Skip to content

linalg · MinimumCompletionCertificate

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

Worked example

The complete checked program Construct S4 natively and inspect its stabilizer chain consequences uses this API directly.

# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Construct S4 natively and inspect its stabilizer chain consequences."""

from noether.groups import Permutation, PermutationGroup


def main() -> None:
    group = PermutationGroup.from_generators(
        4,
        [Permutation.from_images([1, 0, 2, 3]), Permutation.from_images([1, 2, 3, 0])],
    )
    assert group.order == 24
    assert group.is_transitive
    assert group.stabilizer(0).order == 6
    random = group.uniform_random_element(seed=2026)
    assert random.element in group
    print(f"|S4|={group.order}; |Stab(0)|={group.stabilizer(0).order}; sample={random.element}")


if __name__ == "__main__":
    main()

Run it with .venv/bin/python examples/19_permutation_groups.py.

linalg.MinimumCompletionCertificate

Exact evidence that no fixed-rank minimum completion exists.

class MinimumCompletionCertificate

noether::linalg::MinimumCompletionCertificate · Direct Rust declaration

pub struct MinimumCompletionCertificate { /* private fields */ }
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL attached / bounded
Semantic ID noether/linalg/MinimumCompletionCertificate@1

Executable usage: validation/unit/linalg/test_lattice_facade.py:134 · validation/unit/linalg/test_lattice_facade.py:18

linalg.MinimumCompletionCertificate.kind

Return the kind recorded by this MinimumCompletionCertificate.

Detailed contract

Stable certificate kind.

(self) -> str

noether::linalg::MinimumCompletionCertificate::kind · Direct Rust declaration

pub fn kind(&self) -> &'static str
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL attached / bounded
Semantic ID noether/linalg/MinimumCompletionCertificate@1

Executable usage: validation/unit/combinatorics/test_poset.py:95 · validation/unit/commalg/test_curve_facade.py:137 · validation/unit/commalg/test_curve_facade.py:43 · validation/unit/commalg/test_curve_facade.py:44 · validation/unit/commalg/test_curve_facade.py:45 · validation/unit/commalg/test_curve_facade.py:80

linalg.MinimumCompletionCertificate.obstacle_count

Return the obstacle count recorded by this MinimumCompletionCertificate.

Detailed contract

Number of exact separating vectors retained by the evidence.

(self) -> int

noether::linalg::MinimumCompletionCertificate::obstacle_count · Direct Rust declaration

pub fn obstacle_count(&self) -> usize
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL attached / bounded
Semantic ID noether/linalg/MinimumCompletionCertificate@1

linalg.MinimumCompletionCertificate.seed

Return the seed recorded by this MinimumCompletionCertificate.

Detailed contract

Configuration whose fixed-rank completion was requested.

(self) -> IntegralLineConfiguration

noether::linalg::MinimumCompletionCertificate::seed · Direct Rust declaration

pub fn seed(&self) -> &IntegralLineConfiguration
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL attached / bounded
Semantic ID noether/linalg/MinimumCompletionCertificate@1

Executable usage: examples/19_permutation_groups.py:16 · examples/distributed/f2_linear_algebra.py:46 · validation/unit/groups/test_acceptance_workload.py:86 · validation/unit/groups/test_acceptance_workload.py:87 · validation/unit/groups/test_acceptance_workload.py:89 · validation/unit/groups/test_acceptance_workload.py:98

linalg.MinimumCompletionCertificate.verify

Replay and verify the mathematical evidence carried by this MinimumCompletionCertificate.

Detailed contract

Recheck the fixed-rank obstruction exactly.

(self) -> None

noether::linalg::MinimumCompletionCertificate::verify · Direct Rust declaration

pub fn verify(&self) -> Result<(), LineConfigurationError>
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, m4rst, m4rst-distributed, m4rste, mzs, pwvla, spar-core, sparla, sparb, lattice-enum
GIL attached / bounded
Semantic ID noether/linalg/MinimumCompletionCertificate@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