On May 3, 9:27 pm, "William Stein" <[EMAIL PROTECTED]> wrote:
> 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)
Thanks for the very informative reply!
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