Thomas,
These look like quantum energy level equations. Have you looked at 
sympy.physics.quantum to see if they have solved your problem? I seem to 
remember they have defined some special quantities for quantum numbers that 
are limited to integer and half-integer values. I make no promises as I 
have not actually used the package. This is just a recollection from 
scanning through the documents.

Jonathan

On Wednesday, January 6, 2021 at 11:16:46 AM UTC-6 [email protected] 
wrote:

> If I use 1/3 in an expression, I get 0.333..., but I know that I can write 
> Rational(1,3) instead. Now I have some expressions, such as
>
> -((s)/(j))*((4*(j-1)*s+4*j**2+4*j-2-4*(s-j+1)*m+m**2)/(2*(4*j**2-1)-4*m+m**2))
> where m is a symbol that will ultimately be replaced by a floating-point 
> number, and s and j are integers (positive or negative, but never zero). 
> They are replaced (using subs), and when I substitute s by 3 and j by 1, I 
> get 0.333.... In the formula, I can't write Rational(s,j), because Rational 
> does not accept a symbol as an argument.
> Is there a way to do this?
>

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