Implement minpoly() for approximate values

[user202729]

Fixes #36798 .

There are a few things that are worth discussing.

• Is it a good idea to test calling minpoly() where there are insufficient precision or input is transcendental? Currently it returns an "arbitrary" polynomial, but it may raise an error instead in the future or if some floating point changed.

• Is calling the method minpoly actually a good idea? However notice that currently

  sage: minpoly(RR(1.2)*x/x)
  x - 6/5

  because the operation casts it to SR and things just work out… somehow.

  Either we should disable this behavior (and call the method something like minpoly_approximate), or we should implement the method for pure RR for consistency.

📝 Checklist

• The title is concise and informative.
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• I have created tests covering the changes.
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⌛ Dependencies

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[kwankyu]

@mezzarobba ?

[mezzarobba]

On Monday, 10 February 2025 01:20:14 UTC+1 Kwankyu Lee wrote: @mezzarobba ?

Thanks for the notice. I am a bit too busy right now but I will try to take a look later if nobody beats me to it. Feel free to remind me if necessary!

…

-- Marc