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commalg · RationalFunctionFieldMap

9 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.

commalg.RationalFunctionFieldMap

A checked coefficientwise map between finite rational-function fields.

class RationalFunctionFieldMap

noether::commalg::RationalFunctionFieldMap · Direct Rust declaration

pub struct RationalFunctionFieldMap<S, T, M>where S: Field, T: Field, M: CoefficientMap<Source = S, Target = T>,{ /* 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
Semantic ID noether/commalg/RationalFunctionFieldMap@1

Executable usage: validation/unit/commalg/test_rational_function_facade.py:127 · validation/unit/commalg/test_rational_function_facade.py:133 · validation/unit/commalg/test_rational_function_facade.py:17 · validation/unit/infra/test_public_api_index.py:279

commalg.RationalFunctionFieldMap.__call__

Coerce the supplied input through this context or mathematical map.

(self, value: RationalFunction[FiniteField]) -> RationalFunction[FiniteField]

noether::commalg::RationalFunctionFieldMap · 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, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/RationalFunctionFieldMap@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

commalg.RationalFunctionFieldMap.apply

Apply this RationalFunctionFieldMap to the supplied value.

(self, value: RationalFunction[FiniteField]) -> RationalFunction[FiniteField]

noether::commalg::RationalFunctionFieldMap::apply · Direct Rust declaration

fn apply( &self, value: &RationalFunction<S>, ) -> Result<RationalFunction<T>, Self::Error>
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
Semantic ID noether/commalg/RationalFunctionFieldMap@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

commalg.RationalFunctionFieldMap.coefficient_map

Return the coefficient map recorded by this RationalFunctionFieldMap.

Detailed contract

Field-coefficient map inducing this extension.

(self) -> PrimeSubfieldEmbedding

noether::commalg::RationalFunctionFieldMap::coefficient_map · Direct Rust declaration

pub fn coefficient_map(&self) -> &M
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
Semantic ID noether/commalg/RationalFunctionFieldMap@1

Executable usage: validation/unit/commalg/test_base_change.py:121 · validation/unit/commalg/test_base_change.py:123 · validation/unit/commalg/test_base_change.py:69 · validation/unit/commalg/test_polynomial_homomorphism.py:22 · validation/unit/commalg/test_polynomial_homomorphism.py:31 · validation/unit/commalg/test_polynomial_homomorphism.py:46

commalg.RationalFunctionFieldMap.from_json

Deserialize and revalidate a RationalFunctionFieldMap from typed JSON.

Detailed contract

Deserialize and revalidate both exact endpoints.

(cls, value: str) -> RationalFunctionFieldMap

noether::commalg::RationalFunctionFieldMap::from_json · Direct Rust declaration

pub fn from_json(value: &str) -> Result<Self, NoetherError>where S: for<'de> Deserialize<'de>, T: for<'de> Deserialize<'de>, M: for<'de> Deserialize<'de>,
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
Semantic ID noether/commalg/RationalFunctionFieldMap@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

commalg.RationalFunctionFieldMap.source

Return the source recorded by this RationalFunctionFieldMap.

Detailed contract

Explicit source rational-function field.

(self) -> RationalFunctionField[FiniteField]

noether::commalg::RationalFunctionFieldMap::source · Direct Rust declaration

pub fn source(&self) -> &RationalFunctionField<S>
fn source(&self) -> &Self::Source
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
Semantic ID noether/commalg/RationalFunctionFieldMap@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

commalg.RationalFunctionFieldMap.target

Return the target recorded by this RationalFunctionFieldMap.

Detailed contract

Explicit target rational-function field.

(self) -> RationalFunctionField[FiniteField]

noether::commalg::RationalFunctionFieldMap::target · Direct Rust declaration

pub fn target(&self) -> &RationalFunctionField<T>
fn target(&self) -> &Self::Target
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
Semantic ID noether/commalg/RationalFunctionFieldMap@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

commalg.RationalFunctionFieldMap.to_json

Serialize this RationalFunctionFieldMap to its canonical typed JSON representation.

Detailed contract

Serialize both fields and the checked inducing map.

(self) -> str

noether::commalg::RationalFunctionFieldMap::to_json · Direct Rust declaration

pub fn to_json(&self) -> Result<String, NoetherError>where S: Serialize, T: Serialize, M: Serialize + Clone,
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
Semantic ID noether/commalg/RationalFunctionFieldMap@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

commalg.RationalFunctionFieldMap.verify

Replay and verify the mathematical evidence carried by this RationalFunctionFieldMap.

Detailed contract

Verify exact identity of both inducing-map endpoints.

(self) -> None

noether::commalg::RationalFunctionFieldMap::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, groebner-kernel, module-core, poly-core, resolution-kernel
GIL attached / bounded
Semantic ID noether/commalg/RationalFunctionFieldMap@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