Hello,
Is there a way in Sage to express the derivative at one point of a
"formal" function?
I mean: something equivalent to "at(diff(f(x),x), x=123);" in Maxima
or "eval(diff(f(x),x), x=123);" or "D(f)(123);" in Maple or "D[f
[x],x]/.x->123" or "Derivative[1][f][123]" in Mathematica.
For instance, the following does not work:
f=function('f',x)
g=(f(x)).function(x)
h=derivative(g)
h(0)
because Sage sends to Maxima "diff('f(0), 0, 1)" and, of course,
Maxima complains ("Maxima ERROR: Non-variable 2nd argument to diff:").
Of course, if f is explicitly known (e.g. with "f(x):=1+x^2"), there
is no problem.
Actually, I would like to be able to show with Sage that f(x+a)+f(x-
a)-2*f(x) is f''(x) at the first nonvanishing order in a, but it is
still far away from working: Sage's "taylor" does not work with a
"formal" function, and, even though Maxima does slightly better, it's
not enough: for "taylor(f(x-a),a,0,2);", Maxima's result involves "d/
da f(x-a) |a=0", while further simplification to -f'(x) would be
needed.
Thanks for your help,
Christophe Deroulers
University Paris Diderot-Paris 7, Physics Department
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