Skip to content

topology · DominatedVertex

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

Worked example

The complete checked program Decompose the tensor square of the type-A2 letter crystal uses this API directly.

# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Decompose the tensor square of the type-A2 letter crystal."""

from noether.combin import KashiwaraCrystal


def main() -> None:
    letters = KashiwaraCrystal.type_a_letters(2)
    tensor_square = letters.tensor(letters)
    highest_weights = sorted(
        tensor_square.weight(vertex) for vertex in tensor_square.highest_weight_vertices()
    )
    assert tensor_square.vertex_count == 9
    assert highest_weights == [(0, 1), (2, 0)]
    print(f"B(omega_1)^2 has highest weights {highest_weights}")


if __name__ == "__main__":
    main()

Run it with .venv/bin/python examples/23_kashiwara_crystals.py.

topology.DominatedVertex

One replayable dominated-vertex deletion.

DominatedVertex(vertex: int, dominator: int)

noether::topology::DominatedVertex · Direct Rust declaration

pub struct DominatedVertex { /* 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_complex_facade.py:18 · validation/unit/topology/test_simplicial_complex_facade.py:92

topology.DominatedVertex.dominator

Return the dominator recorded by this DominatedVertex.

Detailed contract

A distinct vertex lying in every maximal simplex containing vertex.

(self) -> int

noether::topology::DominatedVertex::dominator · Direct Rust declaration

pub fn dominator(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

topology.DominatedVertex.vertex

Return the vertex recorded by this DominatedVertex.

Detailed contract

Deleted vertex.

(self) -> int

noether::topology::DominatedVertex::vertex · Direct Rust declaration

pub fn vertex(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/23_kashiwara_crystals.py:12 · validation/unit/combinatorics/test_kashiwara_crystal.py:33 · validation/unit/combinatorics/test_kashiwara_crystal.py:35 · validation/unit/combinatorics/test_kashiwara_crystal.py:36 · validation/unit/combinatorics/test_kashiwara_crystal.py:42 · validation/parity/combinatorics/test_crystals_parity.py:101