#12780: Be more careful about setting the Maxima 'domain'
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Reporter: mjo | Owner: burcin
Type: enhancement | Status: closed
Priority: major | Milestone: sage-5.6
Component: symbolics | Resolution: fixed
Keywords: | Work issues:
Report Upstream: N/A | Reviewers: Burcin Erocal
Authors: Michael Orlitzky | Merged in: sage-5.6.beta0
Dependencies: #12845 | Stopgaps:
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Comment (by zimmerma):
if {{{x}}} is assumed to be real the correct answer for {{{sqrt(x^2)}}} is
{{{abs(x)}}}.
However if {{{x}}} is assumed to be complex, the correct answer is either
{{{x}}} or {{{-x}}},
more precisely the one with a positive real part (or a nonnegative
imaginary part if the real part is zero). Then if {{{x}}} is non-real the
answer {{{abs(x)}}} is wrong, since this is the norm of {{{x}}}, and the
norm is real. Consider for example {{{x = -3+4*I}}}, whose norm is 5, but
whose square root is {{{3-4*I}}}.
Maple 15 gives:
{{{
> assume(x,real);
> simplify(sqrt(x^2));
| x~ |
> assume(x,complex);
> simplify(sqrt(x^2));
csgn(x~) x~
}}}
If this ticket did change the default domain of symbolic variables from
real to complex, this is a **MAJOR** change.
Paul
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12780#comment:15>
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