Rational is only needed if you have the division of integer literals,
because SymPy cannot control how Python evaluates 1/3. Once you have a
fraction in an expression, it will stay exact:
>>> (-((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))).subs({s:
>>> 3, j: 1})
-3*(m**2 - 12*m + 6)/(m**2 - 4*m + 6)
It's not necessary to use Rational to create a symbolic fraction.
Using / as you have done is the correct way to do that.
It's possible I'm misunderstanding your question because what you
described is not what happens. The problem that you are perhaps having
is that if one of the numbers you substitute is substituted as a
float, then SymPy will evaluate the entire expression as a float.
>>> (-((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))).subs({s:
>>> 3, j: 1, m: 1.0})
5.00000000000000
If you want an exact number in your answer then all your numeric
constants should be rational numbers rather than floats.
Aaron Meurer
On Wed, Jan 6, 2021 at 10:16 AM Thomas Ligon <[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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