TensorExpression

Number of external tensor ports in the ordered interface.

Whether the expression has no external tensor ports.

Ordered external interface as concrete Slot objects or unresolved Representations.

The optional identity used when this expression describes stored data.

Create an unresolved metric tensor for rep.

Call the result with two indices to fill its ports in logical order.

Create an unresolved musical-isomorphism tensor for rep.

Call the result with two indices to fill its ports in logical order.

Create an unresolved gamma matrix with Minkowski dimension minkowski_dimension.

Its public ports use storage order: bispinor, bispinor, then Minkowski. The bispinor dimension is four. Call the result with (i, j, mu) to index it.

Create an unresolved gamma-five matrix with two bispinor ports of spinor_dimension; call the result with (i, j).

Create an unresolved left-chiral projector with two bispinor ports of spinor_dimension; call the result with (i, j).

Create an unresolved right-chiral projector with two bispinor ports of spinor_dimension; call the result with (i, j).

Create an unresolved sigma matrix with Minkowski dimension minkowski_dimension.

Its logical ports are two Minkowski ports followed by two four-dimensional bispinor ports. Call the result with (mu, nu, i, j) to index it.

Create an unresolved color structure constant.

All three logical ports are adjoint representations of adjoint_dimension; call the result with (a, b, c).

Create an unresolved color generator.

The logical ports are adjoint, fundamental, and antifundamental. Dimensions belong to those representations and are not tensor key arguments.

from symbolica.community.spenso import TensorExpression
generator = TensorExpression.t(8, 3)
indexed = generator("a", "i", "j")

Return a named descriptor without changing the underlying expression.

Drop the structured interface and return an ordinary Symbolica Expression.

Re-parse the underlying symbolic expression and rebuild its ordered tensor interface.

Expand scalar algebra while preserving and validating the tensor interface.

Apply Idenso's gamma-algebra simplifier and re-infer the tensor interface.

Convert bispinor tensors into chain/trace shorthands and join adjacent gamma chains.

Simplify products and linear combinations involving the time-like gamma matrix gamma0.

Rewrite conjugated gamma matrices as gamma0-sandwiched matrices.

Simplify Levi-Civita/metric contractions and pairs of Levi-Civita tensors.

Contract metric and identity tensors and re-infer the external interface.

Apply Idenso's SU(N) color-algebra simplifier and re-infer the interface.

Factor around tensors carrying fundamental, antifundamental, or adjoint color.

Factor around recognized scalar color invariants such as Casimirs and indices.

Rewrite supplied color dimensions and invariants into a representation-aware Casimir basis.

Replace supported cof(N) invariants by explicit dimension formulas.

Expand around color structures and wrap each scalar coefficient with symbol.

Selectively expand around Minkowski structures into (structure, coefficient) pairs.

Selectively expand around bispinor structures into (structure, coefficient) pairs.

Selectively expand around Minkowski and bispinor structures into factorized pairs.

Selectively expand around metric tensors into (structure, coefficient) pairs.

Selectively expand around color structures into (structure, coefficient) pairs.

Selectively expand around the supplied Symbolica patterns into factorized pairs.

Wrap every abstract-index payload with header and return an ordinary expression.

Wrapped payloads are not Spenso abstract indices until they are cooked, so the result intentionally has no TensorExpression interface.

Flatten nested representation-index payloads using index cooking by default.

Encode one function call as an ordinary Symbolica expression.

Wrap only contracted-index payloads with header and re-infer the interface.

Raises ValueError when the expression cannot be parsed as a tensor network.

Return the ordered external, uncontracted indices as Symbolica expressions.

Raises ValueError when the expression cannot be parsed as a tensor network.

Canonically order tensor factors and deterministically rename contracted indices.

Replace nested tensor subexpressions by aliases and return the root plus alias mappings.

Complex-conjugate this tensor expression and re-infer its interface.

Complex-conjugate this expression and transpose slots in representation.

Construct the physics-aware Dirac adjoint and re-infer the tensor interface.

Encode this expression using Idenso's reversible cooking format.

Restore a reversibly cooked expression and re-infer its tensor interface.

Simplify tensor shorthands using the configured Schoonschip traversal.

Parse and contract this expression as a symbolic tensor network.

Convert contracted rank-one tensors into compact dot-product notation.

Canonicalize compact dot-product shorthands without expanding them.

Expand dot products into explicit metric and indexed-vector contractions.

Replace metric shorthand such as g(p(rep), q(rep)) by a compact dot product.

Expand every Idenso tensor shorthand into explicit tensor syntax.

Expand Schoonschip shorthands while leaving dots, chains, and traces compact.

Expand dot-product shorthands while leaving other shorthands compact.

Expand open-chain shorthands while leaving other shorthands compact.

Expand trace shorthands while leaving other shorthands compact.

Join adjacent open chains for representation and re-infer the interface.

Rewrite tensors with two representation slots as open-chain factors.

Convert chains whose endpoints coincide into trace shorthands.

Replace one-factor chain shorthands by their underlying tensor factor.

Materialize unresolved ports and parse this expression as a tensor network.

When library is omitted, use the built-in four-dimensional HEP and SU(3) library.

Fill the unresolved external ports with indices in interface order.

Pass AUTO to leave a port unresolved. Set cook_indices=True to flatten nested symbolic index payloads before insertion. Repeated compatible indices contract their ports, in which case the result no longer carries the original stored-data identity.

Fill the unresolved external ports with indices in interface order.

Form an outer product without contracting compatible ports.

Contract one selected pair of ordered interface positions.

Compose two selected (input, output) matrix channels.

Close channel, or the unique matrix channel when it is omitted.

Format this structured expression using compact Spenso notation.

Format this structured expression as Typst math source.

Build Symbolica's rich display value, including semantic HTML when the optional gammaloop[typst-display] renderer is installed.

notation_source is a trusted complete replacement for the bundled notation.typ module, not a style fragment. Typst executes it. When HTML cannot be rendered, the result retains its LaTeX and text forms.

Compile this expression to semantic HTML with the optional Typst renderer.

Install gammaloop[typst-display] to enable this method. notation_source, when supplied, is trusted Typst code replacing the complete bundled notation.typ module.

Compile this expression to SVG with the optional Typst renderer.

Install gammaloop[typst-display] to enable this method. notation_source, when supplied, is trusted Typst code replacing the complete bundled notation.typ module.