Let's face it. Sage is largely a sum or sometimes a product of all the
decisions
including the bad ones, of all the systems that it incorporates. Plus of
course the bad decisions made by Python and in the Python code combining
them.
It is unreasonable to expect the
possible benefits of one subsystem to magically repair the deficits of
others. The systems that pretend to understand functions of a (single)
complex variable are few if any. Systems that pretend to understand
functions of several complex variables are, so far as I know, non-existent,
programming-wise.
RJF
On 7/28/13 2:32 AM, Emmanuel Charpentier wrote:
> This is inspired by https://groups.google.com/forum/#!topic/sage-support/
> o0rwQId7ELU and http://trac.sagemath.org/ticket/14976.
>
> There seems to be no way to declare explicitly a function and function
> domains. Consider :
>
> (%i1) display2d:false;
>
> (%o1) false
> (%i2) define(h(x), integrate(f(t), t, g1(x), g2(x)));
>
> defint: lower limit of integration must be real; found g1(x)
> -- an error. To debug this try: debugmode(true);
>
> ;; Let's try to declare g1 and g2 as real-valued *symbols*. Kinda sorta
> ;; works :
>
> (%i3) declare(g1, real, g2, real);
>
> (%o3) done
> (%i4) define(h(x), integrate(f(t), t, g1(x), g2(x)));
>
> (%o4) h(x):='integrate(f(t),t,g1(x),g2(x))
> (%i5) diff(h(x), x);
>
> (%o5) f(g2(x))*'diff(g2(x),x,1)-f(g1(x))*'diff(g1(x),x,1)
>
> ;; This was the expected result
> ;; Now, we'd like to *declare* a symbol as a real-valued function
>
> (%i6) declare(s(x), real);
>
> declare: improper argument: s(x)
> -- an error. To debug this try: debugmode(true);
>
> ;; doesn't work!
>
> On the other hand, Sage, which uses Maxima for symbolic calculations,
> allows (needs !) declaration of formal functions, but does not allow to
> declare their domain. There is an horrible workaround (see http://
> trac.sagemath.org/ticket/14976), but the plroblem remains.
>
> Should this be considered a bug ?
>
> Emmanuel Charpentier
>
>
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