Jer?nimo Alaminos Prats wrote:
> Hi all,
> I've using maxima for about a month in a calculus class. I'm writing
> some notes to help the students and now I'm having some trouble with
> the behavior of Taylor series.
> If I define a function and its Taylor polinomial, I have no problem
> plotting both or calculating the difference
>
> (%i3) taylor(log(1+x),x,0,5);
> (%o3) x-x^2/2+x^3/3-x^4/4+x^5/5+...
> (%i5) define(g(x),taylor(f(x),x,0,5));
> (%o5) g(x):=x-x^2/2+x^3/3-x^4/4+x^5/5+...
> (%i6) g(2);
> (%o6) 76/15
> (%i8) f(2)-g(2);
> (%o8) (15*log(3)-76)/15
> but
>
> plot2d[f(x)-g(x),[x,0.1,5])
>
> plots the zero function. I can obtain the expected (at least for me)
> behavior using
>
> plot2d(f(x)-trunc(g(x)),[x,0.1,5])
>
> Is this the right thing to do? I do not understand when it's mandatory
> to use trunc with taylor and when it is optional? I mean, what's the
> difference between taylor(...) and trunc(taylor(...))?
>
> If someone it's interested the notes (in spanish) are available as a
> work in progress at
>
> http://www.ugr.es/~alaminos/docencia_2/calculo_telecomunicaciones/practicas_de_ordenador/
>
> Of course any comments are welcome.
>
> Thank you,
> Jer?nimo.
>
>
>
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>
This looks like a bug to me.
What do others think?
For instance,
(%i37) display2d: false;
(%o37) false
(%i38) f(x):= taylor(log(1+x),x,0,5);
(%o38) f(x):=taylor(log(1+x),x,0,5)
(%i39) g(x):= taylor(log(1+x),x,0,7);
(%o39) g(x):=taylor(log(1+x),x,0,7)
(%i40) f(x);
(%o40) x-x^2/2+x^3/3-x^4/4+x^5/5
(%i41) g(x);
(%o41) x-x^2/2+x^3/3-x^4/4+x^5/5-x^6/6+x^7/7
(%i42) g(x)-f(x);
(%o42) +0
(%i43) ratexpand(g(x)) - ratexpand(f(x));
(%o43) x^7/7-x^6/6
Using 'ratexpand' seems to fix the problem, but I don't think that
should be necessary.
-sen