Skip to content

commalg · ResidueClass

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

Worked example

The complete checked program Calculate in a fixed-cap multivariate weighted power-series ring uses this API directly.

# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Calculate in a fixed-cap multivariate weighted power-series ring."""

from noether import Z
from noether.commalg import PowerSeriesRing, SeriesTruncation


def main() -> None:
    ring = PowerSeriesRing(
        Z,
        ["x", "y", "z"],
        SeriesTruncation.weighted_degree([1, 2, 3], 6),
    )
    x, y, z = ring.generators()
    assert (x**6).is_zero()
    assert not (x**2 * z + y * z).is_zero()
    value = (1 + x + y).pow(4)
    print(f"{value}; coefficient capacity <= {ring.coefficient_capacity_bound()}")


if __name__ == "__main__":
    main()

Run it with .venv/bin/python examples/17_weighted_power_series.py.

commalg.ResidueClass

An exact residue class carrying its concrete ring context.

class ResidueClass

noether::commalg::ResidueClass · Direct Rust declaration

pub struct ResidueClass { /* 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/ResidueClass@1

Executable usage: validation/unit/commalg/test_context_tower_workload.py:13 · validation/unit/commalg/test_context_tower_workload.py:73 · validation/unit/commalg/test_residue_ring_facade.py:10 · validation/unit/commalg/test_residue_ring_facade.py:112 · validation/unit/commalg/test_residue_ring_facade.py:117 · validation/unit/commalg/test_residue_ring_facade.py:20

commalg.ResidueClass.__add__

Add another compatible value to this value.

Detailed contract

Returns the argument unchanged.

(self, other: ResidueClass) -> ResidueClass

noether::commalg::ResidueClass::add · Direct Rust declaration

fn add(self, rhs: &ResidueClass) -> Self::Output
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/ResidueClass@1

Executable usage: validation/unit/infra/test_discovery.py:211 · validation/unit/infra/test_public_api_index.py:293

commalg.ResidueClass.__int__

Compute int for this ResidueClass.

(self) -> int

noether::commalg::ResidueClass · 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/ResidueClass@1

commalg.ResidueClass.__mul__

Multiply this value by another compatible value.

(self, other: ResidueClass) -> ResidueClass

noether::commalg::ResidueClass::mul · Direct Rust declaration

fn mul(self, rhs: &ResidueClass) -> Self::Output
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/ResidueClass@1

Executable usage: validation/unit/infra/test_public_api_index.py:214

commalg.ResidueClass.__neg__

Return the additive inverse of this value.

(self) -> ResidueClass

noether::commalg::ResidueClass::neg · Direct Rust declaration

fn neg(self) -> Self::Output
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/ResidueClass@1

commalg.ResidueClass.__pow__

Raise this value to the supplied power.

(self, exponent: int, modulus: None=None) -> ResidueClass

noether::commalg::ResidueClass · 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/ResidueClass@1

commalg.ResidueClass.__sub__

Subtract another compatible value from this value.

(self, other: ResidueClass) -> ResidueClass

noether::commalg::ResidueClass::sub · Direct Rust declaration

fn sub(self, rhs: &ResidueClass) -> Self::Output
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/ResidueClass@1

Executable usage: validation/unit/infra/test_discovery.py:212

commalg.ResidueClass.from_json

Deserialize and revalidate a residue class and its ring context.

(cls, value: str) -> ResidueClass

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

Compute inverse for this ResidueClass.

Detailed contract

Return the multiplicative inverse of this class when it is a unit.

(self) -> ResidueClass

noether::commalg::ResidueClass::inverse · Direct Rust declaration

pub fn inverse(&self) -> Result<Self, NonUnitError>
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/ResidueClass@1

Executable usage: examples/distributed/f2_linear_algebra.py:37 · examples/distributed/f2_linear_algebra.py:39 · validation/unit/commalg/test_context_tower_workload.py:121 · validation/unit/commalg/test_context_tower_workload.py:122 · validation/unit/commalg/test_context_tower_workload.py:75 · validation/unit/commalg/test_context_tower_workload.py:77

commalg.ResidueClass.is_one

Test whether this ResidueClass is one.

