There is a big difference between 1 and 10 terms.
I typically use 30 using automatic numeric differentiation.
Check the sode link below.
-
Dennis J. Darland
student at dennisdarland.com
http://dennisdarland.com/http://dennisdarland.com/philosophy/http://sode.sourceforge.net/
On Saturday, May 11, 2013 03:09:47 PM you wrote:
Your integral should return instantaneously. I don't know why an earlier correspondent
claimed that this would take a long time and lots of memory.
The fact that Maxima runs forever on this simply indicates that there is a bug. (Sorry!)
Here's a little more detail:
The correct answer is very simple. taylor(f(x),x,a,1) returns
f(a)+('at('diff(f(x),x,1),x = a))*(x-a)
f(a) is clearly independent of x, so integrate(f(a),x) =>x*f(a).
'at('diff(f(x),x,1),x = a) is /also/ independent of x -- x in this expression is a _dummy
variable_, so this expression means the same thing as 'at('diff(f(y),y,1),y = a). So
integrate('at('diff(f(x),x,1),x = a) *(x-a) should be 'at('diff(f(x),x,1),x = a) *(x^2/2-a*x).
Instead, Maxima is apparently getting into an infinite loop. This is a bug. The simplest way
I've found to elicit it is integrate(at(diff(f(x),x),x=3),x).
A simple workaround is to rename all the dummy variables. Here's a simple way to do that:
rename_dummies(expr) :=
subst(nounify(at) =
lambda([ex,vareq],
subst(gensym(),lhs(vareq),at(ex,vareq))),
expr)$
So now you can do
integrate( rename_dummies( taylor(f(x),x,a,1) ), x,a,a+h)
and get the correct answer instantaneously.
Bizarrely, Maxima is numbering gensyms starting at 34100, which makes the answer ugly,
but still correct.
-s
I'm running Maxima 5.28 on GCL 2.6.8 on Windows
On Sat, May 11, 2013 at 2:30 PM, Thomas D. Dean <tomdean at speakeasy.org[1]> wrote:
On 05/09/13 14:39, Dennis J. Darland wrote:
It might take a very long time, if you have enough memory!
http://maxima.sourceforge.net[2]
Maxima at math.utexas.edu[3]
http://www.math.utexas.edu/mailman/listinfo/maxima[4]
--------
[1] mailto:tomdean at speakeasy.org
[2] http://maxima.sourceforge.net
[3] mailto:Maxima at math.utexas.edu
[4] http://www.math.utexas.edu/mailman/listinfo/maxima