[Maxima] Fourier Series for unit step
macrakis at alum.mit.edu
Sun May 11 15:38:52 CDT 2008
On Sun, May 11, 2008 at 11:29 AM, Ismael Garrido <ismaelgf at adinet.com.uy> wrote:
> If I define the function as f(x):= if x>0 then 1 else 0, then
> totalfourier doesn't know how to integrate that....
Unfortunately, none of the standard Maxima mathematical routines
(integrate, diff, etc.) can do anything useful with if/then/else
expressions, even in the simplest cases:
integrate(abs(x),x,0,1) => 1/2 <<< ok with abs when integrand >=0
integrate(if x>=0 then x else -x,x,0,1) (equivalent) => can't do it
In fact, not even Maxima simplification works correctly with
expand(expr) => q resimplification takes assumption into account
expr: if r=0 then r else -r$
expand(expr) => unsimplified (doesn't take assumption into account)
ev(expr) => r (if/then/else acts like a programming construct,
not a mathematical expression)
This is certainly an area we want to improve in future versions.
PS Don't assume from the above that Maxima is brilliant with abs,
either! For example, it can't do integrate(abs(x),x,-1,1).
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