On Tuesday, May 21, 2024 at 3:49:12 PM UTC-7 Oscar wrote:

On Tue, 21 May 2024 at 22:02, Aaron Meurer <[email protected]> wrote: 
> 
> IMO, we should just fix the function to not return intersecting 
> endpoints in the first place. The intervals aren't really isolating if 
> they intersect. 

For rational roots the intervals are of length 0. For irrational roots 
the root lies in the interior of the interval. In other words what is 
returned is a set of individual rational points and open intervals on 
the real line. An open interval might be bounded by one of the 
rational points but they do not intersect because the interval does 
not contain its boundary. 


For rational roots the intervals may not be of length 0. Consider the 
following program:


   - from sympy import Poly
   - from sympy.abc import x
   - from sympy import div, ZZ, QQ, RR
   - print(Poly(4*x**2 - 9, x, domain='QQ').intervals())

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.

Thanking you
Best

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