolic expression

__add__

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

Related type: Expression

Add this expression to other, returning the result.

__getitem__

__getitem__ has 3 variants:

__getitem__ with item: builtins.slice

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

Related type: Expression

Get expanded indices at the specified range of flattened indices.

Parameters

  • item (slice) Slice object defining the range of indices

Returns

  • list of list of int List of expanded indices

__getitem__ with item: typing.Sequence[builtins.int]

TensorIndices.__getitem__(item: typing.Sequence[builtins.int]) -> Expression | builtins.complex | float

Related type: Expression

Get flattened index associated to this expanded index.

Parameters

  • item (list of int) Multi-dimensional index coordinates

Returns

  • int The flat index

__getitem__ with item: builtins.int

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

Related type: Expression

Get expanded index associated to this flat index.

Parameters

  • item (int) Flat index into the tensor

Returns

  • list of int Multi-dimensional index coordinates

__len__

TensorIndices.__len__() -> builtins.int

__mul__

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

Related type: Expression

Add this expression to other, returning the result.

__new__

TensorIndices.__new__(
    *slots: TensorIndices | builtins.list[Slot],
    name: TensorName | builtins.str | Expression | None = None,
) -> TensorIndices

Related types: Slot, TensorName, Expression

Create tensor structure from slots and optional arguments.

Parameters

  • *additional_args (Slot or Expression) Mixed arguments (Slot objects and Expressions for additional arguments)
  • name (TensorName, optional) Optional tensor name to assign to the structure

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)

__radd__

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

Related type: Expression

Add this expression to other, returning the result.

__repr__

TensorIndices.__repr__() -> builtins.str

__rmul__

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

Related type: Expression

Add this expression to other, returning the result.

__rsub__

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

Related type: Expression

Subtract this expression from other, returning the result.

__str__

TensorIndices.__str__() -> builtins.str

__sub__

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

Related type: Expression

Subtract other from this expression, returning the result.

get_name

TensorIndices.get_name() -> typing.Optional[TensorName]

Related type: TensorName

Get the tensor name of this structure.

Returns

  • TensorName or None The tensor name if set, None otherwise

Examples

name = structure.get_name()

set_name

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

Related types: TensorName, Expression

Set the tensor name for this structure.

Parameters

  • name (TensorName) The tensor name to assign

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)

to_expression

TensorIndices.to_expression() -> Expression

Related type: 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()