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topology · EilenbergMacLaneModularCohomology

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

Worked example

The complete checked program Calculate trace and norm in a concrete quadratic finite field uses this API directly.

# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Calculate trace and norm in a concrete quadratic finite field."""

from noether.numthy import FiniteField


def main() -> None:
    field = FiniteField.extension(5, 2)
    generator = field.generator()
    assert generator**2 + field(4) * generator + field(2) == field.zero()
    assert generator.trace() == field(1)
    assert generator.norm() == field(2)
    print(f"{field}: Tr(a)={generator.trace()}, Nm(a)={generator.norm()}")


if __name__ == "__main__":
    main()

Run it with .venv/bin/python examples/08_finite_field_extensions.py.

topology.EilenbergMacLaneModularCohomology

A complete prime-field cohomology presentation of a symbolic K(A,n).

class EilenbergMacLaneModularCohomology

noether::topology::EilenbergMacLaneModularCohomology · Direct Rust declaration

pub struct EilenbergMacLaneModularCohomology { /* private fields */ }
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, geom-core, m4rst, m4rste
GIL attached / bounded
Semantic ID noether/topology/EilenbergMacLaneModularCohomology@1

Executable usage: validation/unit/topology/test_eilenberg_maclane.py:155 · validation/unit/topology/test_eilenberg_maclane.py:16 · validation/unit/topology/test_eilenberg_maclane.py:175

topology.EilenbergMacLaneModularCohomology.field

Return the field recorded by this EilenbergMacLaneModularCohomology.

Detailed contract

Exact coefficient field.

(self) -> FiniteField

noether::topology::EilenbergMacLaneModularCohomology::field · Direct Rust declaration

pub fn field(&self) -> &FiniteField
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, geom-core, m4rst, m4rste
GIL attached / bounded
Semantic ID noether/topology/EilenbergMacLaneModularCohomology@1

Executable usage: examples/08_finite_field_extensions.py:10 · examples/08_finite_field_extensions.py:11 · examples/08_finite_field_extensions.py:12 · examples/08_finite_field_extensions.py:13 · examples/08_finite_field_extensions.py:14 · examples/08_finite_field_extensions.py:3

topology.EilenbergMacLaneModularCohomology.from_json

Deserialize and revalidate a EilenbergMacLaneModularCohomology from typed JSON.

Detailed contract

Deserialize and reconstruct a complete modular presentation.

(cls, value: str) -> EilenbergMacLaneModularCohomology

noether::topology::EilenbergMacLaneModularCohomology::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, geom-core, m4rst, m4rste
GIL attached / bounded
Semantic ID noether/topology/EilenbergMacLaneModularCohomology@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

topology.EilenbergMacLaneModularCohomology.generators

Return the generators recorded by this EilenbergMacLaneModularCohomology.

Detailed contract

Stable generator metadata in the presentation’s generator order.

(self) -> list[EilenbergMacLaneCohomologyGenerator]

noether::topology::EilenbergMacLaneModularCohomology::generators · Direct Rust declaration

pub fn generators(&self) -> &[EilenbergMacLaneCohomologyGenerator]
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, geom-core, m4rst, m4rste
GIL attached / bounded
Semantic ID noether/topology/EilenbergMacLaneModularCohomology@1

Executable usage: examples/14_weighted_polynomials.py:11 · examples/15_groebner_twisted_cubic.py:11 · examples/15_groebner_twisted_cubic.py:19 · examples/17_weighted_power_series.py:15 · examples/18_finite_field_schemes.py:12 · examples/30_modules_and_resolutions.py:20

topology.EilenbergMacLaneModularCohomology.operations

Return the operations recorded by this EilenbergMacLaneModularCohomology.

Detailed contract

Primary operations computed on presentation generators.

(self) -> list[EilenbergMacLaneCohomologyOperation]

noether::topology::EilenbergMacLaneModularCohomology::operations · Direct Rust declaration

pub fn operations(&self) -> &[EilenbergMacLaneCohomologyOperation]
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, geom-core, m4rst, m4rste
GIL attached / bounded
Semantic ID noether/topology/EilenbergMacLaneModularCohomology@1

Executable usage: validation/unit/infra/test_corpus_acceptance.py:106 · validation/unit/infra/test_corpus_acceptance.py:107 · validation/unit/infra/test_corpus_acceptance.py:108 · validation/unit/infra/test_corpus_acceptance.py:92 · validation/unit/infra/test_discovery.py:248 · validation/unit/infra/test_discovery.py:293

topology.EilenbergMacLaneModularCohomology.presentation

Return the presentation recorded by this EilenbergMacLaneModularCohomology.

