CrossFreeFamily

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

`CrossFreeFamily`

class CrossFreeFamily

One cross-free family of denominator surfaces in a CFF orientation.

factors records signed surfaces and their multiplicities. Its expression is the product of coefficient, numerator and the inverse of every entry in factors. Summing these expressions reproduces the parent orientation. Generalized numerator sampling can produce several weighted contributions with the same geometric family but different energy_maps.

Examples

from symbolica.community import hepkit as hep
process = hep.Model.phi3().process(["phi"], ["phi", "phi"])
diagrams = process.generate_diagrams(
    loops=1, max_vertices=3, maximum_bridges=0, progress=None
)
diagram = diagrams.diagrams[0]
result = diagram.integrate_energy(method="cff")
family = result.orientations[0].families[0]
expression = family.to_expression()

Attributes

Name	Description
`coefficient`	Signed coefficient and on-shell factors multiplying this family’s numerator.
`energy_map`	Edge-energy substitutions used to evaluate this contribution’s numerator
`factors`	Signed denominator factors, grouping repeated surfaces into powers.
`id`	Family index within its orientation.
`numerator`	Evaluated numerator, including any generated numerator surface factors.

`coefficient`

CrossFreeFamily.coefficient: TensorExpression

Signed coefficient and on-shell factors multiplying this family’s numerator.

Examples

coefficient = family.coefficient

`energy_map`

CrossFreeFamily.energy_map: builtins.dict[builtins.int, Expression]

Edge-energy substitutions used to evaluate this contribution’s numerator.

Keys are physical edge IDs; values replace Q(edge, cind(0)). Empty for topology-only scalar families. These sampling maps need not be on-shell cuts.

Examples

substitutions = family.energy_map

`factors`

CrossFreeFamily.factors: builtins.list[SurfaceFactor]

Signed denominator factors, grouping repeated surfaces into powers.

Examples

denominators = [f.to_expression() for f in family.factors]

`id`

CrossFreeFamily.id: builtins.int

Family index within its orientation.

Examples

index = family.id

`numerator`

CrossFreeFamily.numerator: TensorExpression

Evaluated numerator, including any generated numerator surface factors.

Examples

numerator = family.numerator

Methods

Name	Description
`__repr__`	Summarize this family’s orientation, index and denominator factors.
`_display_`	Display this family in Marimo.
`_repr_html_`	Inspect only this family’s contribution and surface circlings.
`to_expression`	Return this family’s contribution, including the common energy prefactor.

`repr`

CrossFreeFamily.__repr__() -> builtins.str

Summarize this family’s orientation, index and denominator factors.

Examples

text = repr(family)

`_display_`

CrossFreeFamily._display_() -> typing.Any

Display this family in Marimo.

Examples

view = family._display_()

`_repr_html_`

CrossFreeFamily._repr_html_() -> builtins.str

Inspect only this family’s contribution and surface circlings.

Examples

html = family._repr_html_()

`to_expression`

CrossFreeFamily.to_expression(*, expand_surfaces: builtins.bool = True) -> TensorExpression

Return this family’s contribution, including the common energy prefactor.

Examples

Using the setup in the class example:

expression = family.to_expression()

Parameters

expand_surfaces (bool, optional) Replace stored surface placeholders by affine energy definitions. Defaults to True. On-shell energies remain symbolic in either case.

Returns

TensorExpression The complete family contribution, including its evaluated numerator and energy factors.