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topology · SimplicialSetAnodyneZigzag

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

Worked example

The complete checked program Build and verify an isomorphism between two presentations of F_25 uses this API directly.

# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Build and verify an isomorphism between two presentations of F_25."""

from noether.numthy import FiniteField


def main() -> None:
    source = FiniteField.extension(5, 2)
    target = FiniteField.with_modulus(5, [2, 0, 1])
    isomorphism = source.isomorphism_to(target)
    isomorphism.verify()
    value = source.element_from_coefficients([3, 2])
    assert isomorphism.apply_inverse(isomorphism(value)) == value
    print(f"a maps to {isomorphism.generator_image}")


if __name__ == "__main__":
    main()

Run it with .venv/bin/python examples/09_finite_field_isomorphisms.py.

topology.SimplicialSetAnodyneZigzag

A verified zigzag of horn attachments and collapses.

class SimplicialSetAnodyneZigzag

noether::topology::SimplicialSetAnodyneZigzag · Direct Rust declaration

pub struct SimplicialSetAnodyneZigzag { /* 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/SimplicialSetAnodyneZigzag@1

Executable usage: validation/unit/topology/test_simplicial_set_facade.py:119 · validation/unit/topology/test_simplicial_set_facade.py:123 · validation/unit/topology/test_simplicial_set_facade.py:20

topology.SimplicialSetAnodyneZigzag.from_json

Deserialize and revalidate a SimplicialSetAnodyneZigzag from typed JSON.

Detailed contract

Deserialize and exactly replay every move.

(cls, value: str) -> SimplicialSetAnodyneZigzag

noether::topology::SimplicialSetAnodyneZigzag::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/SimplicialSetAnodyneZigzag@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.SimplicialSetAnodyneZigzag.moves

Return the moves recorded by this SimplicialSetAnodyneZigzag.

Detailed contract

Ordered horn attachments and collapses.

(self) -> list[SimplicialSetAnodyneMove]

noether::topology::SimplicialSetAnodyneZigzag::moves · Direct Rust declaration

pub fn moves(&self) -> &[SimplicialSetAnodyneMove]
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/SimplicialSetAnodyneZigzag@1

Executable usage: validation/unit/topology/test_simplicial_complex_facade.py:128 · validation/unit/topology/test_simplicial_set_facade.py:121

topology.SimplicialSetAnodyneZigzag.source

Return the source recorded by this SimplicialSetAnodyneZigzag.

Detailed contract

Initial simplicial set.

(self) -> SimplicialSet

noether::topology::SimplicialSetAnodyneZigzag::source · Direct Rust declaration

pub fn source(&self) -> &SimplicialSet
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/SimplicialSetAnodyneZigzag@1

Executable usage: examples/09_finite_field_isomorphisms.py:11 · examples/09_finite_field_isomorphisms.py:13 · examples/09_finite_field_isomorphisms.py:9 · examples/30_modules_and_resolutions.py:34 · examples/30_modules_and_resolutions.py:37 · validation/unit/category/test_acceptance_workload.py:25

topology.SimplicialSetAnodyneZigzag.target

Return the target recorded by this SimplicialSetAnodyneZigzag.

Detailed contract

Endpoint reconstructed by exact replay.

(self) -> SimplicialSet

noether::topology::SimplicialSetAnodyneZigzag::target · Direct Rust declaration

pub fn target(&self) -> &SimplicialSet
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/SimplicialSetAnodyneZigzag@1

Executable usage: examples/09_finite_field_isomorphisms.py:10 · examples/09_finite_field_isomorphisms.py:11 · examples/30_modules_and_resolutions.py:33 · examples/30_modules_and_resolutions.py:38 · examples/31_local_fields_and_precision.py:27 · examples/36_affine_normalization.py:16

topology.SimplicialSetAnodyneZigzag.to_json

Serialize this SimplicialSetAnodyneZigzag to its canonical typed JSON representation.

Detailed contract

Serialize the source and replayable moves; the target is derived.

(self) -> str

noether::topology::SimplicialSetAnodyneZigzag::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/SimplicialSetAnodyneZigzag@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.SimplicialSetAnodyneZigzag.verify

Replay and verify the mathematical evidence carried by this SimplicialSetAnodyneZigzag.

Detailed contract

Recheck every horn pair and reconstruct the endpoint.

(self) -> None

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

pub fn verify(&self) -> Result<(), TopologyError>
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/SimplicialSetAnodyneZigzag@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