Slot

Symbolica documentation for getting started, symbolic expressions, numerical evaluation, pattern matching, and APIs in Python and Rust.

`Slot`

class Slot

One abstract tensor index together with its representation.

An index label identifies a possible contraction; it is not a component coordinate. Prefer space("i") to construct a slot for an existing space.

Examples

from symbolica.community.tensor import Representation
slot = Representation.euc(3)("i")
slot.representation == Representation.euc(3)
True

Attributes

Name	Description
`index`	The abstract label carried by this slot.
`representation`	The dimensioned space to which this index belongs.

`index`

Slot.index: Expression

The abstract label carried by this slot.

Returns

Expression Symbolic label or integer; not a component coordinate.

Examples

from symbolica.community.tensor import Representation
slot = Representation.euc(3)("i")
label = slot.index

`representation`

Slot.representation: Representation

The dimensioned space to which this index belongs.

Returns

Representation Includes the duality of the slot.

Examples

from symbolica.community.tensor import Representation
slot = Representation.euc(3)("i")
space = slot.representation

Methods

Name	Description
`__eq__`
`__hash__`	Hash the immutable representation and index label for dictionaries and sets.
`__new__`	Create a labeled index in a registered representation.
`__repr__`	Return a readable object description for inspection.
`__str__`	Return a readable text representation.
`_repr_html_`
`_repr_latex_`
`dual`	Pair this index label with the dual representation.
`to_expression`	Return symbolic syntax for the representation and index.
`to_html`	Render a compact HTML view of this tensor metadata.

`eq`

Slot.__eq__(other: builtins.object) -> builtins.bool

`hash`

Slot.__hash__() -> builtins.int

Hash the immutable representation and index label for dictionaries and sets.

Examples

from symbolica.community import tensor as sp
r = sp.Representation.euc(2)
labels = {r("i"): "free index"}
assert labels[r("i")] == "free index"

`new`

Slot.__new__(
    name: builtins.str,
    dimension: builtins.int,
    aind: builtins.int | Expression | str,
    dual: builtins.bool = False,
) -> Slot

Create a labeled index in a registered representation.

Parameters

name (str) Registered representation name.
dimension (int) Dimension of the index space.
aind (int, str, or Expression) Abstract index label accepted by the shared tensor-structure parser, including numeric, symbolic, tagged named, and scoped indices.
dual (bool, default False) Whether to use the dual of the named representation.

Returns

Slot The representation and index label together.

Notes

Use Representation.euc(3)("i") when working with representation objects.

Examples

from symbolica.community.tensor import Representation, Slot
space = Representation.euc(3)
slot = Slot(space.name.name, 3, "i")
slot == space("i")
True

`repr`

Slot.__repr__() -> builtins.str

Return a readable object description for inspection.

Examples

from symbolica.community import tensor as sp
slot = sp.Representation.mink(4)("mu")
text = repr(slot)

`str`

Slot.__str__() -> builtins.str

Return a readable text representation.

Examples

from symbolica.community import tensor as sp
slot = sp.Representation.mink(4)("mu")
text = str(slot)

`_repr_html_`

Slot._repr_html_() -> builtins.str

`_repr_latex_`

Slot._repr_latex_() -> builtins.str

`dual`

Slot.dual() -> Slot

Pair this index label with the dual representation.

Returns

Slot A new slot with the same label.

Examples

from symbolica.community.tensor import Representation
slot = Representation.euc(3)("i")
paired = slot.dual()

`to_expression`

Slot.to_expression() -> Expression

Return symbolic syntax for the representation and index.

Returns

Expression The encoded slot, for use in raw Symbolica expressions.

Examples

from symbolica.community.tensor import Representation
slot = Representation.euc(3)("i")
encoded = slot.to_expression()

`to_html`

Slot.to_html(*, settings: typing.Optional[DisplaySettings] = None) -> builtins.str

Render a compact HTML view of this tensor metadata.

Parameters

settings (DisplaySettings, optional) Index and tensor presentation choices; defaults to DisplaySettings().

Returns

str HTML fragment for display in a notebook or page.

Examples

from symbolica.community.tensor import Representation
value = Representation.euc(3)("i")
html = value.to_html()