commalg · PointCountEvidence

13 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.PointCountEvidence

Method-specific evidence attached to one exact point count.

PythonRust

class PointCountEvidence

noether::commalg::PointCountEvidence · Direct Rust declaration

pub struct PointCountEvidence { /* 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.PointCountEvidence.certificate

Return the certificate recorded by this PointCountEvidence.

Detailed contract

Enumeration certificate retained by an exhaustive route.

PythonRust

(self) -> PointCountCertificate | None

noether::commalg::PointCountEvidence::certificate · Direct Rust declaration

pub fn certificate(&self) -> Option<&PointCountCertificate>

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:3 · examples/18_finite_field_schemes.py:14 · examples/18_finite_field_schemes.py:15 · validation/unit/commalg/test_acceptance_workload.py:135 · validation/unit/commalg/test_acceptance_workload.py:137 · validation/unit/commalg/test_acceptance_workload.py:138

commalg.PointCountEvidence.coefficient_checksum

Return the coefficient checksum recorded by this PointCountEvidence.

Detailed contract

Stable checksum of coefficients consumed by a trace route.

PythonRust

(self) -> int | None

noether::commalg::PointCountEvidence::coefficient_checksum · Direct Rust declaration

pub fn coefficient_checksum(&self) -> Option<u64>

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/bench/surface_frobenius.py:106

commalg.PointCountEvidence.count_residue

Return the count residue recorded by this PointCountEvidence.

Detailed contract

Canonical count residue used by a trace-formula route.

PythonRust

(self) -> int | None

noether::commalg::PointCountEvidence::count_residue · Direct Rust declaration

pub fn count_residue(&self) -> Option<&Integer>

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.PointCountEvidence.embedding

Return the embedding recorded by this PointCountEvidence.

Detailed contract

Checked embedding of the declared finite base field.

PythonRust

(self) -> FiniteFieldEmbedding

noether::commalg::PointCountEvidence::embedding · Direct Rust declaration

pub fn embedding(&self) -> &FiniteFieldEmbedding

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/commalg/test_base_change.py:101 · validation/unit/commalg/test_base_change.py:108 · validation/unit/commalg/test_base_change.py:110 · validation/unit/commalg/test_base_change.py:111 · validation/unit/commalg/test_base_change.py:112 · validation/unit/commalg/test_base_change.py:113

commalg.PointCountEvidence.extension_field

Return the extension field recorded by this PointCountEvidence.

Detailed contract

Exact extension field used for this count.

PythonRust

(self) -> FiniteField

noether::commalg::PointCountEvidence::extension_field · Direct Rust declaration

pub fn extension_field(&self) -> &FiniteField

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/bench/magma_release.py:916 · validation/bench/magma_release.py:919

commalg.PointCountEvidence.independently_verified

Compute independently verified for this PointCountEvidence.

Detailed contract

Whether the count is exhaustively replayable or an additional route independently checked an accelerated computation.

PythonRust

(self) -> bool

noether::commalg::PointCountEvidence::independently_verified · Direct Rust declaration

pub fn independently_verified(&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

Executable usage: validation/unit/commalg/test_surface_facade.py:48 · validation/unit/commalg/test_surface_facade.py:57 · validation/bench/macaulay2_scorecard.py:169 · validation/bench/macaulay2_scorecard.py:180 · validation/bench/macaulay2_scorecard.py:190 · validation/bench/macaulay2_scorecard.py:199

commalg.PointCountEvidence.largest_matrix_dimension

Return the largest matrix dimension recorded by this PointCountEvidence.

Detailed contract

Largest trace-operator matrix dimension in a trace route.

PythonRust

(self) -> int | None

noether::commalg::PointCountEvidence::largest_matrix_dimension · Direct Rust declaration

pub fn largest_matrix_dimension(&self) -> Option<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

Executable usage: validation/unit/commalg/test_surface_facade.py:91 · validation/bench/surface_frobenius.py:105

commalg.PointCountEvidence.method

Return the method recorded by this PointCountEvidence.

Detailed contract

Mathematical route used by this evidence.

PythonRust

(self) -> PointCountMethod

noether::commalg::PointCountEvidence::method · Direct Rust declaration

pub fn method(&self) -> PointCountMethod

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/commalg/test_surface_facade.py:47 · validation/unit/commalg/test_surface_facade.py:88 · validation/unit/infra/test_docs_site_generator.py:101 · validation/unit/infra/test_docs_site_generator.py:102 · validation/unit/infra/test_docs_site_generator.py:151 · validation/unit/infra/test_docs_site_generator.py:36

commalg.PointCountEvidence.modulus

Return the modulus recorded by this PointCountEvidence.

Detailed contract

Exact p-adic modulus used by a trace-formula route.

PythonRust

(self) -> int | None

noether::commalg::PointCountEvidence::modulus · Direct Rust declaration

pub fn modulus(&self) -> Option<&Integer>

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/commalg/test_context_tower_workload.py:87 · validation/unit/commalg/test_residue_ring_facade.py:101 · validation/unit/commalg/test_residue_ring_facade.py:105 · validation/unit/commalg/test_residue_ring_facade.py:110 · validation/unit/commalg/test_residue_ring_facade.py:128 · validation/unit/commalg/test_residue_ring_facade.py:141

commalg.PointCountEvidence.precision

Return the precision recorded by this PointCountEvidence.

Detailed contract

Number of p-adic digits used by a trace-formula route.

PythonRust

(self) -> int | None

noether::commalg::PointCountEvidence::precision · Direct Rust declaration

pub fn precision(&self) -> Option<u64>

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/10_padic_hensel_lifting.py:3 · examples/11_qadic_witt_vectors.py:3 · examples/31_local_fields_and_precision.py:3 · examples/31_local_fields_and_precision.py:34 · examples/31_local_fields_and_precision.py:38 · validation/unit/commalg/test_polynomial_facade.py:102

commalg.PointCountEvidence.stratum_count

Return the stratum count recorded by this PointCountEvidence.

Detailed contract

Number of projective coordinate-support strata in a trace route.

PythonRust

(self) -> int | None

noether::commalg::PointCountEvidence::stratum_count · Direct Rust declaration

pub fn stratum_count(&self) -> Option<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

Executable usage: validation/bench/surface_frobenius.py:117

commalg.PointCountEvidence.trace_bound

Return the trace bound recorded by this PointCountEvidence.

Detailed contract

Weil trace bound used by a trace-formula route.

PythonRust

(self) -> int | None

noether::commalg::PointCountEvidence::trace_bound · Direct Rust declaration

pub fn trace_bound(&self) -> Option<&Integer>

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/bench/surface_frobenius.py:104