On Sat, May 3, 2008 at 6:53 PM, dvase <[EMAIL PROTECTED]> wrote:
>
> Hello,
> It seems as though I am missing something obvious, but I can not
> figure out how to use complex number manipulations on symbolic
> variables in sage.
>
> A trivial example would be to have a function that returns the
> imaginary portion of a given complex value:
>
> sage: f(x) = imag(x)
> sage: f(i*1)
> I
>
> However, the result of this currently gives me zero, as it seems the
> imag() function is not captured by the function declaration. Any
> insights on this quandary?
At present, depending on what you're doing your best bet in this case
is probably just to define a Python function instead of a formal symbolic
function. For example, paste in this:
def f(x):
return imag(x) + 5
Then
sage: f(3+I)
6
The rest of this email has some details about what is going on.
Since symbolic calculus in Sage is currently being massively
rewritten by Bill Furnish, I don't recommend people worry
too much about making changes to the current system to
address this problem.
Complex number support for Sage's current symbolics is not very good.
It wasn't a high priority in the initial implementation.
In particular, imag is just a Python function:
sage: type(imag)
<type 'function'>
whereas for something like the above to work well it should be a
symbolic function.
Second, even if imag were symbolic Maxima (which does expression simplification
of Sage symbolic expressions behind the scenes) would view x by default
as real, and imag(x) = 0.
sage: sage.calculus.calculus.maxima('imagpart(x)') # imagpart = imag in maxima
0
sage: sage.calculus.calculus.maxima('realpart(x)')
x
This behavior can be changed as follows:
sage: sage.calculus.calculus.maxima('declare(x, complex)')
done
sage: sage.calculus.calculus.maxima('imagpart(x)') # imagpart = imag in maxima
?%imagpart(x)
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