Hi Michael,

I am sorry for my previous reply. I think I missed one word in your
question:

On 5 Jun., 18:26, Michael Friedman <ois3...@gmail.com> wrote:
> I'm pretty new to Sage, so I'm sorry in advance for the trivial
> question.
> I have a set of (non-linear) equations, and I need to find the multiplicity
               ^^^

Unfortunately it seems that the multiplicities option of the "solve"
function is not available for (simultaneous solutions of) sets of
equations:
  sage: E=[(z^3-1)^3,(z^4-1)^3]
  sage: solve(E,z,multiplicities=True)
  [[z == 1]]

I hope other people know a better answer to your question.

Best regards,
    Simon

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