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commalg · DivisorRankLowerBound

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

Worked example

The complete checked program Compute and verify a Bézout certificate over the integers uses this API directly.

# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Compute and verify a Bézout certificate over the integers."""

from noether import Z


def main() -> None:
    identity = Z.extended_gcd(987_654_321, 123_456_789)
    identity.verify(Z, 987_654_321, 123_456_789)
    assert (
        identity.coefficient_a * 987_654_321 + identity.coefficient_b * 123_456_789 == identity.gcd
    )
    print(identity)


if __name__ == "__main__":
    main()

Run it with .venv/bin/python examples/01_bezout_certificates.py.

commalg.DivisorRankLowerBound

Lower divisor-rank bound from an exact component intersection pairing.

class DivisorRankLowerBound

noether::commalg::DivisorRankLowerBound · Direct Rust declaration

pub struct DivisorRankLowerBound { /* private fields */ }
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/DivisorRankLowerBound@1

commalg.DivisorRankLowerBound.from_json

Deserialize and revalidate a DivisorRankLowerBound from typed JSON.

Detailed contract

Restore and exactly reverify a lower bound.

(cls, value: str) -> DivisorRankLowerBound

noether::commalg::DivisorRankLowerBound::from_json · Direct Rust declaration

pub fn from_json(value: &str) -> Result<Self, NoetherError>
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/DivisorRankLowerBound@1

Executable usage: validation/unit/category/test_category.py:14 · validation/unit/combin/test_acceptance_workload.py:65 · validation/unit/combin/test_acceptance_workload.py:86 · validation/unit/combin/test_graph_facade.py:106 · validation/unit/combin/test_graph_facade.py:25 · validation/unit/combinatorics/test_kashiwara_crystal.py:32

commalg.DivisorRankLowerBound.intersection_matrix

Return the intersection matrix recorded by this DivisorRankLowerBound.

Detailed contract

Exact component intersection matrix.

(self) -> Matrix[IntegerRing]

noether::commalg::DivisorRankLowerBound::intersection_matrix · Direct Rust declaration

pub fn intersection_matrix(&self) -> &Matrix<IntegerRing>
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/DivisorRankLowerBound@1

commalg.DivisorRankLowerBound.lower_bound

Return the lower bound recorded by this DivisorRankLowerBound.

Detailed contract

Rank proved by that pairing.

(self) -> int

noether::commalg::DivisorRankLowerBound::lower_bound · Direct Rust declaration

pub fn lower_bound(&self) -> usize
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/DivisorRankLowerBound@1

Executable usage: validation/unit/commalg/test_surface_facade.py:74 · validation/unit/numthy/test_padic_ring_facade.py:51 · validation/unit/numthy/test_padic_ring_facade.py:54 · validation/corpus/numthy/padic-newton-cube-root.py:19

commalg.DivisorRankLowerBound.split_pullback

Return the split pullback recorded by this DivisorRankLowerBound.

Detailed contract

Geometric splitting evidence for the represented divisor classes.

(self) -> SplitCyclicPullback

noether::commalg::DivisorRankLowerBound::split_pullback · Direct Rust declaration

pub fn split_pullback(&self) -> &SplitCyclicPullback
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/DivisorRankLowerBound@1

commalg.DivisorRankLowerBound.to_json

Serialize this DivisorRankLowerBound to its canonical typed JSON representation.

Detailed contract

Serialize the split geometry and exact pairing.

(self) -> str

noether::commalg::DivisorRankLowerBound::to_json · Direct Rust declaration

pub fn to_json(&self) -> Result<String, NoetherError>
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/DivisorRankLowerBound@1

Executable usage: validation/unit/category/test_category.py:14 · validation/unit/category/test_category.py:15 · validation/unit/combin/test_acceptance_workload.py:30 · validation/unit/combin/test_acceptance_workload.py:65 · validation/unit/combin/test_acceptance_workload.py:86 · validation/unit/combin/test_graph_facade.py:106

commalg.DivisorRankLowerBound.verify

Replay and verify the mathematical evidence carried by this DivisorRankLowerBound.

Detailed contract

Recompute the intersection formula and exact integer rank.

(self) -> None

noether::commalg::DivisorRankLowerBound::verify · Direct Rust declaration

pub fn verify(&self) -> Result<(), FrobeniusError>
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/DivisorRankLowerBound@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