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to_dots

symbolica.community.idenso Function

to_dots(self_: Expression) -> Expression

Converts contracted Lorentz/Minkowski indices into dot product notation.

Automatically identifies and converts patterns like p(mink(D, mu)) * q(mink(D, mu)) into the compact, representation-carrying dot(p(mink(D)), q(mink(D))) notation. This simplification is essential for physics calculations involving four-vectors.

The function recognizes:

  • Contracted vector indices: pᵘqᵤ → p·q
  • Multiple contractions: pᵘqᵤrᵛsᵥ → (p·q)(r·s)
  • Self-contractions: pᵘpᵤ → p²

Arguments

  • self_: expression containing contracted Minkowski vector indices

Returns

The expression with vector contractions converted to dot products.

Examples

from symbolica.community.idenso import to_dots
from symbolica.community.spenso import Representation, TensorName
p = TensorName("p")
q = TensorName("q")
rep = Representation.euc(3)
# With slots (creates TensorIndices)
mu = rep("mu")
nu = rep("nu")

print(to_dots( p(mu)*q(mu)))

View generated signature source: docs/api/python/idenso-community.pyi:445