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It is stated at the Wolfram Documentation Center (FullSimplify/Possible Issues) that:

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Why and when this could happen? How to avoid it? Any patterns?

Edit:

As pointed out in the comments, this question is a duplicate.

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  • $\begingroup$ The first examle mighe be FullSimplify[(1 - b^2)/c^2, c^2 + b^2 == 1]. $\endgroup$
    – Artes
    Dec 2, 2014 at 13:54
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    $\begingroup$ @Artes yes, it seems that the alphabetic order is the problem. The symbol inside the parenthesis has to come first considering the alphabet order. It's obvious with these examples : FullSimplify[(1 - abx^2)/aby^2, abx^2 + aby^2 == 1] and FullSimplify[(1 - aby^2)/abx^2, abx^2 + aby^2 == 1]. The first example gives 1 because abx is "before" aby (if you sort them alphabetically) ... $\endgroup$
    – SquareOne
    Dec 2, 2014 at 14:10
  • $\begingroup$ Why doesn't Wolfram relabel the symbols, simplify, and restore the original names...? $\endgroup$
    – tclamb
    Dec 2, 2014 at 15:59
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    $\begingroup$ I have the impression that this happens because trying out all possible replacements would involve going through large numbers of permutations which would generally lead to a combinatoric explosion. So, some choices have to be made, and not all possible replacements are actually tried. $\endgroup$
    – Sjoerd C. de Vries
    Dec 2, 2014 at 16:42
  • $\begingroup$ Maybe an option should be available for us. $\endgroup$
    – Giovanni F.
    Dec 2, 2014 at 16:43

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