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numthy · QadicRingRestriction

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

Worked example

The complete checked program Apply and multiply canonical sparse exact operators uses this API directly.

# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Apply and multiply canonical sparse exact operators."""

from noether import Z
from noether.linalg import SparseMatrix, Vector


def main() -> None:
    operator = SparseMatrix.from_triplets(
        Z,
        (3, 3),
        [(0, 0, 2), (0, 2, -1), (1, 1, 3), (2, 0, 4)],
    )
    vector = Vector.from_values(Z, [5, 7, 11])
    image = operator.apply(vector)
    assert image.to_values() == [-1, 21, 20]
    assert (operator @ operator).nnz == 4
    print(f"A v = {image.to_values()}; nnz(A^2) = {(operator @ operator).nnz}")


if __name__ == "__main__":
    main()

Run it with .venv/bin/python examples/05_sparse_exact_operators.py.

numthy.QadicRingRestriction

An explicit digit-discarding map between fixed-cap Witt rings.

class QadicRingRestriction

noether::numthy::QadicRingRestriction · Direct Rust declaration

pub struct QadicRingRestriction { /* private fields */ }
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core
GIL attached / bounded
Semantic ID noether/numthy/QadicRingRestriction@1

Executable usage: validation/unit/numthy/test_qadic_ring_facade.py:18 · validation/unit/numthy/test_qadic_ring_facade.py:78 · validation/unit/numthy/test_qadic_ring_facade.py:81

numthy.QadicRingRestriction.__call__

Coerce the supplied input through this context or mathematical map.

(self, value: QadicElement) -> QadicElement

noether::numthy::QadicRingRestriction · Python projection

Python projection convenience over this Rust mathematical type
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core
GIL attached / bounded
Semantic ID noether/numthy/QadicRingRestriction@1

Executable usage: validation/unit/infra/test_discovery.py:57 · validation/unit/infra/test_public_api_index.py:155 · validation/unit/infra/test_public_api_index.py:169

numthy.QadicRingRestriction.apply

Apply this QadicRingRestriction to the supplied value.

Detailed contract

Discard the high digits of a value from the exact source context.

(self, value: QadicElement) -> QadicElement

noether::numthy::QadicRingRestriction::apply · Direct Rust declaration

pub fn apply( &self, value: &QadicElement, ) -> Result<QadicElement, QadicRestrictionError>
fn apply(&self, value: &QadicElement) -> Result<QadicElement, Self::Error>
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core
GIL attached / bounded
Semantic ID noether/numthy/QadicRingRestriction@1

Executable usage: examples/05_sparse_exact_operators.py:16 · validation/unit/commalg/test_local_algebra.py:94 · validation/unit/commalg/test_local_algebra.py:97 · validation/unit/commalg/test_polynomial_facade.py:199 · validation/unit/commalg/test_quotient_facade.py:186 · validation/unit/groups/test_weight_characters.py:39

numthy.QadicRingRestriction.apply_matrix

Compute apply matrix for this QadicRingRestriction.

(self, value: Matrix[QadicRing]) -> Matrix[QadicRing]

noether::numthy::QadicRingRestriction · Python projection

Python projection convenience over this Rust mathematical type
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core
GIL attached / bounded
Semantic ID noether/numthy/QadicRingRestriction@1

Executable usage: validation/unit/numthy/test_padic_field_facade.py:86 · validation/unit/numthy/test_padic_field_facade.py:95 · validation/unit/numthy/test_padic_local_field_facade.py:148 · validation/unit/numthy/test_padic_local_field_facade.py:161 · validation/unit/numthy/test_padic_ring_facade.py:102 · validation/unit/numthy/test_qadic_field_facade.py:113

numthy.QadicRingRestriction.apply_polynomial

Compute apply polynomial for this QadicRingRestriction.

(self, value: Polynomial[QadicRing]) -> Polynomial[QadicRing]

noether::numthy::QadicRingRestriction · Python projection

Python projection convenience over this Rust mathematical type
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core
GIL attached / bounded
Semantic ID noether/numthy/QadicRingRestriction@1

Executable usage: validation/unit/numthy/test_padic_field_facade.py:84 · validation/unit/numthy/test_padic_field_facade.py:92 · validation/unit/numthy/test_padic_local_field_facade.py:129 · validation/unit/numthy/test_padic_local_field_facade.py:158 · validation/unit/numthy/test_padic_local_field_facade.py:164 · validation/unit/numthy/test_padic_ring_facade.py:99

numthy.QadicRingRestriction.apply_power_series

Compute apply power series for this QadicRingRestriction.

