I have found this annoying problem in sympy. I want to simply the following simple fraction expression below but can't make it work... Sympy even recognizes the two equations as equal making it even more frustrating.

import sympy as sp
a,b,c,d = sp.symbols('a, b, c, d', positive = True)
expr = (a*b*c+2*d*a*c+b*c*d)/(2*a+b)
correct_simpl = c*(d +  a*b/(2*a+b))
display(expr)
display(expr.simplify())
display(correct_simpl)
correct_simpl.equals(expr)

Returns:

I have found this annoying problem in sympy. I want to simply the following simple fraction expression below but can't make it work... Sympy even recognizes the two equations as equal making it even more frustrating.

import sympy as sp
a,b,c,d = sp.symbols('a, b, c, d', positive = True)
expr = (a*b*c+2*d*a*c+b*c*d)/(2*a+b)
correct_simpl = c*(d +  a*b/(2*a+b))
display(expr)
display(expr.simplify())
display(correct_simpl)
correct_simpl.equals(expr)

Returns:

• python
• sympy
• simplification

• 3 Why do you think the third version is better from the second? Possibly it is just a question of taste (and so on how to program). I definitely prefer the second one (as the simplest) – Giacomo Catenazzi Commented 14 hours ago
• The third version has fewer symbols (7 vs 11 symbols in version 2) and shows the dependency of the expression on the different parameters more clearly. – Pancake_stack_with_syrup Commented 13 hours ago
• 1 Other tools had different function to simplify (according preferences). I do not know about sympy. Just different people have different opinion on the "standard simplification". So I think it is the answer: it depends on opinion (of the programmer) – Giacomo Catenazzi Commented 12 hours ago
• 2 Most computer algebra systems and libraries, sympy included, are not designed to produce, not even in simplification, expressions in the form considered by humans as the nicest. The fact that it verified the expressions are equal is an excellent result and that's typically what you'd use sympy for. You can usually "wrestle" an expression to the form you want, applying more or less naturally the various functions available to rewrite it - for your expression you may use expr.apart(d).collect(c). – kikon Commented 10 hours ago

2 Answers 2

The following can give you your expression of taste. You can use your interactive prompt to see what each of the steps is doing. The cse is there to collect that 2a+b into a single term that doesn't expand when doing the expansion: r,e=cse(factor_terms(collect(expr,d)));expand(e[0]).subs(r)

The fact that expr.simplify() does not return the exact result is due to the heuristics used by Sympy’s general simplify() function—it doesn’t guarantee a unique “simplest” form, only that the result is mathematically equivalent (as confirmed by correct_simpl.equals(expr)).

If you require the result in that specific form, you can try using a more targeted function such as:

sp.factor_terms(expr)