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commalg · LocalCompletionMap

10 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.LocalCompletionMap

An explicit finite-precision map to a local power-series completion.

class LocalCompletionMap

noether::commalg::LocalCompletionMap · Direct Rust declaration

pub struct LocalCompletionMap<R: Field> { /* 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/LocalCompletionMap@1

Executable usage: validation/unit/commalg/test_local_algebra.py:8 · validation/unit/commalg/test_local_algebra.py:99

commalg.LocalCompletionMap.apply

Apply this LocalCompletionMap to the supplied value.

Detailed contract

Map one local fraction to its finite jet.

(self, value: LocalPolynomial[_ProjectedIdealFieldContext]) -> PowerSeries[_ProjectedIdealFieldContext]

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

pub fn apply( &self, value: &LocalPolynomial<R>, ) -> Result<PowerSeries<R>, LocalAlgebraError>
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/LocalCompletionMap@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.LocalCompletionMap.from_json

Deserialize and revalidate a LocalCompletionMap from typed JSON.

Detailed contract

Deserialize and reconstruct the derived series target.

(cls, value: str) -> LocalCompletionMap[CoefficientRing]

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

pub fn from_json(value: &str) -> Result<Self, NoetherError>where R: for<'de> Deserialize<'de>, R::Element: 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/LocalCompletionMap@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.LocalCompletionMap.precision

Return the precision recorded by this LocalCompletionMap.

Detailed contract

Strict total-degree precision bound.

(self) -> int

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

pub const fn precision(&self) -> 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
Semantic ID noether/commalg/LocalCompletionMap@1

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.LocalCompletionMap.restrict

Compute restrict for this LocalCompletionMap.

Detailed contract

Restrict this map to one positive, no-finer precision.

(self, precision: int) -> LocalCompletionMap[_ProjectedIdealFieldContext]

noether::commalg::LocalCompletionMap::restrict · Direct Rust declaration

pub fn restrict(&self, precision: u64) -> Result<Self, LocalAlgebraError>
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/LocalCompletionMap@1

Executable usage: validation/unit/commalg/test_local_algebra.py:93 · validation/unit/groups/test_weight_characters.py:48 · validation/unit/numthy/test_padic_local_field_facade.py:100 · validation/unit/numthy/test_padic_ring_facade.py:62 · validation/unit/numthy/test_qadic_ring_facade.py:48

commalg.LocalCompletionMap.restrict_value

Compute restrict value for this LocalCompletionMap.

Detailed contract

Explicitly restrict one value in this target to a no-finer precision.

(self, value: PowerSeries[_ProjectedIdealFieldContext], precision: int) -> PowerSeries[_ProjectedIdealFieldContext]

noether::commalg::LocalCompletionMap::restrict_value · Direct Rust declaration

pub fn restrict_value( &self, value: &PowerSeries<R>, precision: u64, ) -> Result<PowerSeries<R>, LocalAlgebraError>
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/LocalCompletionMap@1

Executable usage: validation/unit/commalg/test_local_algebra.py:97

commalg.LocalCompletionMap.source

Return the source recorded by this LocalCompletionMap.

Detailed contract

Exact source localization.

(self) -> LocalPolynomialRing[_ProjectedIdealFieldContext]

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

pub fn source(&self) -> &LocalPolynomialRing<R>
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/LocalCompletionMap@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.LocalCompletionMap.target

Return the target recorded by this LocalCompletionMap.

Detailed contract

Fixed-truncation power-series target.

(self) -> PowerSeriesRing[_ProjectedIdealFieldContext]

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

pub fn target(&self) -> &PowerSeriesRing<R>
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/LocalCompletionMap@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.LocalCompletionMap.to_json

Serialize this LocalCompletionMap to its canonical typed JSON representation.

Detailed contract

Serialize the source and strict completion precision.

(self) -> str

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

pub fn to_json(&self) -> Result<String, NoetherError>where R: Serialize, R::Element: Serialize,
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/LocalCompletionMap@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.LocalCompletionMap.verify_restriction

Compute verify restriction for this LocalCompletionMap.

Detailed contract

Verify that applying this map and then restricting agrees with a declared coarser map on one exact source value.

(self, coarser: LocalCompletionMap[_ProjectedIdealFieldContext], value: LocalPolynomial[_ProjectedIdealFieldContext]) -> None

noether::commalg::LocalCompletionMap::verify_restriction · Direct Rust declaration

pub fn verify_restriction( &self, coarser: &Self, value: &LocalPolynomial<R>, ) -> Result<(), LocalAlgebraError>
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/LocalCompletionMap@1

Executable usage: validation/unit/commalg/test_local_algebra.py:98