Hi Michael,
Thanks for your message. I'm still a little confused about the way Sage
handles assumptions, can you maybe shine your light on this?
On Monday, July 1, 2013 8:55:43 PM UTC+1, Michael Orlitzky wrote:
>
>
> > sage: u = var('u')
> > sage: assume(u, 'real')
>
> This makes an assumption in Maxima, where most of the symbolic algebra
> takes place.
>
As far as I can tell, setting domain to complex in maxima has the effect
that sin, cos, etc are now seen as de facto complex-valued functions, even
when the input x is assumed to be real. This is probably why maxima refuses
to simplify abs(cos(x))^2 + abs(sin(x))^2 to 1.
> sage: u = var('u', domain='real')
>
> This sets a flag in pynac, which does nothing as far as I can tell.
>
But the example in my original message works -- this really confuses me.
Clearly, simplify_trig invokes maxima to do the simplification, so why does
setting this flag in pynac make it work? Are functions of real variables
treated differently from functions taking a complex argument?
Thanks!
Joris
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