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numthy · PadicLocalFieldRestriction

13 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.PadicLocalFieldRestriction

A checked digit-discarding map between ramified local precision contexts.

class PadicLocalFieldRestriction

noether::numthy::PadicLocalFieldRestriction · Direct Rust declaration

pub struct PadicLocalFieldRestriction { /* 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/PadicLocalFieldRestriction@1

Executable usage: validation/unit/numthy/test_padic_local_field_facade.py:17 · validation/unit/numthy/test_padic_local_field_facade.py:92 · validation/unit/numthy/test_padic_local_field_facade.py:98

numthy.PadicLocalFieldRestriction.__call__

Coerce the supplied input through this context or mathematical map.

(self, value: PadicLocalFieldElement) -> PadicLocalFieldElement

noether::numthy::PadicLocalFieldRestriction · 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/PadicLocalFieldRestriction@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.PadicLocalFieldRestriction.apply

Apply this PadicLocalFieldRestriction to the supplied value.

Detailed contract

Apply the restriction after checking exact source identity.

(self, value: PadicLocalFieldElement) -> PadicLocalFieldElement

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

pub fn apply( &self, value: &PadicLocalFieldElement, ) -> Result<PadicLocalFieldElement, PadicLocalFieldRestrictionError>
fn apply( &self, value: &<Self::Source as Ring>::Element, ) -> Result<<Self::Target as Ring>::Element, 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/PadicLocalFieldRestriction@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.PadicLocalFieldRestriction.apply_matrix

Compute apply matrix for this PadicLocalFieldRestriction.

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

noether::numthy::PadicLocalFieldRestriction · 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/PadicLocalFieldRestriction@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.PadicLocalFieldRestriction.apply_polynomial

Compute apply polynomial for this PadicLocalFieldRestriction.

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

noether::numthy::PadicLocalFieldRestriction · 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/PadicLocalFieldRestriction@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.PadicLocalFieldRestriction.apply_power_series

Compute apply power series for this PadicLocalFieldRestriction.

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

noether::numthy::PadicLocalFieldRestriction · 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/PadicLocalFieldRestriction@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.PadicLocalFieldRestriction.apply_sparse_matrix

Compute apply sparse matrix for this PadicLocalFieldRestriction.

(self, value: SparseMatrix[PadicLocalField]) -> SparseMatrix[PadicLocalField]

noether::numthy::PadicLocalFieldRestriction · 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/PadicLocalFieldRestriction@1

Executable usage: validation/unit/numthy/test_padic_local_field_facade.py:149 · validation/unit/numthy/test_padic_local_field_facade.py:162 · validation/unit/numthy/test_padic_ring_facade.py:103

numthy.PadicLocalFieldRestriction.apply_vector

Compute apply vector for this PadicLocalFieldRestriction.

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

noether::numthy::PadicLocalFieldRestriction · 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/PadicLocalFieldRestriction@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.PadicLocalFieldRestriction.from_json

Deserialize and revalidate a PadicLocalFieldRestriction from typed JSON.

Detailed contract

Deserialize and revalidate both endpoint contexts and their relation.

(cls, value: str) -> PadicLocalFieldRestriction

noether::numthy::PadicLocalFieldRestriction::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/PadicLocalFieldRestriction@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.PadicLocalFieldRestriction.source

Return the source recorded by this PadicLocalFieldRestriction.

Detailed contract

Exact source context.

(self) -> PadicLocalField

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

pub fn source(&self) -> &PadicLocalField
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/PadicLocalFieldRestriction@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.PadicLocalFieldRestriction.target

Return the target recorded by this PadicLocalFieldRestriction.

Detailed contract

Distinct lower-cap target context.

(self) -> PadicLocalField

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

pub fn target(&self) -> &PadicLocalField
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/PadicLocalFieldRestriction@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.PadicLocalFieldRestriction.to_json

Serialize this PadicLocalFieldRestriction to its canonical typed JSON representation.

Detailed contract

Canonical JSON containing both endpoint contexts.

(self) -> str

noether::numthy::PadicLocalFieldRestriction::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/PadicLocalFieldRestriction@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.PadicLocalFieldRestriction.verify

Replay and verify the mathematical evidence carried by this PadicLocalFieldRestriction.

Detailed contract

Recheck the presentation identity and direction of precision loss.

(self) -> None

noether::numthy::PadicLocalFieldRestriction::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/PadicLocalFieldRestriction@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