Detailed contract

Complete graded-commutative quotient presentation.

(self) -> GradedCommutativePresentation

noether::topology::EilenbergMacLaneModularCohomology::presentation · Direct Rust declaration

pub fn presentation(&self) -> &GradedCommutativePresentation
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, geom-core, m4rst, m4rste
GIL attached / bounded
Semantic ID noether/topology/EilenbergMacLaneModularCohomology@1

Executable usage: examples/34_finite_group_cohomology.py:3 · validation/unit/category/test_category.py:70 · validation/unit/category/test_category.py:71 · validation/unit/category/test_category.py:72 · validation/unit/commalg/test_graded_commutative_facade.py:24 · validation/unit/commalg/test_graded_commutative_facade.py:25

topology.EilenbergMacLaneModularCohomology.space

Return the space recorded by this EilenbergMacLaneModularCohomology.

Detailed contract

Symbolic source space.

(self) -> EilenbergMacLaneSpace

noether::topology::EilenbergMacLaneModularCohomology::space · Direct Rust declaration

pub fn space(&self) -> &EilenbergMacLaneSpace
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, geom-core, m4rst, m4rste
GIL attached / bounded
Semantic ID noether/topology/EilenbergMacLaneModularCohomology@1

Executable usage: examples/03_exact_linear_systems.py:3 · validation/unit/commalg/test_curve_facade.py:116 · validation/unit/commalg/test_curve_facade.py:123 · validation/unit/commalg/test_curve_facade.py:124 · validation/unit/commalg/test_curve_facade.py:126 · validation/unit/commalg/test_curve_facade.py:73

topology.EilenbergMacLaneModularCohomology.strategy

Return the strategy recorded by this EilenbergMacLaneModularCohomology.

Detailed contract

Closed-form completeness strategy.

(self) -> Literal['trivial_space', 'classifying_space_decomposition', 'free_abelian_second_delooping']

noether::topology::EilenbergMacLaneModularCohomology::strategy · Direct Rust declaration

pub fn strategy(&self) -> EilenbergMacLaneModularCohomologyStrategy
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, geom-core, m4rst, m4rste
GIL attached / bounded
Semantic ID noether/topology/EilenbergMacLaneModularCohomology@1

Executable usage: validation/unit/linalg/test_exact_linear_algebra_facade.py:319 · validation/unit/linalg/test_exact_linear_algebra_facade.py:330 · validation/unit/linalg/test_exact_linear_algebra_facade.py:428 · validation/unit/linalg/test_exact_linear_algebra_facade.py:439 · validation/unit/topology/test_eilenberg_maclane.py:112 · validation/unit/topology/test_eilenberg_maclane.py:119

topology.EilenbergMacLaneModularCohomology.to_json

Serialize this EilenbergMacLaneModularCohomology to its canonical typed JSON representation.

Detailed contract

Serialize the complete presentation and operation data as typed JSON.

(self) -> str

noether::topology::EilenbergMacLaneModularCohomology::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, geom-core, m4rst, m4rste
GIL attached / bounded
Semantic ID noether/topology/EilenbergMacLaneModularCohomology@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

topology.EilenbergMacLaneModularCohomology.verify

Replay and verify the mathematical evidence carried by this EilenbergMacLaneModularCohomology.

Detailed contract

Reconstruct the complete presentation and every recorded operation.

(self) -> None

noether::topology::EilenbergMacLaneModularCohomology::verify · Direct Rust declaration

pub fn verify(&self) -> Result<(), VerificationError>
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, geom-core, m4rst, m4rste
GIL attached / bounded
Semantic ID noether/topology/EilenbergMacLaneModularCohomology@1

Executable usage: examples/01_bezout_certificates.py:10 · examples/01_bezout_certificates.py:3 · examples/03_exact_linear_systems.py:13 · examples/03_exact_linear_systems.py:3 · examples/04_smith_normal_form.py:12 · examples/06_shortest_lattice_vectors.py:12