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linalg · MinimumRealizationDiagnostic

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

Worked example

The complete checked program Certify symmetries, realizations, and completions of integral lines uses this API directly.

# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Certify symmetries, realizations, and completions of integral lines."""

from noether.linalg import IntegralLineConfiguration


def main() -> None:
    axes = IntegralLineConfiguration(2, [[1, 0], [0, 1]])
    symmetries = axes.automorphism_group()
    symmetries.verify()
    assert symmetries.order == 8

    a2_lines = IntegralLineConfiguration(2, [[1, 0], [0, 1], [1, -1]])
    realization = a2_lines.realize_minimum(max_iterations=20)
    realization.verify()
    assert realization.status == "realized"
    assert realization.realization is not None

    completion = axes.complete_minimum(max_iterations=20)
    completion.verify()
    assert completion.status == "completed"
    assert completion.realization is not None

    print(
        "integral lines:",
        f"axis symmetry order={symmetries.order}",
        f"A2 Gram matrix={realization.realization.gram_matrix}",
        f"axis completion={completion.realization.configuration.vectors}",
    )


if __name__ == "__main__":
    main()

Run it with .venv/bin/python examples/29_integral_line_configurations.py.

linalg.MinimumRealizationDiagnostic

Diagnostic information from an inconclusive minimum-realization computation.

class MinimumRealizationDiagnostic

noether::linalg::MinimumRealizationDiagnostic · Direct Rust declaration

pub struct MinimumRealizationDiagnostic { /* 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/MinimumRealizationDiagnostic@1

Executable usage: validation/unit/linalg/test_lattice_facade.py:21 · validation/unit/linalg/test_lattice_facade.py:216

linalg.MinimumRealizationDiagnostic.configuration

Return the configuration recorded by this MinimumRealizationDiagnostic.

Detailed contract

Candidate whose realization remains undecided.

(self) -> IntegralLineConfiguration

noether::linalg::MinimumRealizationDiagnostic::configuration · Direct Rust declaration

pub fn configuration(&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/MinimumRealizationDiagnostic@1

Executable usage: examples/29_integral_line_configurations.py:29 · validation/unit/linalg/test_lattice_facade.py:100 · validation/unit/linalg/test_lattice_facade.py:101 · validation/unit/linalg/test_lattice_facade.py:102 · validation/unit/linalg/test_lattice_facade.py:103 · validation/unit/linalg/test_lattice_facade.py:106

linalg.MinimumRealizationDiagnostic.iterations

Return the iterations recorded by this MinimumRealizationDiagnostic.

Detailed contract

Completed cutting-plane iterations.

(self) -> int

noether::linalg::MinimumRealizationDiagnostic::iterations · Direct Rust declaration

pub fn iterations(&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/MinimumRealizationDiagnostic@1

Executable usage: validation/unit/linalg/test_lattice_facade.py:217 · validation/bench/macaulay2_quotient.py:228

linalg.MinimumRealizationDiagnostic.obstacle_count

Return the obstacle count recorded by this MinimumRealizationDiagnostic.

Detailed contract

Number of exact separating vectors accumulated before stopping.

(self) -> int

noether::linalg::MinimumRealizationDiagnostic::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/MinimumRealizationDiagnostic@1

linalg.MinimumRealizationDiagnostic.reason

Return the reason recorded by this MinimumRealizationDiagnostic.

Detailed contract

Stable explanation of why no mathematical verdict was returned.

(self) -> str

noether::linalg::MinimumRealizationDiagnostic::reason · Direct Rust declaration

pub fn reason(&self) -> &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/MinimumRealizationDiagnostic@1

Executable usage: validation/unit/infra/test_oracle_requirement.py:107 · validation/parity/combinatorics/test_crystals_parity.py:29 · validation/parity/combinatorics/test_matroid_parity.py:29 · validation/parity/combinatorics/test_poset_gap_parity.py:17 · validation/parity/combinatorics/test_poset_parity.py:29 · validation/parity/combinatorics/test_symmetric_functions_parity.py:30

linalg.MinimumRealizationDiagnostic.verify

Replay and verify the mathematical evidence carried by this MinimumRealizationDiagnostic.

Detailed contract

Check that the diagnostic makes no false terminal claim.

(self) -> None

noether::linalg::MinimumRealizationDiagnostic::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/MinimumRealizationDiagnostic@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