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homalg · ModulePowerKind

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

Worked example

The complete checked program Split rational primes and factor an ideal in the Gaussian integers uses this API directly.

# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Split rational primes and factor an ideal in the Gaussian integers."""

from noether import Q
from noether.commalg import PolynomialRing
from noether.numthy import NumberField


def main() -> None:
    polynomials = PolynomialRing(Q, ["x"])
    field = NumberField(polynomials.generator("x") ** 2 + 1, name="i")
    order = field.maximal_order()
    primes = order.prime_ideals_above(5)
    assert len(primes) == 2
    assert all(prime.norm() == 5 for prime in primes)
    ideal = order.fractional_ideal([1 + field.generator])
    assert ideal.norm() == 2
    print(f"(5) splits into norms {[prime.norm() for prime in primes]}; N(1+i)={ideal.norm()}")


if __name__ == "__main__":
    main()

Run it with .venv/bin/python examples/12_number_field_ideals.py.

homalg.ModulePowerKind

Symmetric or exterior module-power kind.

ModulePowerKind(name: Literal['symmetric', 'exterior'])

noether::homalg::ModulePowerKind · Direct Rust declaration

pub enum ModulePowerKind { Symmetric, Exterior, }
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, m4rst, m4rste, module-core, resolution-kernel, sparla
GIL attached / bounded
Semantic ID noether/homalg/ModulePowerKind@1

Executable usage: validation/unit/homalg/test_module_powers.py:12 · validation/unit/homalg/test_module_powers.py:36 · validation/unit/homalg/test_module_powers.py:54

homalg.ModulePowerKind.from_json

Deserialize and revalidate a ModulePowerKind from typed JSON.

Detailed contract

Deserialize an exact construction kind.

(cls, value: str) -> ModulePowerKind

noether::homalg::ModulePowerKind::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, m4rst, m4rste, module-core, resolution-kernel, sparla
GIL attached / bounded
Semantic ID noether/homalg/ModulePowerKind@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

homalg.ModulePowerKind.name

Return the name recorded by this ModulePowerKind.

Detailed contract

Stable short name.

(self) -> Literal['symmetric', 'exterior']

noether::homalg::ModulePowerKind::name · Direct Rust declaration

pub const fn name(self) -> &'static str
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, flint-core, groebner-kernel, m4rst, m4rste, module-core, resolution-kernel, sparla
GIL attached / bounded
Semantic ID noether/homalg/ModulePowerKind@1

Executable usage: examples/12_number_field_ideals.py:12 · validation/unit/commalg/test_polynomial_facade.py:345 · validation/unit/commalg/test_polynomial_facade.py:44 · validation/unit/commalg/test_polynomial_facade.py:61 · validation/unit/commalg/test_polynomial_facade.py:65 · validation/unit/commalg/test_polynomial_facade.py:72

homalg.ModulePowerKind.to_json

Serialize this ModulePowerKind to its canonical typed JSON representation.

Detailed contract

Serialize this exact construction kind.

(self) -> str

noether::homalg::ModulePowerKind::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, m4rst, m4rste, module-core, resolution-kernel, sparla
GIL attached / bounded
Semantic ID noether/homalg/ModulePowerKind@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