Detailed contract

Whether this class is one.

(self) -> bool

noether::commalg::ResidueClass::is_one · Direct Rust declaration

pub fn is_one(&self) -> bool
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/ResidueClass@1

Executable usage: validation/unit/commalg/test_rational_function_facade.py:31 · validation/unit/commalg/test_residue_ring_facade.py:25 · validation/unit/numthy/test_number_field_facade.py:29 · validation/corpus/commalg/evolution-algebra-isomorphism.py:34 · validation/corpus/numthy/diagonal-quadric-local-density-sums.py:36

commalg.ResidueClass.is_unit

Test whether this ResidueClass is unit.

Detailed contract

Whether this class has a multiplicative inverse.

(self) -> bool

noether::commalg::ResidueClass::is_unit · Direct Rust declaration

pub fn is_unit(&self) -> bool
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/ResidueClass@1

Executable usage: validation/unit/commalg/test_local_algebra.py:44 · validation/unit/commalg/test_local_algebra.py:59 · validation/unit/commalg/test_prime_localization.py:25 · validation/unit/commalg/test_prime_localization.py:26 · validation/unit/commalg/test_prime_localization.py:47 · validation/unit/commalg/test_quotient_facade.py:51

commalg.ResidueClass.is_zero

Test whether this ResidueClass is zero.

Detailed contract

Whether this class is zero.

(self) -> bool

noether::commalg::ResidueClass::is_zero · Direct Rust declaration

pub fn is_zero(&self) -> bool
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/ResidueClass@1

Executable usage: examples/17_weighted_power_series.py:16 · examples/17_weighted_power_series.py:17 · examples/39_kahler_differentials.py:20 · validation/unit/commalg/test_graded_commutative_facade.py:26 · validation/unit/commalg/test_kahler_differentials.py:113 · validation/unit/commalg/test_kahler_differentials.py:38

commalg.ResidueClass.pow

Compute pow for this ResidueClass.

Detailed contract

Raise this class to a nonnegative power.

(self, exponent: int) -> ResidueClass

noether::commalg::ResidueClass::pow · Direct Rust declaration

pub fn pow(&self, exponent: u64) -> Self
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/ResidueClass@1

Executable usage: examples/17_weighted_power_series.py:18 · validation/unit/commalg/test_polynomial_ideal_facade.py:368 · validation/unit/commalg/test_polynomial_ideal_facade.py:369 · validation/unit/commalg/test_polynomial_ideal_facade.py:370 · validation/unit/commalg/test_polynomial_ideal_facade.py:373 · validation/unit/commalg/test_polynomial_ideal_facade.py:381

commalg.ResidueClass.representative

Return the representative recorded by this ResidueClass.

Detailed contract

The canonical representative in [0, n).

(self) -> int

noether::commalg::ResidueClass::representative · Direct Rust declaration

pub fn representative(&self) -> &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
Semantic ID noether/commalg/ResidueClass@1

Executable usage: validation/unit/commalg/test_residue_ring_facade.py:101 · validation/unit/commalg/test_residue_ring_facade.py:110 · validation/unit/commalg/test_residue_ring_facade.py:129 · validation/unit/commalg/test_residue_ring_facade.py:26 · validation/unit/commalg/test_residue_ring_facade.py:80 · validation/unit/groups/test_acceptance_workload.py:125

commalg.ResidueClass.ring

Return the ring recorded by this ResidueClass.

Detailed contract

The concrete residue ring containing this value.

(self) -> ResidueRing

noether::commalg::ResidueClass::ring · Direct Rust declaration

pub fn ring(&self) -> &ResidueRing
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/ResidueClass@1

Executable usage: examples/11_qadic_witt_vectors.py:3 · examples/13_chinese_remainder_theorem.py:10 · examples/13_chinese_remainder_theorem.py:12 · examples/13_chinese_remainder_theorem.py:9 · examples/14_weighted_polynomials.py:10 · examples/14_weighted_polynomials.py:11

commalg.ResidueClass.to_json

Serialize the ring context and canonical representative as typed JSON.

(self) -> str

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