On 05/13/2013 04:56 PM, John H Palmieri wrote:
> On Monday, May 13, 2013 2:11:59 PM UTC-7, ManDay wrote:
>
> Could anyone shed a bit of light on this?
>
> The more I try, the more SAGE's types get in my way. It turns out to be
> an unpredictable element. Unless I make sure *every* involved function
> really returns one specific type, calculations are becoming practically
> impossible, because the results are completely random (malfunctions).
>
> Here is just the last and most annoying of my encounters I can't make
> heads or tails of, enjoy:
>
> http://alpha.sagenb.org/home/pub/701/
> <http://alpha.sagenb.org/home/pub/701/>
>
>
> The issue is, if you define a number a by
>
> sage: a = -CDF(2.4995)
>
> then the imaginary part of a is "-0.0", and it is treated as negative.
> When a**(1/2) is computed, it is computed (according to the
> documentation) as exp(log(a)*(1/2)), and since the imaginary part of a
> is negative, its log has imaginary part approximately equal to -pi. This
> choice of branch cut is documented: type "log?" On the other hand:
>
> sage: b = CDF(-2.4995)
>
> Then b has imaginary part which is 0.0, treated as positive, so log(b)
> has imaginary part approximately equal to +pi.
Also, this not restricted to sage. Try this little C program (using C99
standard, so don't try it on Visual Studio):
#include <stdio.h>
#include <math.h>
#include <complex.h>
int main() {
complex a = 2.4995, b = -2.4995;
printf("%g %g\n", cimag(csqrt(-a)), cimag(csqrt(b)));
}
This really is what the C99 standard requires.
--
You received this message because you are subscribed to the Google Groups
"sage-devel" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-devel+unsubscr...@googlegroups.com.
To post to this group, send email to sage-devel@googlegroups.com.
Visit this group at http://groups.google.com/group/sage-devel?hl=en.
For more options, visit https://groups.google.com/groups/opt_out.
