Michael, I appreciate your very thoughtful reply.
On Jan 20, 10:45 pm, Michael Orlitzky <mich...@orlitzky.com> wrote:
> > ---------- Forwarded message ----------
> > From: storne...@mathisasport.com<storne...@mathisasport.com>
>
> > That's fine, but now I want to solve for dy/dx, so I try:
>
> > sage: solve(equation2.diff(),diff(f(x),x,1))
> > /home/stornetta/sage-4.7.2/local/lib/python2.6/site-packages/IPython/iplib.
> > py:2260:
> > DeprecationWarning: Substitution using function-call syntax and
> > unnamed arguments is deprecated and will be removed from a future
> > release of Sage; you can use named arguments instead, like EXPR(x=...,
> > y=...)
> > exec code_obj in self.user_global_ns, self.user_ns
> > [D[0](f)(x) == -f(x)/(x + 4*f(x))]
>
> > as you can see, I do get an answer, but the interpreter indicates my
> > approach is deprecated, and I'm not clear on how one would use named
> > arguments in this situation to achieve the same result.
>
> f here is a symbolic function taking one argument (forget for a second
> that the argument is called 'x'). f(x) means f evaluated at x, which of
> course is... f(x), whatever that is. What I'm trying to get at here is
> that f(x) isn't the function, f is.
>
> You can try:
>
> f = function('f',x)
> sage: y = var('y')
> sage: f(y)
> f(y)
>
> the call f(y) just substitutes 'y' for 'x' in the definition of f, even
> though we don't really have one, we just refer to it by name, f. It's
> the same as f(x = y).
>
> Thus, your call to f(x) up there makes an unnecessary substitution --
> it's equivalent to f(x = x). In fact, to avoid the warning, f(x = x) is
> what you would do. Of course, it's better to just pass in f and not
> evaluate it:
>
> sage: f = function('f',x)
> sage: equation2 = x*f + 2*f^2 == 1
> sage: solve(equation2.diff(),diff(f,x,1))
> [D[0](f)(x) == -f(x)/(x + 4*f(x))]
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