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topology · SimplicialSetElementaryHornCollapse

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

Worked example

The complete checked program Recover the exact face structure of a rational square uses this API directly.

# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Recover the exact face structure of a rational square."""

from fractions import Fraction

from noether.geometry import convex_hull


def main() -> None:
    square = convex_hull([[0, 0], [1, 0], [0, 1], [1, 1], [Fraction(1, 2), Fraction(1, 2)]])
    square.verify()
    assert square.f_vector == [1, 4, 4, 1]
    assert not square.is_vertex([Fraction(1, 2), Fraction(1, 2)])
    print(f"vertices={square.vertices}; f-vector={square.f_vector}")


if __name__ == "__main__":
    main()

Run it with .venv/bin/python examples/25_exact_geometry.py.

topology.SimplicialSetElementaryHornCollapse

One elementary simplicial-set collapse inverse to a horn attachment.

SimplicialSetElementaryHornCollapse(simplex_dimension: int, simplex: int, face: int, free_face: int)

noether::topology::SimplicialSetElementaryHornCollapse · Direct Rust declaration

pub struct SimplicialSetElementaryHornCollapse { /* 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

Executable usage: validation/unit/topology/test_simplicial_set_facade.py:105 · validation/unit/topology/test_simplicial_set_facade.py:22 · validation/unit/topology/test_simplicial_set_facade.py:93

topology.SimplicialSetElementaryHornCollapse.face

Return the face recorded by this SimplicialSetElementaryHornCollapse.

Detailed contract

Missing horn-face index k.

(self) -> int

noether::topology::SimplicialSetElementaryHornCollapse::face · Direct Rust declaration

pub const fn face(&self) -> usize
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/25_exact_geometry.py:3 · validation/unit/topology/test_filtration_builders.py:73 · validation/unit/topology/test_persistence_facade.py:92 · validation/unit/topology/test_persistence_facade.py:95 · validation/unit/topology/test_simplicial_complex_facade.py:112 · validation/parity/polyhedral/test_convex_hull_parity.py:230

topology.SimplicialSetElementaryHornCollapse.free_face

Return the free face recorded by this SimplicialSetElementaryHornCollapse.

Detailed contract

Index of the removed nondegenerate free face in dimension n-1.

(self) -> int

noether::topology::SimplicialSetElementaryHornCollapse::free_face · Direct Rust declaration

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

topology.SimplicialSetElementaryHornCollapse.simplex

Return the simplex recorded by this SimplicialSetElementaryHornCollapse.

Detailed contract

Index of the removed nondegenerate horn filler.

(self) -> int

noether::topology::SimplicialSetElementaryHornCollapse::simplex · Direct Rust declaration

pub const fn simplex(&self) -> usize
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/geometry/test_geometry_facade.py:82 · validation/unit/topology/test_simplicial_complex_facade.py:205 · validation/unit/topology/test_simplicial_complex_facade.py:206 · validation/unit/topology/test_simplicial_complex_facade.py:209 · validation/unit/topology/test_simplicial_complex_facade.py:213 · validation/unit/topology/test_simplicial_complex_facade.py:74

topology.SimplicialSetElementaryHornCollapse.simplex_dimension

Return the simplex dimension recorded by this SimplicialSetElementaryHornCollapse.

Detailed contract

Dimension of the removed horn filler.

(self) -> int

noether::topology::SimplicialSetElementaryHornCollapse::simplex_dimension · Direct Rust declaration

pub const fn simplex_dimension(&self) -> usize
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/topology/test_simplicial_set_facade.py:171 · validation/unit/topology/test_simplicial_set_facade.py:197 · validation/unit/topology/test_simplicial_set_facade.py:228 · validation/unit/topology/test_simplicial_set_facade.py:233 · validation/unit/topology/test_simplicial_set_facade.py:238