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root · ComplexBallField

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

Worked example

The complete checked program Certify a familiar identity with real and complex balls uses this API directly.

# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Certify a familiar identity with real and complex balls."""

from fractions import Fraction

from noether import ComplexBallField, RealBallField


def main() -> None:
    reals = RealBallField(192)
    one_third = reals(Fraction(1, 3))
    assert (3 * one_third).overlaps(reals.one())

    complexes = ComplexBallField(192)
    imaginary_unit = complexes(0, 1)
    assert (imaginary_unit**2).overlaps(complexes(-1))
    assert (1 + imaginary_unit).overlaps(complexes(1, 1))
    print(f"1/3 = {one_third}; i^2 = {imaginary_unit**2}")


if __name__ == "__main__":
    main()

Run it with .venv/bin/python examples/02_ball_arithmetic.py.

ComplexBallField

A fixed-working-precision certified complex-ball context.

ComplexBallField(precision: int)

noether::ComplexBallField · Direct Rust declaration

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

Executable usage: examples/02_ball_arithmetic.py:15 · examples/02_ball_arithmetic.py:7 · validation/unit/linalg/test_sparse_matrix_facade.py:146 · validation/unit/linalg/test_sparse_matrix_facade.py:7 · validation/unit/numthy/test_number_field_facade.py:55 · validation/unit/numthy/test_number_field_facade.py:7

ComplexBallField.__call__

Call self as a function.

(self, real: int | _Fraction, imaginary: int | _Fraction | None=None) -> ComplexBall

noether::root::ComplexBallField · Python projection

Python projection convenience over this Rust mathematical type
Contract Value
Guarantee rigorous enclosure
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core
GIL attached / bounded
Semantic ID noether/root/ComplexBallField@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

ComplexBallField.from_json

Restore and validate a canonical context representation.

Detailed contract

Deserialize and validate a complex-ball context from canonical JSON.

(cls, value: str) -> ComplexBallField

noether::root::ComplexBallField::from_json · Direct Rust declaration

pub fn from_json(value: &str) -> Result<Self, NoetherError>
Contract Value
Guarantee rigorous enclosure
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core
GIL attached / bounded
Semantic ID noether/root/ComplexBallField@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

ComplexBallField.one

Multiplicative identity.

(self) -> ComplexBall

noether::root::ComplexBallField::one · Direct Rust declaration

fn one(&self) -> Self::Element
Contract Value
Guarantee rigorous enclosure
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core
GIL attached / bounded
Semantic ID noether/root/ComplexBallField@1

Executable usage: examples/02_ball_arithmetic.py:13 · examples/11_qadic_witt_vectors.py:11 · examples/24_homology_and_persistence.py:3 · examples/31_local_fields_and_precision.py:27 · validation/unit/combinatorics/test_poset.py:3 · validation/unit/commalg/test_acceptance_workload.py:37

ComplexBallField.precision

Working precision in bits.

(self) -> int

noether::root::ComplexBallField::precision · Direct Rust declaration

fn precision(&self) -> &Self::Precision
Contract Value
Guarantee rigorous enclosure
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core
GIL attached / bounded
Semantic ID noether/root/ComplexBallField@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

ComplexBallField.to_json

Canonical JSON representation.

Detailed contract

Serialize this context to canonical JSON.

(self) -> str

noether::root::ComplexBallField::to_json · Direct Rust declaration

pub fn to_json(self) -> Result<String, NoetherError>
Contract Value
Guarantee rigorous enclosure
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core
GIL attached / bounded
Semantic ID noether/root/ComplexBallField@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

ComplexBallField.zero

Additive identity.

(self) -> ComplexBall

noether::root::ComplexBallField::zero · Direct Rust declaration

fn zero(&self) -> Self::Element
Contract Value
Guarantee rigorous enclosure
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core
GIL attached / bounded
Semantic ID noether/root/ComplexBallField@1

Executable usage: examples/08_finite_field_extensions.py:11 · examples/10_padic_hensel_lifting.py:15 · examples/40_exterior_algebra.py:26 · examples/distributed/f2_linear_algebra.py:28 · examples/distributed/f2_linear_algebra.py:29 · examples/distributed/f2_linear_algebra.py:30