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topology · SimplicialSetHornCollapseSequence

8 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.SimplicialSetHornCollapseSequence

Replayable finite sequence of elementary simplicial-set horn collapses.

class SimplicialSetHornCollapseSequence

noether::topology::SimplicialSetHornCollapseSequence · Direct Rust declaration

pub struct SimplicialSetHornCollapseSequence { /* 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/SimplicialSetHornCollapseSequence@1

Executable usage: validation/unit/topology/test_simplicial_set_facade.py:101 · validation/unit/topology/test_simplicial_set_facade.py:23 · validation/unit/topology/test_simplicial_set_facade.py:97

topology.SimplicialSetHornCollapseSequence.from_json

Deserialize and revalidate a SimplicialSetHornCollapseSequence from typed JSON.

Detailed contract

Deserialize, replay, and verify the complete collapse sequence.

(cls, value: str) -> SimplicialSetHornCollapseSequence

noether::topology::SimplicialSetHornCollapseSequence::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/SimplicialSetHornCollapseSequence@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.SimplicialSetHornCollapseSequence.is_terminal

Test whether this SimplicialSetHornCollapseSequence is terminal.

Detailed contract

Whether the target admits no further elementary horn collapse.

(self) -> bool

noether::topology::SimplicialSetHornCollapseSequence::is_terminal · Direct Rust declaration

pub fn is_terminal(&self) -> bool
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/SimplicialSetHornCollapseSequence@1

Executable usage: validation/unit/topology/test_simplicial_complex_facade.py:106 · validation/unit/topology/test_simplicial_set_facade.py:99

topology.SimplicialSetHornCollapseSequence.source

Return the source recorded by this SimplicialSetHornCollapseSequence.

Detailed contract

Source before any collapse.

(self) -> SimplicialSet

noether::topology::SimplicialSetHornCollapseSequence::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/SimplicialSetHornCollapseSequence@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.SimplicialSetHornCollapseSequence.steps

Return the steps recorded by this SimplicialSetHornCollapseSequence.

Detailed contract

Ordered horn-filler/free-face pairs.

(self) -> list[SimplicialSetElementaryHornCollapse]

noether::topology::SimplicialSetHornCollapseSequence::steps · Direct Rust declaration

pub fn steps(&self) -> &[SimplicialSetElementaryHornCollapse]
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/SimplicialSetHornCollapseSequence@1

Executable usage: validation/unit/groups/test_acceptance_workload.py:69 · validation/unit/groups/test_acceptance_workload.py:70 · validation/unit/groups/test_acceptance_workload.py:71 · validation/unit/topology/test_simplicial_complex_facade.py:84 · validation/corpus/numthy/padic-newton-cube-root.py:3

topology.SimplicialSetHornCollapseSequence.target

Return the target recorded by this SimplicialSetHornCollapseSequence.

Detailed contract

Target reconstructed by replaying every step.

(self) -> SimplicialSet

noether::topology::SimplicialSetHornCollapseSequence::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/SimplicialSetHornCollapseSequence@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.SimplicialSetHornCollapseSequence.to_json

Serialize this SimplicialSetHornCollapseSequence to its canonical typed JSON representation.

Detailed contract

Serialize only the source and replayable steps; the target is derived.

(self) -> str

noether::topology::SimplicialSetHornCollapseSequence::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/SimplicialSetHornCollapseSequence@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.SimplicialSetHornCollapseSequence.verify

Replay and verify the mathematical evidence carried by this SimplicialSetHornCollapseSequence.

Detailed contract

Recheck every freeness condition and reconstruct the target.

(self) -> None

noether::topology::SimplicialSetHornCollapseSequence::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/SimplicialSetHornCollapseSequence@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