uconf.core.vertex_decoration

Shared typing alias for tree-vertex decoration providers.

The shared tree-decorated base modules uconf.algebraic.free_algebra.FreeAlgebraModule and uconf.algebraic.cofree_coalgebra.CofreeCoalgebraModule only require arity-indexed components with grading and differential.

In practice, both operad-like and cooperad-like providers are used. This module defines a common alias for those accepted inputs.

Module Attributes

VertexDecorationLike	Accepted decoration providers for shared tree-decorated base modules.
QuasiPlanarLike	Accepted decoration providers for free/cofree algebra composite modules.

uconf.core.vertex_decoration.VertexDecorationLike: TypeAlias = type[uconf.core.operad.OperadComponent] | uconf.core.operad.OperadFactory | type[uconf.core.cooperad.CooperadComponent] | uconf.core.cooperad.CooperadFactory

Accepted decoration providers for shared tree-decorated base modules.

uconf.core.vertex_decoration.QuasiPlanarLike: TypeAlias = type[uconf.core.operad.OperadComponent] | uconf.core.operad.OperadFactory | type[uconf.core.cooperad.CooperadComponent] | uconf.core.cooperad.CooperadFactory

Accepted decoration providers for free/cofree algebra composite modules.

A quasi-planar operad/cooperad is one whose arity-n component P(n) satisfies P(n) ≅ P_pl(n) ⊗ k[S_n] and exposes a planarize linear map decomposing each element into its planar representative and symmetric-group factor.

Supported examples: Associative, Surjection, BarrattEccles, and wrappers thereof.

Non-quasi-planar operads (e.g. Commutative, Lie) are not accepted; they have non-trivial coinvariants and cannot be enumerated as P_pl(n) ⊗ M^{⊗n}.