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numthy · PadicLocalFieldCoefficientFrobenius

16 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.PadicLocalFieldCoefficientFrobenius

Coefficient Frobenius from a local field to its conjugate presentation.

class PadicLocalFieldCoefficientFrobenius

noether::numthy::PadicLocalFieldCoefficientFrobenius · Direct Rust declaration

pub struct PadicLocalFieldCoefficientFrobenius { /* 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/PadicLocalFieldCoefficientFrobenius@1

Executable usage: validation/unit/numthy/test_padic_local_field_facade.py:111 · validation/unit/numthy/test_padic_local_field_facade.py:119 · validation/unit/numthy/test_padic_local_field_facade.py:14

numthy.PadicLocalFieldCoefficientFrobenius.__call__

Coerce the supplied input through this context or mathematical map.

(self, value: PadicLocalFieldElement) -> PadicLocalFieldElement

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

Apply this PadicLocalFieldCoefficientFrobenius to the supplied value.

Detailed contract

Twist every normalized q-adic coordinate and fix the uniformizer.

(self, value: PadicLocalFieldElement) -> PadicLocalFieldElement

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

pub fn apply( &self, value: &PadicLocalFieldElement, ) -> Result<PadicLocalFieldElement, PadicLocalCoefficientFrobeniusError>
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/PadicLocalFieldCoefficientFrobenius@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.PadicLocalFieldCoefficientFrobenius.apply_matrix

Compute apply matrix for this PadicLocalFieldCoefficientFrobenius.

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

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

Compute apply polynomial for this PadicLocalFieldCoefficientFrobenius.

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

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

Compute apply power series for this PadicLocalFieldCoefficientFrobenius.

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

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

Compute apply sparse matrix for this PadicLocalFieldCoefficientFrobenius.

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

noether::numthy::PadicLocalFieldCoefficientFrobenius · 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/PadicLocalFieldCoefficientFrobenius@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.PadicLocalFieldCoefficientFrobenius.apply_vector

Compute apply vector for this PadicLocalFieldCoefficientFrobenius.

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

noether::numthy::PadicLocalFieldCoefficientFrobenius · 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/PadicLocalFieldCoefficientFrobenius@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.PadicLocalFieldCoefficientFrobenius.compose

Compose this PadicLocalFieldCoefficientFrobenius with another compatible map.

Detailed contract

Compose self after a map ending at this source presentation.

(self, inner: PadicLocalFieldCoefficientFrobenius) -> PadicLocalFieldCoefficientFrobenius

noether::numthy::PadicLocalFieldCoefficientFrobenius::compose · Direct Rust declaration

pub fn compose( &self, inner: &Self, ) -> Result<Self, PadicLocalCoefficientFrobeniusError>
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/PadicLocalFieldCoefficientFrobenius@1

Executable usage: validation/unit/commalg/test_context_tower_workload.py:3 · validation/unit/commalg/test_polynomial_facade.py:200 · validation/unit/commalg/test_power_series_facade.py:151 · validation/unit/commalg/test_power_series_facade.py:245 · validation/unit/commalg/test_power_series_facade.py:248 · validation/unit/groups/test_permutation_group_facade.py:41

numthy.PadicLocalFieldCoefficientFrobenius.exponent

Return the exponent recorded by this PadicLocalFieldCoefficientFrobenius.

Detailed contract

Unreduced nonnegative coefficient Frobenius exponent.

(self) -> int

noether::numthy::PadicLocalFieldCoefficientFrobenius::exponent · Direct Rust declaration

pub fn exponent(&self) -> u64
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/PadicLocalFieldCoefficientFrobenius@1

Executable usage: examples/31_local_fields_and_precision.py:38 · validation/unit/commalg/test_base_change.py:93 · validation/unit/commalg/test_groebner_verification_budget.py:32 · validation/unit/commalg/test_groebner_verification_budget.py:33 · validation/unit/commalg/test_groebner_verification_budget.py:34 · validation/unit/commalg/test_groebner_verification_budget.py:35

numthy.PadicLocalFieldCoefficientFrobenius.from_json

Deserialize and revalidate a PadicLocalFieldCoefficientFrobenius from typed JSON.

Detailed contract

Deserialize and revalidate the conjugated target presentation.

(cls, value: str) -> PadicLocalFieldCoefficientFrobenius

noether::numthy::PadicLocalFieldCoefficientFrobenius::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/PadicLocalFieldCoefficientFrobenius@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.PadicLocalFieldCoefficientFrobenius.is_endomorphism

Test whether this PadicLocalFieldCoefficientFrobenius is endomorphism.

Detailed contract

Whether coefficient conjugation returns to the same presented context.

(self) -> bool

noether::numthy::PadicLocalFieldCoefficientFrobenius::is_endomorphism · Direct Rust declaration

pub fn is_endomorphism(&self) -> bool
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/PadicLocalFieldCoefficientFrobenius@1

Executable usage: validation/unit/numthy/test_padic_local_field_facade.py:114

numthy.PadicLocalFieldCoefficientFrobenius.source

Return the source recorded by this PadicLocalFieldCoefficientFrobenius.

Detailed contract

Exact presented source field.

(self) -> PadicLocalField

noether::numthy::PadicLocalFieldCoefficientFrobenius::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/PadicLocalFieldCoefficientFrobenius@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.PadicLocalFieldCoefficientFrobenius.target

Return the target recorded by this PadicLocalFieldCoefficientFrobenius.

Detailed contract

Exact coefficient-conjugate target field.

(self) -> PadicLocalField

noether::numthy::PadicLocalFieldCoefficientFrobenius::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/PadicLocalFieldCoefficientFrobenius@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.PadicLocalFieldCoefficientFrobenius.to_json

Serialize this PadicLocalFieldCoefficientFrobenius to its canonical typed JSON representation.

Detailed contract

Canonical JSON preserving both endpoint presentations.

(self) -> str

noether::numthy::PadicLocalFieldCoefficientFrobenius::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/PadicLocalFieldCoefficientFrobenius@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.PadicLocalFieldCoefficientFrobenius.verify

Replay and verify the mathematical evidence carried by this PadicLocalFieldCoefficientFrobenius.

Detailed contract

Recompute the conjugate presentation and verify the stored target.

(self) -> None

noether::numthy::PadicLocalFieldCoefficientFrobenius::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/PadicLocalFieldCoefficientFrobenius@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