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topology · EilenbergMacLaneCohomologyGenerator

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

Worked example

The complete checked program Decompose a polynomial by a nonstandard positive grading uses this API directly.

# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Decompose a polynomial by a nonstandard positive grading."""

from noether import Z
from noether.commalg import PolynomialRing, WeightedGrading


def main() -> None:
    ring = PolynomialRing(Z, ["x", "y", "z"], grading=WeightedGrading([1, 2, 3]))
    x, y, z = ring.generators()
    sparse = ring.from_terms([([0, 0, 0], 1), ([2, 0, 0], 1), ([0, 1, 0], 1)])
    polynomial = sparse + z
    assert sparse * (x + y) == (1 + x**2 + y) * (x + y)
    components = polynomial.homogeneous_components()
    assert [degree for degree, _ in components] == [0, 2, 3]
    assert x**2 + y == components[1][1]
    print(f"weighted homogeneous degrees: {[degree for degree, _ in components]}")


if __name__ == "__main__":
    main()

Run it with .venv/bin/python examples/14_weighted_polynomials.py.

topology.EilenbergMacLaneCohomologyGenerator

One named generator in a complete modular cohomology presentation.

class EilenbergMacLaneCohomologyGenerator

noether::topology::EilenbergMacLaneCohomologyGenerator · Direct Rust declaration

pub struct EilenbergMacLaneCohomologyGenerator { /* 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

topology.EilenbergMacLaneCohomologyGenerator.degree

Return the degree recorded by this EilenbergMacLaneCohomologyGenerator.

Detailed contract

Cohomological degree.

(self) -> int

noether::topology::EilenbergMacLaneCohomologyGenerator::degree · Direct Rust declaration

pub fn degree(&self) -> u32
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, geom-core, m4rst, m4rste
GIL attached / bounded

Executable usage: examples/14_weighted_polynomials.py:16 · examples/14_weighted_polynomials.py:18 · examples/15_groebner_twisted_cubic.py:15 · examples/15_groebner_twisted_cubic.py:28 · examples/31_local_fields_and_precision.py:37 · examples/33_simplicial_cohomology_operations.py:26

topology.EilenbergMacLaneCohomologyGenerator.display_name

Return the display name recorded by this EilenbergMacLaneCohomologyGenerator.

Detailed contract

Mathematical display name, such as iota_2 or beta(iota_1).

(self) -> str

noether::topology::EilenbergMacLaneCohomologyGenerator::display_name · Direct Rust declaration

pub fn display_name(&self) -> &str
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, geom-core, m4rst, m4rste
GIL attached / bounded

Executable usage: examples/35_eilenberg_maclane_spaces.py:23 · validation/unit/homalg/test_finite_group_cohomology.py:203 · validation/unit/homalg/test_finite_group_cohomology.py:205 · validation/unit/topology/test_eilenberg_maclane.py:160 · validation/unit/topology/test_eilenberg_maclane.py:167 · validation/unit/topology/test_eilenberg_maclane.py:202

topology.EilenbergMacLaneCohomologyGenerator.id

Return the id recorded by this EilenbergMacLaneCohomologyGenerator.

Detailed contract

Stable algebra-generator id.

(self) -> str

noether::topology::EilenbergMacLaneCohomologyGenerator::id · Direct Rust declaration

pub fn id(&self) -> &str
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, geom-core, m4rst, m4rste
GIL attached / bounded

Executable usage: validation/unit/infra/test_corpus_acceptance.py:137 · validation/unit/infra/test_corpus_acceptance.py:147 · validation/unit/infra/test_corpus_acceptance.py:162 · validation/unit/infra/test_corpus_acceptance.py:166 · validation/unit/infra/test_corpus_acceptance.py:52 · validation/unit/infra/test_corpus_acceptance.py:81

topology.EilenbergMacLaneCohomologyGenerator.origin

Return the origin recorded by this EilenbergMacLaneCohomologyGenerator.

Detailed contract

Evidence-backed mathematical origin of the name.

(self) -> _EilenbergMacLaneGeneratorOrigin

noether::topology::EilenbergMacLaneCohomologyGenerator::origin · Direct Rust declaration

pub fn origin(&self) -> &EilenbergMacLaneGeneratorOrigin
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, geom-core, m4rst, m4rste
GIL attached / bounded

Executable usage: examples/26_elliptic_descent_functions.py:24 · validation/unit/numthy/test_elliptic_curve_facade.py:76 · validation/unit/topology/test_eilenberg_maclane.py:121 · validation/unit/topology/test_eilenberg_maclane.py:161 · validation/unit/topology/test_eilenberg_maclane.py:207 · validation/unit/topology/test_eilenberg_maclane.py:208