(self, value: PowerSeries[QadicRing]) -> PowerSeries[QadicRing]

noether::numthy::QadicRingRestriction · Python projection

Python projection convenience over this Rust mathematical type
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core
GIL attached / bounded
Semantic ID noether/numthy/QadicRingRestriction@1

Executable usage: validation/unit/commalg/test_power_series_facade.py:315 · validation/unit/commalg/test_power_series_facade.py:320 · validation/unit/numthy/test_padic_local_field_facade.py:135 · validation/unit/numthy/test_padic_local_field_facade.py:159 · validation/unit/numthy/test_padic_local_field_facade.py:167 · validation/unit/numthy/test_padic_ring_facade.py:100

numthy.QadicRingRestriction.apply_vector

Compute apply vector for this QadicRingRestriction.

(self, value: Vector[QadicRing]) -> Vector[QadicRing]

noether::numthy::QadicRingRestriction · Python projection

Python projection convenience over this Rust mathematical type
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core
GIL attached / bounded
Semantic ID noether/numthy/QadicRingRestriction@1

Executable usage: validation/unit/numthy/test_padic_field_facade.py:85 · validation/unit/numthy/test_padic_field_facade.py:94 · validation/unit/numthy/test_padic_local_field_facade.py:147 · validation/unit/numthy/test_padic_local_field_facade.py:160 · validation/unit/numthy/test_padic_ring_facade.py:101 · validation/unit/numthy/test_qadic_field_facade.py:112

numthy.QadicRingRestriction.from_json

Deserialize and revalidate a QadicRingRestriction from typed JSON.

Detailed contract

Deserialize and revalidate both endpoint contexts and their precision relation.

(cls, value: str) -> QadicRingRestriction

noether::numthy::QadicRingRestriction::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
GIL attached / bounded
Semantic ID noether/numthy/QadicRingRestriction@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

numthy.QadicRingRestriction.source

Return the source recorded by this QadicRingRestriction.

Detailed contract

Source fixed-cap Witt ring.

(self) -> QadicRing

noether::numthy::QadicRingRestriction::source · Direct Rust declaration

pub fn source(&self) -> &QadicRing
fn source(&self) -> &Self::Source
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core
GIL attached / bounded
Semantic ID noether/numthy/QadicRingRestriction@1

Executable usage: examples/09_finite_field_isomorphisms.py:11 · examples/09_finite_field_isomorphisms.py:13 · examples/09_finite_field_isomorphisms.py:9 · examples/30_modules_and_resolutions.py:34 · examples/30_modules_and_resolutions.py:37 · validation/unit/category/test_acceptance_workload.py:25

numthy.QadicRingRestriction.target

Return the target recorded by this QadicRingRestriction.

Detailed contract

Target fixed-cap Witt ring.

(self) -> QadicRing

noether::numthy::QadicRingRestriction::target · Direct Rust declaration

pub fn target(&self) -> &QadicRing
fn target(&self) -> &Self::Target
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core
GIL attached / bounded
Semantic ID noether/numthy/QadicRingRestriction@1

Executable usage: examples/09_finite_field_isomorphisms.py:10 · examples/09_finite_field_isomorphisms.py:11 · examples/30_modules_and_resolutions.py:33 · examples/30_modules_and_resolutions.py:38 · examples/31_local_fields_and_precision.py:27 · examples/36_affine_normalization.py:16

numthy.QadicRingRestriction.to_json

Serialize this QadicRingRestriction to its canonical typed JSON representation.

Detailed contract

Canonical JSON containing both endpoint contexts.

(self) -> str

noether::numthy::QadicRingRestriction::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
GIL attached / bounded
Semantic ID noether/numthy/QadicRingRestriction@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

numthy.QadicRingRestriction.verify

Replay and verify the mathematical evidence carried by this QadicRingRestriction.

Detailed contract

Recheck the source/target relationship defining this map.

(self) -> None

noether::numthy::QadicRingRestriction::verify · Direct Rust declaration

pub fn verify(&self) -> Result<(), VerificationError>
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core
GIL attached / bounded
Semantic ID noether/numthy/QadicRingRestriction@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