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simplify is not realible

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Michal
Michal on 30 Mar 2023
Commented: Michal on 31 Mar 2023
How to simplify the folowing very simple expression:
syms a b c
e1 = -(b*(b^2 - 4*a*c)^(1/2) - 4*a*c + b^2)/(2*a*(b^2 - 4*a*c)^(1/2))
which is equal to the
e2 = -(b + (b^2 - 4*a*c)^(1/2))/(2*a)
simplify(e1-e2)
ans =
0
>> isAlways(e1 == e2)
ans =
logical
1
but
simplify(e1)
produce only identical expression with "e1", not with "e2" as expected?!
Is there any possibility to use "simplify" command in a different way, to get expected result?
  7 Comments
John D'Errico
John D'Errico on 31 Mar 2023
@Michal - Just because one (or more) tool can find a particular solution that you happen to like does not mean that all tools will do so. They are equivalent.
Michal
Michal on 31 Mar 2023
@John D'Errico Yes, of course! But your claim - "They are equivalent" is very vague or controversial, because then any simplification attempt loses sense.
I hope you understand my point. Anyone wants to see the expression, which is simplest as possible of all (infinitely) others equivalent expressions (typically, from the point of required operations number, for example).
But once again, this case is so trivial that I am just a bit surprised, why all CAS cannot find the same simplest expression.

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