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groups · DoubleCoset

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.DoubleCoset

One exact double coset of two subgroups in a concrete ambient group.

class DoubleCoset

noether::groups::DoubleCoset · Direct Rust declaration

pub struct DoubleCoset { /* 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/DoubleCoset@1

Executable usage: validation/unit/groups/test_acceptance_workload.py:10 · validation/unit/groups/test_acceptance_workload.py:145 · validation/unit/groups/test_acceptance_workload.py:148

groups.DoubleCoset.degree

Degree of the common permutation action.

(self) -> int

noether::groups::DoubleCoset::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/DoubleCoset@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.DoubleCoset.inverse_representative

Canonical representative of the inverse double coset for equal subgroups.

Detailed contract

Canonical representative of the inverse double coset when the left and right subgroups are equal.

(self) -> Permutation | None

noether::groups::DoubleCoset::inverse_representative · Direct Rust declaration

pub fn inverse_representative(&self) -> Option<&Perm>
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/DoubleCoset@1

groups.DoubleCoset.representative

Canonical ambient-group representative.

Detailed contract

Canonical element representing this double coset.

(self) -> Permutation

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

pub fn representative(&self) -> &Perm
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/DoubleCoset@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.DoubleCoset.right_coset_count

Number of right-subgroup cosets in this double coset.

Detailed contract

Number of right-subgroup cosets contained in this double coset.

(self) -> int

noether::groups::DoubleCoset::right_coset_count · Direct Rust declaration

pub fn right_coset_count(&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/DoubleCoset@1

Executable usage: validation/unit/groups/test_acceptance_workload.py:146

groups.DoubleCoset.size

Exact number of ambient elements in this double coset.

Detailed contract

Exact number of ambient group elements in this double coset.

(self) -> int

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

pub fn size(&self) -> &BigUInt
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/DoubleCoset@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.DoubleCoset.verify

Recompute this double coset and verify its evidence.

Detailed contract

Recompute and verify this double coset exactly.

(self, ambient: PermutationGroup, left: PermutationGroup, right: PermutationGroup) -> None

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

pub fn verify( &self, ambient: &PermGroup, left: &PermGroup, right: &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/DoubleCoset@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