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combin · SemistandardTableaux

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

Worked example

The complete checked program Weight characters and second Chern classes for polynomial GL representations uses this API directly.

# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Weight characters and second Chern classes for polynomial GL representations."""

from noether.combin import Partition, Tableau
from noether.groups import PolynomialGlRepresentation

shape = Partition((2, 1))
tableaux = Tableau.semistandard(shape, 3)
assert tableaux.cardinality == 8
assert next(tableaux).content(3) == (2, 1, 0)

wedge_two = PolynomialGlRepresentation(4, Partition((1, 1)))
assert wedge_two.weyl_dimension == 6
assert wedge_two.descends_to_sl_quotient(2)
assert wedge_two.second_chern_index() == 2
assert wedge_two.second_chern_index_from_weights() == 2

example = PolynomialGlRepresentation(6, shape)
assert example.weyl_dimension == 70
assert example.second_chern_index() == 33
example.verify_second_chern_index()

character = example.sl_character()
assert character.dimension == 70
assert character.chern_class(2).nonzero_term_count > 0

print("tableaux=8; c2(wedge^2 gamma_4)=2c2; c2(gamma_6^(2,1))=33c2")

Run it with .venv/bin/python examples/27_weight_characters.py.

combin.SemistandardTableaux

A lazy finite iterator over semistandard tableaux of fixed shape.

SemistandardTableaux(shape: Partition, maximum_entry: int)

noether::combin::SemistandardTableaux · Direct Rust declaration

pub struct SemistandardTableaux { /* private fields */ }
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, graph-core, perm-core
GIL attached / bounded

Executable usage: validation/unit/groups/test_weight_characters.py:22 · validation/unit/groups/test_weight_characters.py:5

combin.SemistandardTableaux.__iter__

Iterate over the canonical finite contents of this object.

(self) -> SemistandardTableaux

noether::combin::SemistandardTableaux · Python projection

Python projection convenience over this Rust mathematical type
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, graph-core, perm-core
GIL attached / bounded

combin.SemistandardTableaux.__next__

Return the next value in this canonical iterator.

(self) -> Tableau

noether::combin::SemistandardTableaux · Python projection

Python projection convenience over this Rust mathematical type
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, graph-core, perm-core
GIL attached / bounded

combin.SemistandardTableaux.cardinality

Exact hook-content cardinality as an arbitrary-size Python integer.

Detailed contract

Exact number of tableaux in the complete enumeration.

(self) -> int

noether::combin::SemistandardTableaux::cardinality · Direct Rust declaration

pub const fn cardinality(&self) -> &Integer
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, graph-core, perm-core
GIL attached / bounded

Executable usage: examples/27_weight_characters.py:10 · validation/unit/commalg/test_residue_ring_facade.py:23 · validation/unit/groups/test_weight_characters.py:25 · validation/unit/numthy/test_finite_field_facade.py:29 · validation/unit/numthy/test_qadic_ring_facade.py:33 · validation/parity/combinatorics/test_poset_parity.py:59

combin.SemistandardTableaux.maximum_entry

Largest positive letter in the alphabet.

Detailed contract

Largest letter in the finite positive alphabet.

(self) -> int

noether::combin::SemistandardTableaux::maximum_entry · Direct Rust declaration

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

Executable usage: validation/unit/groups/test_weight_characters.py:24

combin.SemistandardTableaux.shape

Shared shape of every yielded tableau.

Detailed contract

Shape shared by every yielded tableau.

(self) -> Partition

noether::combin::SemistandardTableaux::shape · Direct Rust declaration

pub const fn shape(&self) -> &Partition
Contract Value
Guarantee checked deterministic result
Determinism deterministic
Availability default CPU build
Domain implementation crates noether, graph-core, perm-core
GIL attached / bounded

Executable usage: examples/27_weight_characters.py:19 · examples/27_weight_characters.py:8 · examples/27_weight_characters.py:9 · examples/distributed/f2_linear_algebra.py:51 · examples/distributed/f2_linear_algebra.py:52 · validation/unit/combin/test_acceptance_workload.py:38