On Aug 18, 7:02 pm, Markus Dangl <s...@q1cc.net> wrote:
> Hi,
>
> i've looked through this group and sage-support and could not find
> anything related. I'm using sage 4.5.2 on 64 bit Linux (Ubuntu) - if
> this is even relevant.
>
> The simplify_radical() method for symbolic expression seems to assume
> that sqrt(z*z) == abs(z) in all cases. This is wrong for complex
> numbers, where only sqrt(z * z.conjugate()) == abs(z). I'm relatively
> new to sage, so please excuse me if i missed it, but there seems to be
> no way to tell "simplify_radical()" to respect complex numbers. If i
> am wrong, this is not a bug, hence the post here before opening a bug
> report.

Thanks for your report, Markus.  I don't have time to look into this
in general, but the quick answer almost certainly is also the correct
one - namely, that the various simplify_*() methods implicitly make
assumptions.  simplify_log(), at least, has good documentation about
this (thanks Robert M.!), and some of the others will too.  The
simplify methods are Sage's best guess at what simplifications might
be useful to people from the plethora that Maxima provides for us, but
certainly not all of them are correct in full generality.  You may
wish to look at Maxima's documentation for its various simplification
routines as well.

That doesn't mean this isn't a bug, but if it's consistently assuming
z is real, for this simplification and the documentation doesn't say
so, it's more likely to be lacking documentation for this.  If in
other places z could be complex and it behaves appropriately, maybe it
is a bug.

- kcrisman

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