Inspiration is this ask.sagemath question 
<https://ask.sagemath.org/question/53185/solve-a-system-of-polynomial-equations-getting-different-results-using-symbolic-math-toolbox-of-matlab-and-sage/>.
 
Roughly, the original question was a discrepancy between the *numerical* 
results obtained by Sage and by Matlab when solving a set of three 
equations with three unknowns.

I wanted to compare the numerical results with those obtained by 
rearranging the original equations into rational fractions and solving 
their numerators (while watching out for null denominators). My code so far 
is in the attached SolutionExacte.sage.

What succeeds :

   - Rearranging the equations in rational fractions 
   - creating the relevant polynomial ring 
   - creating the ideal J representing the set of solutions 
   - checking that its dimension is 0 

What fails is enumerating the solutions : S=J.variety(QQbar) hasn’t 
returned for more than eight hours (!). When throwing the towel (*i. e. 
interrupting), I got the following message in a message box of the Jupyter 
notebook :

/usr/local/sage-9/local/lib/python3.7/site-packages/sage/rings/qqbar.py:2078: 
RuntimeWarning: cypari2 leaked 2081168 bytes on the PARI stack df = factor(d)

Questions :

   1. Is that a known bug ? 
   2. Is that possibly a *new* bug ? 
   3. If so, how to file the most informative ticket ? 
   4. Are you aware of possible workarounds ? 

HTH,
​

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