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groups · SubsetOrbit

7 accepted declarations. Python and Rust forms, contracts, evidence, failure boundaries, and checked usages are kept together below.

Worked example

The complete checked program Decompose a polynomial by a nonstandard positive grading uses this API directly.

# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Decompose a polynomial by a nonstandard positive grading."""

from noether import Z
from noether.commalg import PolynomialRing, WeightedGrading


def main() -> None:
    ring = PolynomialRing(Z, ["x", "y", "z"], grading=WeightedGrading([1, 2, 3]))
    x, y, z = ring.generators()
    sparse = ring.from_terms([([0, 0, 0], 1), ([2, 0, 0], 1), ([0, 1, 0], 1)])
    polynomial = sparse + z
    assert sparse * (x + y) == (1 + x**2 + y) * (x + y)
    components = polynomial.homogeneous_components()
    assert [degree for degree, _ in components] == [0, 2, 3]
    assert x**2 + y == components[1][1]
    print(f"weighted homogeneous degrees: {[degree for degree, _ in components]}")


if __name__ == "__main__":
    main()

Run it with .venv/bin/python examples/14_weighted_polynomials.py.

groups.SubsetOrbit

One exact orbit under a permutation group's action on subsets.

class SubsetOrbit

noether::groups::SubsetOrbit · Direct Rust declaration

pub struct SubsetOrbit { /* private fields */ }
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, perm-core
GIL attached / bounded
Semantic ID noether/groups/SubsetOrbit@1

Executable usage: validation/unit/groups/test_acceptance_workload.py:129 · validation/unit/groups/test_acceptance_workload.py:130 · validation/unit/groups/test_acceptance_workload.py:20

groups.SubsetOrbit.degree

Degree of the underlying point action.

(self) -> int

noether::groups::SubsetOrbit::degree · Direct Rust declaration

pub fn degree(&self) -> usize
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, perm-core
GIL attached / bounded
Semantic ID noether/groups/SubsetOrbit@1

Executable usage: examples/14_weighted_polynomials.py:16 · examples/14_weighted_polynomials.py:18 · examples/15_groebner_twisted_cubic.py:15 · examples/15_groebner_twisted_cubic.py:28 · examples/31_local_fields_and_precision.py:37 · examples/33_simplicial_cohomology_operations.py:26

groups.SubsetOrbit.elements

Every subset in stable lexical order.

Detailed contract

Every subset in the orbit, in stable lexical order.

(self) -> list[list[int]]

noether::groups::SubsetOrbit::elements · Direct Rust declaration

pub fn elements(&self) -> &[Vec<u32>]
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, perm-core
GIL attached / bounded
Semantic ID noether/groups/SubsetOrbit@1

Executable usage: examples/28_steiner_categories.py:26 · validation/unit/groups/test_acceptance_workload.py:135 · validation/unit/groups/test_acceptance_workload.py:166 · validation/unit/groups/test_acceptance_workload.py:93 · validation/unit/groups/test_acceptance_workload.py:94 · validation/unit/groups/test_acceptance_workload.py:95

groups.SubsetOrbit.representative

Lexicographically least subset in the orbit.

(self) -> list[int]

noether::groups::SubsetOrbit::representative · Direct Rust declaration

pub fn representative(&self) -> &[u32]
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, perm-core
GIL attached / bounded
Semantic ID noether/groups/SubsetOrbit@1

Executable usage: validation/unit/commalg/test_residue_ring_facade.py:101 · validation/unit/commalg/test_residue_ring_facade.py:110 · validation/unit/commalg/test_residue_ring_facade.py:129 · validation/unit/commalg/test_residue_ring_facade.py:26 · validation/unit/commalg/test_residue_ring_facade.py:80 · validation/unit/groups/test_acceptance_workload.py:125

groups.SubsetOrbit.size

Exact orbit cardinality.

(self) -> int

noether::groups::SubsetOrbit::size · Direct Rust declaration

pub fn size(&self) -> usize
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, perm-core
GIL attached / bounded
Semantic ID noether/groups/SubsetOrbit@1

Executable usage: examples/20_conjugacy_classes.py:16 · examples/20_conjugacy_classes.py:17 · examples/20_conjugacy_classes.py:18 · examples/distributed/f2_linear_algebra.py:14 · examples/distributed/f2_linear_algebra.py:60 · validation/unit/combinatorics/test_partition_composition.py:15

groups.SubsetOrbit.subset_size

Common cardinality of the subsets in this orbit.

Detailed contract

Common cardinality of the subsets in the orbit.

(self) -> int

noether::groups::SubsetOrbit::subset_size · Direct Rust declaration

pub fn subset_size(&self) -> usize
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, perm-core
GIL attached / bounded
Semantic ID noether/groups/SubsetOrbit@1

Executable usage: validation/unit/groups/test_acceptance_workload.py:131

groups.SubsetOrbit.verify

Recompute the orbit and orbit-stabilizer identity exactly.

Detailed contract

Recompute the orbit and the orbit-stabilizer identity exactly.

(self, group: PermutationGroup) -> None

noether::groups::SubsetOrbit::verify · Direct Rust declaration

pub fn verify(&self, group: &PermGroup) -> Result<(), GroupError>
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, perm-core
GIL attached / bounded
Semantic ID noether/groups/SubsetOrbit@1

Executable usage: examples/01_bezout_certificates.py:10 · examples/01_bezout_certificates.py:3 · examples/03_exact_linear_systems.py:13 · examples/03_exact_linear_systems.py:3 · examples/04_smith_normal_form.py:12 · examples/06_shortest_lattice_vectors.py:12