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CRT_vectors does not handle non-coprime moduli #39158

@user202729

Description

@user202729

Steps To Reproduce

sage: CRT_vectors([[3, 5], [3, 5]], [4, 6])
ValueError: moduli must be coprime

Expected Behavior

Actual Behavior

Additional Information

Lead to a test failure here https://github.com/sagemath/sage/actions/runs/12390050306/job/34584290514?pr=39153#step:10:8784

sage -t --warn-long 5.0 --random-seed=171635645973753757565886362497935495350 src/sage/schemes/elliptic_curves/ell_point.py
**********************************************************************
File "src/sage/schemes/elliptic_curves/ell_point.py", line 276, in sage.schemes.elliptic_curves.ell_point.?._add_
Failed example:
    R = P + Q
Exception raised:
    Traceback (most recent call last):
      File "/Users/runner/work/sage/sage/src/sage/doctest/forker.py", line 716, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/Users/runner/work/sage/sage/src/sage/doctest/forker.py", line 1137, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.schemes.elliptic_curves.ell_point.?._add_[13]>", line 1, in <module>
        R = P + Q
            ~~^~~
      File "sage/structure/element.pyx", line 1219, in sage.structure.element.Element.__add__
        return (<Element>left)._add_(right)
      File "sage/structure/element.pyx", line 2376, in sage.structure.element.ModuleElement._add_
        cpdef _add_(self, other):
      File "/Users/runner/work/sage/sage/src/sage/schemes/elliptic_curves/ell_point.py", line 344, in _add_
        pt = CRT_vectors([pt, [x2.lift(), y2.lift(), z2.lift()]], [mod, mod_2nd])
             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
      File "/Users/runner/work/sage/sage/src/sage/arith/misc.py", line 3675, in CRT_vectors
        a = CRT_basis(moduli)
            ^^^^^^^^^^^^^^^^^
      File "/Users/runner/work/sage/sage/src/sage/arith/misc.py", line 3641, in CRT_basis
        raise ValueError('moduli must be coprime')
    ValueError: moduli must be coprime
**********************************************************************

Environment

  • OS: Linux
  • Sage Version: latest develop

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

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