#14628: Zero solution does not result in zero
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Reporter: gagern | Owner: burcin
Type: defect | Status: new
Priority: major | Milestone: sage-5.10
Component: symbolics | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Comment (by kcrisman):
Ah, got it. The problem is related to #6862 in that `phi` wasn't actually
real. Unfortunately, it doesn't seem to be quite that simple; somehow the
imaginary part in Maxima is different from in Pynac.
{{{
sage: phi = var('phi')
sage: z = (I + 1)*sqrt(-I)/((e^(I*phi) - 1)*((I + 1)/(e^(I*phi) - 1) -
I*e^(-I*phi)))
sage: z.maxima_methods().imagpart()
-1/2*(((cos(phi) - 1)*((sin(phi) + cos(phi) - 1)/((cos(phi) - 1)^2 +
sin(phi)^2) - sin(phi)) -
<more stuff>
sage: z.imag()
-sqrt(2)*e^imag_part(phi)*cos(-real_part(phi))/((e^(-2*imag_part(phi))*sin(real_part(phi))^2
+
<a whole lot of stuff with imaginary and real part>
sage: assume(phi,'real')
sage: z.imag().simplify()
sqrt(2)*sin(phi)^2/((sin(phi)^2 +
<a whole bunch of stuff without imag part and real part, correctly>
+ 2*cos(phi)^2/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 -
4*cos(phi)/(sin(phi)^2 + cos(phi)^2 - 2*cos(phi) + 1)^2 + 2/(sin(phi)^2 +
cos(phi)^2 - 2*cos(phi) + 1)^2))
}}}
But it isn't evident that the last thing and the `maxima_methods()` thing
are the same (unless fully simplified, but that's not what we're talking
about here, as see the post mentioned it the description).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14628#comment:4>
Sage <http://www.sagemath.org>
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