Thank you for the quick response. 

Yes, it looks like refine_root() does the job more efficiently. Thank you 
for the note.

I am facing issues in getting _find_poly_sign_univariate function to work. 
When I run from sympy import find_poly_sign, I get the following error: 

ImportError: cannot import name 'find_poly_sign' from 'sympy' 
(/path_to_python/python3.8/site-packages/sympy/__init__.py)

The documentation of SymPy here 
<https://docs.sympy.org/latest/search.html?q=find_poly_sign&check_keywords=yes&area=default>
 does 
not seem to have this function. Would be great to get some pointers on how 
to import
the function in the code.


Best

On Tuesday, May 21, 2024 at 4:41:35 PM UTC-7 Oscar wrote:

> On Wed, 22 May 2024 at 00:23, Ani J <[email protected]> wrote:
> >
> > The polynomial 4x^2 - 9 has rational roots, whereas the output of the 
> print statement is: [((-2, -1), 1), ((1, 2), 1)]
> > All intervals here are of length more than 0.
> > It would be great if in general it is possible that the endpoints of 
> different intervals are never the same. Because,
> > in my use case, I would like to use the points between the endpoints of 
> two consecutive intervals and not inside any
> > interval to find out the sign of the polynomial. For example., with the 
> above two intervals (-2,-1), (1,2) , I would use
> > the points -3,0,3 note that all points are outside the intervals and lie 
> in particular regions not in the intervals.
> > I would like to use these points to find out the sign of the polynomial 
> (4x^2-9) in my use case. It would be great if
> > the tool itself gives separate intervals.
>
> See the function _find_poly_sign_univariate in
> https://github.com/sympy/sympy/issues/26177
>
> That function finds points where a univariate polynomial is nonzero
> that separate all roots.
>
> --
> Oscar
>

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