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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 14:31:02 -0700
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"I.N. Galidakis" <morpheus@olympus.mons> writes:

> Joe Riel wrote:
>> "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);
>
> Thanks. I thought of premature evaluation, but I didn't know what
> delimiters to put around HW. On Maple V rel 5, it was `HW`(..) so I
> tried that and it didn't work.
>
> Now it seems to be 'HW'(...).

The interpretation of backquotes and forward quotes has not changed.
Backquotes create a symbol from non-alphanumeric characters.
Forward quotes delay evaluation.

-- 
Joe Riel