TensorPattern

symbolica.community.spenso Class

TensorPattern(head: TensorName, *, args: Sequence[Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal]] = [], ports: Sequence[Slot | Representation | Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal]] = [])

A tagged Symbolica expression intended for tensor rewrite rules.

args contains scalar tensor arguments and ports contains structural syntax. The two named sections are concatenated in that order. Since this is a pattern expression rather than a concrete tensor, either section may contain ordinary or sequence-wildcard Symbolica expressions.

Examples

import symbolica as sp
from symbolica.community.spenso import (
    PortPattern, TensorExpression, TensorName, TensorPattern,
)
k_, D_, mu_, i_, j_, rest___ = sp.S(
    "k_", "D_", "mu_", "i_", "j_", "rest___",
)
fixed = TensorPattern(
    TensorName("A"),
    args=[k_],
    ports=[PortPattern.any("R_", D_, i_), rest___],
)
generic = TensorPattern.any("T_", ports=[rest___])
target = TensorExpression.gamma(4)("i", "j", "mu").to_expression()
rule = TensorPattern.gamma(D_, i_, j_, mu_)
target.replace(rule, 0)

Constructor

Create a pattern for the fixed tensor head.

Scalar args are always emitted before structural ports.

Parameters

Name	Type	Default	Description
`head`	`TensorName`	`—`	—
`args`	`Sequence[Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]]`	`[]`	—
`ports`	`Sequence[Slot \| Representation \| Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]]`	`[]`	—

Member details

`any`

Static method

any(name: str, *, args: Sequence[Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal]] = [], ports: Sequence[Slot | Representation | Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal]] = []) -> TensorPattern

Match any tensor-tagged head.

name must end in one underscore, for example "T_".

Parameters

Name	Type	Default	Description
`name`	`str`	`—`	—
`args`	`Sequence[Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]]`	`[]`	—
`ports`	`Sequence[Slot \| Representation \| Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]]`	`[]`	—

`vector`

Static method

vector(name: str, *, args: Sequence[Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal]] = [], ports: Sequence[Slot | Representation | Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal]] = []) -> TensorPattern

Match any rank-one tensor head.

Pattern construction intentionally does not impose a concrete arity, so a sequence wildcard may describe the scalar arguments or structural port.

Parameters

Name	Type	Default	Description
`name`	`str`	`—`	—
`args`	`Sequence[Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]]`	`[]`	—
`ports`	`Sequence[Slot \| Representation \| Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]]`	`[]`	—

`g`

Static method

g(rep_pattern: Representation | Expression, i: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], j: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal]) -> TensorPattern

Match a metric tensor in logical index order.

Parameters

Name	Type	Default	Description
`rep_pattern`	`Representation \| Expression`	`—`	—
`i`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`j`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—

`flat`

Static method

flat(rep_pattern: Representation | Expression, i: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], j: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal]) -> TensorPattern

Match a musical-isomorphism tensor in logical index order.

Parameters

Name	Type	Default	Description
`rep_pattern`	`Representation \| Expression`	`—`	—
`i`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`j`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—

`gamma`

Static method

gamma(minkowski_dimension: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], i: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], j: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], mu: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal]) -> TensorPattern

Match a gamma matrix in storage (i, j, mu) order.

Parameters

Name	Type	Default	Description
`minkowski_dimension`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`i`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`j`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`mu`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—

`gamma5`

Static method

gamma5(spinor_dimension: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], i: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], j: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal]) -> TensorPattern

Match a gamma-five matrix in logical (i, j) order.

Parameters

Name	Type	Default	Description
`spinor_dimension`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`i`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`j`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—

`projm`

Static method

projm(spinor_dimension: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], i: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], j: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal]) -> TensorPattern

Match a left-chiral projector in logical (i, j) order.

Parameters

Name	Type	Default	Description
`spinor_dimension`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`i`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`j`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—

`projp`

Static method

projp(spinor_dimension: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], i: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], j: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal]) -> TensorPattern

Match a right-chiral projector in logical (i, j) order.

Parameters

Name	Type	Default	Description
`spinor_dimension`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`i`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`j`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—

`sigma`

Static method

sigma(minkowski_dimension: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], mu: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], nu: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], i: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], j: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal]) -> TensorPattern

Match a sigma matrix. Arguments use logical (mu, nu, i, j) order.

Parameters

Name	Type	Default	Description
`minkowski_dimension`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`mu`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`nu`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`i`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`j`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—

`f`

Static method

f(adjoint_dimension: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], a: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], b: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], c: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal]) -> TensorPattern

Match a color structure constant in logical (a, b, c) order.

Parameters

Name	Type	Default	Description
`adjoint_dimension`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`a`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`b`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`c`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—

`t`

Static method

t(adjoint_dimension: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], fundamental_dimension: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], a: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], i: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal], j: Expression | int | Float | int | float | str | decimal.Decimal | ComplexFloat | Float | int | float | str | decimal.Decimal | complex | tuple[Float | int | float | str | decimal.Decimal, Float | int | float | str | decimal.Decimal]) -> TensorPattern

Match a color generator in logical (a, i, j) order.

Parameters

Name	Type	Default	Description
`adjoint_dimension`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`fundamental_dimension`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`a`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`i`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—
`j`	`Expression \| int \| Float \| int \| float \| str \| decimal.Decimal \| ComplexFloat \| Float \| int \| float \| str \| decimal.Decimal \| complex \| tuple[Float \| int \| float \| str \| decimal.Decimal, Float \| int \| float \| str \| decimal.Decimal]`	`—`	—

View generated signature source: docs/api/python/spynso3.pyi:2083