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From: Joe Riel <joer@san.rr.com>
Newsgroups: comp.soft-sys.math.maple
Subject: Re: Plot problem with function
Date: Thu, 28 Jul 2011 12:18:42 -0700
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"I.N. Galidakis" <morpheus@olympus.mons> writes:

> I am having some problems with Maple 9 when plotting a certain
> function. The function is:
>
>> HW:=proc()
>> local y,n,c,s,p,sol,i,aprx,dy,dist,r,oldr,newr,fun,dfun,eps;
>> if nargs<2 then ERROR("At least two arguments required.") fi;
>> n:= args[-1];y:=args[-2];c:= [args[1..-3]];
>> if y=0 then 0 else
>>  dist:=infinity;
>>  eps:=1e-32;
>>  fun:= 1;
>>  for i from 1 to nargs-2 do fun:= exp(c[i]*fun) od;
>>  fun:= z*fun-y;
>>  dfun:=diff(fun,z);
>>  s:=series(fun,z,n);
>>  p:=convert(s,polynom);
>>  sol:={fsolve(p=0,z,complex)}; #complex?
>>  for i from 1 to nops(sol) do
>>   aprx:=evalf(subs(z=op(i,sol),fun));
>>   dy:=evalf(abs(aprx));
>>   if dy<=dist then r:=op(i,sol);dist:=dy;fi;
>>  od;
>> #start Newton with approximate zero found.
>>  oldr:=r;
>>  newr:=r-evalf(subs(z=r,fun)/subs(z=r,dfun));
>>  for i from 1 to 1000 while (abs((oldr-newr)/oldr)>eps) do
>>   oldr:=newr;
>>   newr:=newr-evalf(subs(z=newr,fun)/subs(z=newr,dfun));
>>  od;
>> newr;
>> fi;
>> end:
>
> When I try to plot it (in this case the arguments make it equivalent
> to arcsin) I get:
>
>> with(plots):
>> plot(HW(log(sin(z)/z),y,10),y=-1..1);
> Error, (in fsolve) y is in the equation, and is not solved for
>
> while if I do a:
>
>> N:=50;x1:=-1;x2:=1;
>> x:=n->x1+abs(x2-x1)/N*n;
>> L:=[seq([x(n),HW(log(sin(z)/z),x(n),10)],n=0..N)]:
>> plot(L,scaling=constrained);
>
> It works (shows the graph of arcsin).
>
> Individual values seem to be calculated correctly. For example:
>
>> HW(log(sin(z)/z),0.245,10);
> .247519692533815916885429116210
>
> Does anyone know why the plot command doesn't work with this function?

The cause is premature evaluation.  The plot procedures (as most Maple
procedures) first evaluates its arguments.   But

 HW(log(sin(z)/z),y,10);

raises the error because y is not numeric.  An easy solution is
to delay the evaluation of HW.  You can do that via

  plot('HW'(log(sin(z)/z),y,10),y=-1..1);

-- 
Joe Riel