Overview

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

`Sector decomposition`

Sector decomposition of native HEPKit diagrams and integral families.

sector_decompose generates a Laurent integrand. Compilation and numerical integration remain explicit, caller-owned operations on the returned objects.

Classes

`CancelledError`
`Chart`	Original chart ordinals and their retained native representative/kernel association.
`CoefficientExpansionSnapshot`	Native per-representative coefficient work for the current or last attempt.
`CoefficientRequestCounts`	Native representation counts, reset at each coefficient-series attempt.
`CompactCoefficient`	A retained Symbolica alias root and definitions, without restoring a full expression.
`CompilationSettings`
`CoordinateMap`	Native density pullback before endpoint subtraction, including its positive measure.
`DiscreteSectorAllocation`	Selection probability in the native discrete grid and global points per batch.
`DomainAssessment`	The native domain and threshold policy, including historical assessments.
`EndpointPower`	Exact b + c epsilon power and required Taylor coefficients; not a pole count.
`EvaluationDiagnostics`	Native caller-aggregated evaluation counters, including failed attempts.
`EvaluatorOperations`	Native shared evaluator counts; these are not optimized machine-operation counts.
`EvaluatorStatistics`	Complete shared sector evaluator size on the current backend.
`EvaluatorTiming`
`FactorAssessment`
`FastSecDecError`
`FormulaPreparationSnapshot`	Coordinator-owned counts for unique subtraction-formula precomputation.
`GeneratedIntegral`
`GeneratedSector`	A numerical sector at its native kernel-association index, with shared ownership.
`GenerationMetadata`	Retained domain and chart associations; no decomposition is repeated by inspection.
`GenerationSession`
`GenerationSnapshot`	Generation progress copied from the native caller-owned observer.
`GenerationTimings`	Native observed generation wall times in seconds
`HavanaDiscreteSession`	Caller-owned native sector importance sampling
`HavanaDiscreteSettings`	Native global-batch allocation and discrete/continuous Havana grid settings.
`Integral`	Native diagram, assumptions and explicit normalized loop measure.
`IntegrationObservation`
`IntegrationSnapshot`	Coverage and estimates from the native caller-driven integration session.
`Kernels`	Compiled native evaluator owners
`LiveEstimate`
`LiveObservation`
`LiveSector`
`PreSubtractionMetadata`	Mapped density before symmetry, multiplicity, endpoint subtraction or expansion.
`PreSubtractionTerm`	One mapped term; its potentially large regular body is never materialized.
`QmcSession`	Caller-owned bounded execution, with no background loop or worker pool.
`QmcSettings`
`SectorContribution`
`SectorMap`	The retained exact integer geometry, with native Numerica-to-Python integer transport.
`SectorSnapshot`	Native per-sector work and complete-replica coverage.
`StabilitySettings`
`VectorEstimate`	Native joint Laurent estimate with signed orders and full covariance

Functions

`sector_decompose`	Generate from an existing native diagram or an explicitly weighted family
`with_diagram_expressions`	Copy a complete native diagram, replacing only the supplied expressions

`sector_decompose`

sector_decompose(
    input: typing.Union[symbolica.community.hepkit.FeynmanDiagram, symbolica.community.hepkit.IntegralFamily],
    *,
    regulator: symbolica.Expression,
    kinematics: typing.Optional[symbolica.community.hepkit.Kinematics] = None,
    dimension: typing.Optional[symbolica.Expression] = None,
    powers: typing.Optional[typing.Union[collections.abc.Mapping[int, int], collections.abc.Sequence[int]]] = None,
    numerator: typing.Optional[symbolica.Expression] = None,
    scalar_values: typing.Optional[dict[symbolica.Expression, symbolica.Expression]] = None,
    auxiliary_momenta: typing.Optional[collections.abc.Sequence[symbolica.Expression]] = None,
    measure_multiplier: typing.Optional[symbolica.Expression] = None,
    runtime_parameters: typing.Optional[list[symbolica.Expression]] = None,
    model_parameters: str = 'runtime',
    max_order: int = 0,
    coefficient_expansion: str = 'full_expression',
    mode: str = 'symbolic',
    subtraction: str = 'taylor',
    observer: typing.Optional[collections.abc.Callable[[symbolica.community.hepkit.sector_decomposition.GenerationSnapshot], typing.Optional[bool]]] = None,
    progress: typing.Union[typing.Literal['auto'], typing.Callable[[symbolica.community.hepkit.sector_decomposition.GenerationSnapshot], typing.Optional[bool]], None] = 'auto',
) -> symbolica.community.hepkit.sector_decomposition.GeneratedIntegral

Generate from an existing native diagram or an explicitly weighted family.

Diagrams require kinematics, use their owned numerator/weights, and take an optional positive-power mapping by stable edge ID. Families require a signed power sequence in native denominator order and a weighted scalar numerator; auxiliary slots never default to power one. Kinematics overrides must retain original external products after scalar binding, but may add auxiliary data. Dimension defaults to 4-2*regulator. Compilation and sessions are explicit. progress=“auto” shows HEPKit progress in marimo when observer is absent. None disables display; a callable receives every snapshot after observer. None/True continues, False cancels; original callback exceptions propagate.

`with_diagram_expressions`

with_diagram_expressions(
    diagram: FeynmanDiagram,
    *,
    numerator: typing.Optional[Expression] = None,
    projector: typing.Optional[Expression] = None,
    overall_factor: typing.Optional[Expression] = None,
) -> FeynmanDiagram

Copy a complete native diagram, replacing only the supplied expressions. Native numerator validation and all graph/model ownership are preserved.