Skip to content

commalg · WeightedHypersurfaceJacobianEvidence

6 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.WeightedHypersurfaceJacobianEvidence

Exact affine-cone Jacobian evidence, distinct from ambient quotient strata.

class WeightedHypersurfaceJacobianEvidence

noether::commalg::WeightedHypersurfaceJacobianEvidence · Direct Rust declaration

pub struct WeightedHypersurfaceJacobianEvidence<R: CommutativeRing> { /* 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

commalg.WeightedHypersurfaceJacobianEvidence.ambient_quotient_strata

Return the ambient quotient strata recorded by this WeightedHypersurfaceJacobianEvidence.

Detailed contract

Ambient quotient strata, kept distinct from cone singularities.

(self) -> list[WeightedProjectiveStratum]

noether::commalg::WeightedHypersurfaceJacobianEvidence::ambient_quotient_strata · Direct Rust declaration

pub fn ambient_quotient_strata(&self) -> &[WeightedProjectiveStratum]
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

commalg.WeightedHypersurfaceJacobianEvidence.hypersurface

Return the hypersurface recorded by this WeightedHypersurfaceJacobianEvidence.

Detailed contract

Hypersurface checked by this evidence.

(self) -> WeightedProjectiveHypersurface[C]

noether::commalg::WeightedHypersurfaceJacobianEvidence::hypersurface · Direct Rust declaration

pub fn hypersurface(&self) -> &WeightedProjectiveHypersurface<R>
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

Executable usage: validation/unit/infra/test_macaulay2_benchmark_protocol.py:1041 · validation/unit/infra/test_macaulay2_benchmark_protocol.py:935 · validation/bench/macaulay2_decomposition.py:263 · validation/bench/macaulay2_quotient.py:161 · validation/bench/macaulay2_quotient.py:162 · validation/bench/macaulay2_quotient.py:209

commalg.WeightedHypersurfaceJacobianEvidence.is_quasismooth

Test whether this WeightedHypersurfaceJacobianEvidence is quasismooth.

Detailed contract

Whether the cone has no critical point away from its vertex.

(self) -> bool

noether::commalg::WeightedHypersurfaceJacobianEvidence::is_quasismooth · Direct Rust declaration

pub fn is_quasismooth(&self) -> bool
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

commalg.WeightedHypersurfaceJacobianEvidence.saturated_critical_ideal

Return the saturated critical ideal recorded by this WeightedHypersurfaceJacobianEvidence.

Detailed contract

Critical ideal after removing the cone vertex.

(self) -> Ideal[PolynomialRing[C]]

noether::commalg::WeightedHypersurfaceJacobianEvidence::saturated_critical_ideal · Direct Rust declaration

pub fn saturated_critical_ideal(&self) -> &Ideal<PolynomialRing<R>>
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

commalg.WeightedHypersurfaceJacobianEvidence.verify

Replay and verify the mathematical evidence carried by this WeightedHypersurfaceJacobianEvidence.

Detailed contract

Recompute and compare the complete Jacobian result.

(self) -> None

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

pub fn verify(&self) -> Result<(), WeightedProjectiveError>
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

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