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commalg · CurveFunctionEvaluation

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

Worked example

The complete checked program Use the fixed-precision Witt ring W(F_9) uses this API directly.

# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Use the fixed-precision Witt ring W(F_9)."""

from noether.numthy import FiniteField, QadicRing


def main() -> None:
    residue_field = FiniteField.extension(3, 2)
    witt_ring = QadicRing(residue_field, absolute_precision=4)
    residue = residue_field.generator() + residue_field.one()
    lift = witt_ring.teichmuller(residue)
    assert witt_ring.residue(lift) == residue
    assert lift**residue_field.order == lift
    print(f"Teichmuller({residue}) = {lift}")


if __name__ == "__main__":
    main()

Run it with .venv/bin/python examples/11_qadic_witt_vectors.py.

commalg.CurveFunctionEvaluation

Typed regular value, zero, or pole of a curve function.

class CurveFunctionEvaluation

noether::commalg::CurveFunctionEvaluation · Direct Rust declaration

pub enum CurveFunctionEvaluation<R: Field> { Regular(R::Element), Zero { order: Option<Integer>, }, Pole { order: Integer, }, }
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

Executable usage: validation/unit/commalg/test_curve_facade.py:10 · validation/unit/commalg/test_curve_facade.py:42

commalg.CurveFunctionEvaluation.kind

Return the kind recorded by this CurveFunctionEvaluation.

(self) -> Literal['regular', 'zero', 'pole']

noether::commalg::CurveFunctionEvaluation · 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

Executable usage: validation/unit/combinatorics/test_poset.py:95 · validation/unit/commalg/test_curve_facade.py:137 · validation/unit/commalg/test_curve_facade.py:43 · validation/unit/commalg/test_curve_facade.py:44 · validation/unit/commalg/test_curve_facade.py:45 · validation/unit/commalg/test_curve_facade.py:80

commalg.CurveFunctionEvaluation.order

Return the order recorded by this CurveFunctionEvaluation.

(self) -> int | None

noether::commalg::CurveFunctionEvaluation · 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

Executable usage: examples/11_qadic_witt_vectors.py:14 · examples/12_number_field_ideals.py:13 · examples/12_number_field_ideals.py:14 · examples/12_number_field_ideals.py:17 · examples/15_groebner_twisted_cubic.py:18 · examples/19_permutation_groups.py:13

commalg.CurveFunctionEvaluation.value

Return the value recorded by this CurveFunctionEvaluation.

(self) -> CurveCoefficient | None

noether::commalg::CurveFunctionEvaluation · 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

Executable usage: examples/09_finite_field_isomorphisms.py:13 · examples/09_finite_field_isomorphisms.py:14 · examples/13_chinese_remainder_theorem.py:12 · examples/13_chinese_remainder_theorem.py:13 · examples/13_chinese_remainder_theorem.py:14 · examples/17_weighted_power_series.py:18