random doctest error in QuaternionFractionalIdeal_rational.is_principal

[dcoudert]

Steps To Reproduce

sage -t --warn-long 5.0 --random-seed=64954994004742655361672586966720031388 src/sage/algebras/quatalg/quaternion_algebra.py

Expected Behavior

All tests passed!

Actual Behavior

sage -t --warn-long 5.0 --random-seed=64954994004742655361672586966720031388 src/sage/algebras/quatalg/quaternion_algebra.py
**********************************************************************
File "src/sage/algebras/quatalg/quaternion_algebra.py", line 3716, in sage.algebras.quatalg.quaternion_algebra.QuaternionFractionalIdeal_rational.is_principal
Failed example:
    bool, alpha = I.is_principal(True)
Exception raised:
    Traceback (most recent call last):
      File "sage/misc/misc_c.pyx", line 726, in sage.misc.misc_c.sized_iter.__next__
        x = next(self.iterator)
    StopIteration

    During handling of the above exception, another exception occurred:

    Traceback (most recent call last):
      File "/Users/dcoudert/sage/src/sage/doctest/forker.py", line 715, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/Users/dcoudert/sage/src/sage/doctest/forker.py", line 1136, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.algebras.quatalg.quaternion_algebra.QuaternionFractionalIdeal_rational.is_principal[4]>", line 1, in <module>
        bool, alpha = I.is_principal(True)
      File "/Users/dcoudert/sage/src/sage/algebras/quatalg/quaternion_algebra.py", line 3726, in is_principal
        c = self.theta_series_vector(2)[1]
      File "/Users/dcoudert/sage/src/sage/algebras/quatalg/quaternion_algebra.py", line 3010, in theta_series_vector
        Q = self.quadratic_form()
      File "sage/misc/cachefunc.pyx", line 2316, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__
        self.cache = f(self._instance)
      File "/Users/dcoudert/sage/src/sage/algebras/quatalg/quaternion_algebra.py", line 3037, in quadratic_form
        gram_matrix = self.gram_matrix()
      File "sage/misc/cachefunc.pyx", line 2316, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__
        self.cache = f(self._instance)
      File "/Users/dcoudert/sage/src/sage/algebras/quatalg/quaternion_algebra.py", line 3142, in gram_matrix
        return M44(m, coerce=False)
      File "sage/structure/parent.pyx", line 903, in sage.structure.parent.Parent.__call__
        return mor._call_with_args(x, args, kwds)
      File "sage/structure/coerce_maps.pyx", line 183, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args
        raise
      File "sage/structure/coerce_maps.pyx", line 173, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args
        return C._element_constructor(x, **kwds)
      File "/Users/dcoudert/sage/src/sage/matrix/matrix_space.py", line 1154, in _element_constructor_
        return self.element_class(self, entries, **kwds)
      File "sage/matrix/matrix_rational_dense.pyx", line 189, in sage.matrix.matrix_rational_dense.Matrix_rational_dense.__init__
        for t in ma.iter(coerce, True):
      File "sage/matrix/args.pyx", line 606, in iter
        x = next(it)
      File "sage/misc/misc_c.pyx", line 728, in sage.misc.misc_c.sized_iter.__next__
        raise ValueError(f"sequence too short (expected length {self.size}, got {self.index})")
    ValueError: sequence too short (expected length 16, got 1)
**********************************************************************
File "src/sage/algebras/quatalg/quaternion_algebra.py", line 3717, in sage.algebras.quatalg.quaternion_algebra.QuaternionFractionalIdeal_rational.is_principal
Failed example:
    bool
Expected:
    True
Got:
    <class 'bool'>
**********************************************************************
File "src/sage/algebras/quatalg/quaternion_algebra.py", line 3719, in sage.algebras.quatalg.quaternion_algebra.QuaternionFractionalIdeal_rational.is_principal
Failed example:
    I == O*alpha
Exception raised:
    Traceback (most recent call last):
      File "/Users/dcoudert/sage/src/sage/doctest/forker.py", line 715, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/Users/dcoudert/sage/src/sage/doctest/forker.py", line 1136, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.algebras.quatalg.quaternion_algebra.QuaternionFractionalIdeal_rational.is_principal[6]>", line 1, in <module>
        I == O*alpha
    NameError: name 'alpha' is not defined
**********************************************************************
File "src/sage/algebras/quatalg/quaternion_algebra.py", line 3954, in sage.algebras.quatalg.quaternion_algebra.QuaternionFractionalIdeal_rational.primitive_decomposition
Warning: slow doctest:
    for d in ( m for m in range(400, 750) if is_squarefree(m) ):
        A = QuaternionAlgebra(d)
        O = A.maximal_order()
        for _ in range(10):
            a = O.random_element()
            if not a.is_constant(): # avoids a = 0
                I = a*O + a.reduced_norm()*O
                if I.is_integral():
                    J,g = I.primitive_decomposition()
                    assert J*g == I
                    assert J.is_primitive()
Test ran for 5.55s cpu, 5.57s wall
Check ran for 0.00s cpu, 0.00s wall
**********************************************************************
1 item had failures:
   3 of   8 in sage.algebras.quatalg.quaternion_algebra.QuaternionFractionalIdeal_rational.is_principal
    [686 tests, 3 failures, 10.63s wall]
----------------------------------------------------------------------
sage -t --warn-long 5.0 --random-seed=64954994004742655361672586966720031388 src/sage/algebras/quatalg/quaternion_algebra.py  # 3 doctests failed
----------------------------------------------------------------------

Additional Information

observed in https://github.com/sagemath/sage/actions/runs/11755696820/job/32751042118?pr=38941

Environment

• OS: macOS 14.7.1
• Sage Version: 10.5.beta9

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide

[dcoudert]

use this method to identify the failing case:

def foo():
    B.<i,j,k> = QuaternionAlgebra(419)
    O = B.quaternion_order([1/2 + 3/2*j, 1/6*i + 2/3*j + 1/2*k, 3*j, k])
    while True:
        beta = O.random_element()
        I = O*beta
        try:
            bool, alpha = I.is_principal(True)
        except:
            return beta

then

sage: beta = foo()
sage: type(beta)
<class 'sage.algebras.quatalg.quaternion_algebra_element.QuaternionAlgebraElement_rational_field'>
sage: beta
0

[yyyyx4]

@S17A05, this may be of interest to you?

[S17A05]

At first glance it seems that one just needs to exclude the zero ideal here - I'll take a closer look at it.