Classic Fourier Series

[salvomic]

(01-31-2015 09:11 PM)Snorre Wrote:  a program is always a good idea ;-)

Just two tips:

Hi Snorre,
after some tries now I'm working on this idea, just for fun (and to understand):

Code:


#cas
fourcoeff(fun,k)
BEGIN
local nstr := instring(string(fun),"t");
// check if t is in string fun
local tipo:=type(fun);
// check the type: DOM_FUNC, DOM_SYMBOLIC, ...
local a0, ak, bk;
CASE
IF tipo = DOM_FUNC THEN
a0:=(int(fun(t),t,0,2*PI))/(2*PI);
ak:=(int(fun(t)*cos(k*t),t,0,2*PI))/PI;
bk:=(int(fun(t)*sin(k*t),t,0,2*PI))/PI;
return {a0,ak,bk};  // a list
END;
IF nstr != 0 THEN
// not t
a0:=(int(fun,t,0,2*PI))/(2*PI);
ak:=(int(fun*cos(k*t),t,0,2*PI))/PI;
bk:=(int(fun*sin(k*t),t,0,2*PI))/PI;
return {a0,ak,bk};  // a list
END;
DEFAULT return "Input must be function or expr with t";
END;
END;
#end

With this, after having defined g(t):=t^2, I get:
fourcoeff(g,1) -> ok, correct value
fourcoeff(t^2,1) -> ok, correct value, without any warning
fourcoeff(x^2,1) -> exit with the message.

This is a workaround, sure, and the the program could be strongly improved!

So the "type" control is working (it now handle a function in t and and expression in t), but it would better to set another control to say "if tipo=DOM_SYMBOLIC and the letter is not "t" substitute any letter like x, y, z... into "t") or reformat fun in fun(t) in some way but a efficient one (now the expression could have "t" without to be correct)...

Thank you for patience