BUG: ndarray.conjugate() regression for legacy user-defined dtypes in 2.5.0 #31754

Describe the issue:

ndarray.conjugate() (and .conj()) raises TypeError: cannot conjugate non-numeric dtype for legacy (pre-NEP-42) user-defined dtypes in NumPy 2.5.0. It worked in 2.4.x and earlier. This affects any dtype registered via PyArray_RegisterDataType, including ones that register their own conjugate ufunc loop. The np.conjugate(arr) ufunc is unaffected — only the ndarray.conjugate()/.conj() method regressed.

The example below uses NumPy's own in-tree rational test dtype, so it needs no third-party packages:

• 2.4.6: a.conjugate() → [1 2 3] (no-op, correct for this real-valued dtype)
• 2.5.0: a.conjugate() → TypeError: cannot conjugate non-numeric dtype

A real-world case is numpy-quaternion, whose dtype registers a genuine conjugate ufunc loop; arr.conjugate() used to compute the quaternion conjugate via that loop and now errors (moble/quaternion#270).

Root cause: #31264 / commit b6bc683 ("ENH: Allow user-dtypes return views on .conjugate()") rewrote the dispatch in
PyArray_Conjugate (numpy/_core/src/multiarray/calculation.c):

-    if (PyArray_ISCOMPLEX(self) || PyArray_ISOBJECT(self) ||
-            PyArray_ISUSERDEF(self) || !NPY_DT_is_legacy(PyArray_DESCR(self))) {
+    if (NPY_DT_SLOTS(NPY_DTYPE(PyArray_DTYPE(self)))->imag_meth != NULL) {

The old condition routed user-defined dtypes (PyArray_ISUSERDEF) to the conjugate ufunc. The new one routes only dtypes whose DType defines an imag_meth slot. Legacy user dtypes have no imag_meth (a NEP-42/43 slot) and are never flagged NPY_DT_NUMERIC (for legacy descriptors that flag is set only when PyTypeNum_ISNUMBER(descr->type_num), always false for type_num >= NPY_USERDEF), so they fall through to the new !NPY_DT_is_numeric(...) branch and error — even when a conjugate loop is registered.

(For clarity: the "cannot conjugate non-numeric dtype" message predates this and came from the expired no-op-fallthrough deprecation; that expiry was fine, since in 2.4.x the PyArray_ISUSERDEF carve-out kept user dtypes off that path. The regression is specifically the removal of that carve-out in #31264, which doesn't appear to have been intended to change legacy-dtype behavior.)

Expected behavior: as in 2.4.x — dispatch to the registered conjugate ufunc loop if one exists, otherwise return a view (real-valued no-op). Legacy user dtypes should not unconditionally error.

Reproduce the code example:

import numpy as np
from numpy._core._rational_tests import rational

a = np.array([1, 2, 3], dtype=rational)
print("dtype:", a.dtype, "type_num:", a.dtype.num)  # rational 256
print("np.conjugate (ufunc) works:", np.conjugate(a))  # [1 2 3]
print(a.conjugate())  # TypeError on 2.5.0, was [1 2 3] on 2.4.6

Error message:

Traceback (most recent call last):
  File "<python-input-0>", line 7, in <module>
    print(a.conjugate())  # TypeError on 2.5.0, was [1 2 3] on 2.4.6
          ~~~~~~~~~~~^^
TypeError: cannot conjugate non-numeric dtype

Python and NumPy Versions:

2.5.0
3.14.6 | packaged by conda-forge | (main, Jun 12 2026, 08:47:56) [Clang 20.1.8 ]

Runtime Environment:

[{'numpy_version': '2.4.6',
'python': '3.14.6 | packaged by conda-forge | (main, Jun 12 2026, 08:47:56) '
'[Clang 20.1.8 ]',
'uname': uname_result(system='Darwin', node='Beasty', release='23.6.0', version='Darwin Kernel Version 23.6.0: Mon Jul 29 21:13:04 PDT 2024; root:xnu-10063.141.2~1/RELEASE_ARM64_T6020', machine='arm64')},
{'simd_extensions': {'baseline': ['NEON', 'NEON_FP16', 'NEON_VFPV4', 'ASIMD'],
'found': ['ASIMDHP', 'ASIMDDP'],
'not_found': ['ASIMDFHM']}},
{'ignore_floating_point_errors_in_matmul': True},
{'architecture': 'VORTEX',
'filepath': '/Users/boyle/.continuum/mambaforge/envs/science/lib/libopenblas.0.dylib',
'internal_api': 'openblas',
'num_threads': 12,
'prefix': 'libopenblas',
'threading_layer': 'openmp',
'user_api': 'blas',
'version': '0.3.33'},
{'filepath': '/Users/boyle/.continuum/mambaforge/envs/science/lib/libomp.dylib',
'internal_api': 'openmp',
'num_threads': 12,
'prefix': 'libomp',
'user_api': 'openmp',
'version': None}]

How does this issue affect you or how did you find it:

Found via a downstream bug report against the quaternion package (moble/quaternion#270): a user's array-conjugation code that worked on numpy <= 2.4.6 began raising TypeError on 2.5.0. The same regression reproduces on NumPy's own in-tree rational dtype, so it affects any legacy user-defined dtype, not just quaternion.