fix: conjugate right operand in co-rep a0.u construction#289
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The co-rep multiplication law Gamma(a) . Gamma(u)^* = omega(a, u) . Gamma(a.u)
(a anti-linear, u in D) gives Gamma(a.u) = conj(omega(a, u)) . U . conj(Gamma(u))
once |omega| = 1 is used -- an assumption that holds for every factor system
spgrep builds (non-symmorphic exp(-2pi i g.w) is unit-modulus; spinor factor
takes values in {-1, +1}).
All three xi in {+1, -1, 0} branches of
`_enumerate_small_corepresentations_with_factor_system` applied the right
operand without the complex conjugation, violating the co-rep law whenever
the underlying unitary-subgroup irrep Gamma(u) has non-real entries. The
spinor path `enumerate_spinor_small_corepresentations` reuses this helper, so
the bug affected it too.
The bug was invisible to the existing tests because every fixture happened to
produce real Gamma(u) matrices; conj(Gamma(u)) = Gamma(u) masked the
error. SG 221 Pm-3m at k = (1/4, 1/4, 1/4) with the 2-dim E irrep of D_3
triggers it (72/144 pairs fail before the fix).
- `src/spgrep/corep.py`: add `np.conj(...)` on the right operand in all
three xi branches.
- `docs/formulation/irreps/corep.md`: add `^*` on Gamma-tilde(u) in each
Gamma-tilde(a_0 u) formula to match the corrected code.
- `tests/test_corep.py`: add `_assert_corep_composition_law` helper; add
`test_corep_composition_law_pm3m_lambda` regression using the reproducer
from the issue; extend spinor co-rep test to assert the composition law
on every produced co-irrep.
lan496
commented
Apr 24, 2026
Address PR review: identify the group by ITA number rather than the Hermann-Mauguin symbol in both the test name and docstring.
Add the standard Keep a Changelog preamble and restructure the Unreleased section into the conventional categorized subsections (Added, Changed, Fixed, ...). Historical version entries are left untouched.
Update the release-workflow note to mention the Unreleased-section pattern introduced with the Keep a Changelog format. Add two conventions: changelog format/policy, and the co-representation multiplication-law rule that explains why the right operand is conjugated in `corep.py`.
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Pull request overview
Fixes co-representation construction in spgrep.corep by correctly complex-conjugating the right operand in the anti-linear multiplication rule, and adds documentation + regression tests to prevent recurrence.
Changes:
- Correct
_enumerate_small_corepresentations_with_factor_systemto use@ np.conj(...)when formingΓ(a₀u)across all Frobenius–Schur indicator branches. - Add/extend tests to assert the co-representation multiplication law (including a targeted non-real irrep regression for SG 221 at k = (1/4,1/4,1/4)).
- Update theory docs and changelog/release guidance to reflect the correct
Γ(u)^*convention and Keep-a-Changelog structure.
Reviewed changes
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Show a summary per file
| File | Description |
|---|---|
src/spgrep/corep.py |
Fixes the co-rep extension formula by conjugating the right operand for anti-linear composition. |
tests/test_corep.py |
Adds a reusable assertion for the co-rep law and introduces a regression test that fails without the fix. |
docs/formulation/irreps/corep.md |
Updates formulas to include the required conjugation on \tilde{\Gamma}(u). |
docs/changelog.md |
Adds an Unreleased/Fixed entry describing the bug fix under Keep a Changelog structure. |
CLAUDE.md |
Updates release instructions and documents the co-representation multiplication convention used in the codebase. |
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Summary
_enumerate_small_corepresentations_with_factor_system: the right operand was applied without complex conjugation, violating the co-rep multiplication lawΓ(a) · Γ(u)^* = ω(a, u) · Γ(a · u)whenever the unitary-subgroup irrepΓ(u)has non-real entries. Solving forΓ(a · u)with|ω| = 1(unit-modulus for every factor system spgrep builds) givesconj(ω(a, u)) · U · conj(Γ(u)).enumerate_spinor_small_corepresentationsreuses this helper, so the same bug affected the spinor path.docs/formulation/irreps/corep.mdby adding^*onΓ̃(u)in eachΓ̃(a₀u)formula.Γ(u)matrices (soconj(Γ(u)) = Γ(u)masked the error). A dedicated test on SG 221 Pm-3m atk = (1/4, 1/4, 1/4)-- where the 2-dimEirrep ofD₃appears and is non-real -- reproduces the bug (72/144 pairs fail before the fix). The spinor co-rep test is also extended to assert the multiplication law on every co-irrep it produces.Test plan
uv run pytest tests/test_corep.py-- new regression passes; extended spinor test still passes.uv run pytest tests/-- full suite (132 passed, 1 skipped).prek run --files src/spgrep/corep.py tests/test_corep.py docs/formulation/irreps/corep.md-- ruff / mypy / format clean.uv run sphinx-build docs docs_build) shows no new warnings.[Claude Code] Generated with Claude Code