---------- 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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