Yes, it is a bug. Maybe somebody should report it.
----- Original Message -----
From: "Richard Hennessy" <rich.hennessy at verizon.net>
To: "Leo Butler" <l.butler at ed.ac.uk>; "Stanislav Maslovski"
<stanislav.maslovski at gmail.com>
Cc: <maxima at math.utexas.edu>
Sent: Friday, October 09, 2009 9:52 PM
Subject: Re: [Maxima] plotting a parametric integral
> (%o6) is not right, I noticed. Is this a bug?
>
> Rich
>
> ----- Original Message -----
> From: "Richard Hennessy" <rich.hennessy at verizon.net>
> To: "Leo Butler" <l.butler at ed.ac.uk>; "Stanislav Maslovski"
> <stanislav.maslovski at gmail.com>
> Cc: <maxima at math.utexas.edu>
> Sent: Friday, October 09, 2009 9:04 PM
> Subject: Re: [Maxima] plotting a parametric integral
>
>
>> This integral cannot be done by Maxima. Try
>>
>> (%i4) display2d:false;
>>
>> (%o4) false
>> (%i5) load(noninteractive);
>>
>> (%o5)
>> "C:/Maxima-5.19.2/share/maxima/5.19.2/share/contrib/noninteractive/noninteractive.mac"
>> (%i6) integrate(exp(%i*k*x)*sin(x)/x,x,minf,inf);
>>
>> (%o6) if k-1 < 0 then integrate(%e^(%i*k*x)*sin(x)/x,x,minf,inf) elseif
>> equal(k-1,0) then %pi else 0
>>
>> The answer shows that when k-1<0 Maxima can't do the integration.
>>
>> Rich
>>
>> ----- Original Message -----
>> From: "Leo Butler" <l.butler at ed.ac.uk>
>> To: "Stanislav Maslovski" <stanislav.maslovski at gmail.com>
>> Cc: <maxima at math.utexas.edu>
>> Sent: Friday, October 09, 2009 4:03 AM
>> Subject: Re: [Maxima] plotting a parametric integral
>>
>>
>>>
>>>
>>> On Fri, 9 Oct 2009, Stanislav Maslovski wrote:
>>>
>>> < Hello,
>>> <
>>> < I am trying to plot this simple Fourier integral in Maxima 5.17.1:
>>> <
>>> < (%i1) display2d : false$
>>> <
>>> < (%i2) f(k):=integrate(exp(%i*k*x)*sin(x)/x,x,minf,inf)$
>>> <
>>> < (%i3) [f(0), f(1), f(3/2)];
>>> <
>>> < (%o3) [%pi,%pi,0]
>>> <
>>> < So far so good.
>>> <
>>> < (%i4) plot2d(f,[x,-3,3]);
>>> <
>>> < (%o4)
>>> < (%i5) Warning: empty y range [0:0], adjusting to [-1:1]
>>> <
>>> < Theoretically, f(k) must be equal to %pi for k in [-1;1] and 0
>>> < outside. The plot does not show anything in [-1;1].
>>> <
>>> < Moreover, if I try this plotting command
>>> <
>>> < plot2d(f(k),[k,-3,3]);
>>> <
>>> < I get a stupid question about the sign of k-1.
>>> <
>>> < Can anyone explain what is wrong here?
>>>
>>> There are a few things. The integral, f(k), is a piece-wise constant
>>> function. At the moment, Maxima lacks the ability to return an answer in
>>> this form. Work is being done to correct this.
>>>
>>> I would suggest that you try the following definition:
>>>
>>> (%i2) f(t) ::= buildq([k:t],
>>> integrate(exp(%i*k*x)*sin(x)/x,x,minf,inf));
>>> (%o2) f(t)::=buildq([k:t],integrate(exp(%i*k*x)*sin(x)/x,x,minf,inf))
>>>
>>> This will avoid any calls to 'asksign' (which is asking about the sign
>>> of k) when t is a constant. I have also set ratprint to false to avoid
>>> the annoying warnings about floats being converted to rationals.
>>>
>>> (%i3) l : makelist(i/10,i,-20,20)$
>>> (%i4) fl : float(map(f,l));
>>> (%o4) [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,3.141592653589793,
>>> 3.141592653589793,3.141592653589793,3.141592653589793,
>>> 3.141592653589793,3.141592653589793,3.141592653589793,
>>> 3.141592653589793,3.141592653589793,3.141592653589793,
>>> 3.141592653589793,3.141592653589793,3.141592653589793,
>>> 3.141592653589793,3.141592653589793,3.141592653589793,
>>> 3.141592653589793,3.141592653589793,3.141592653589793,
>>> 3.141592653589793,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]
>>> (%i5) plot2d([discrete,l,fl]);
>>> This plots what you want.
>>>
>>> Incidentally, you will find that this is very slow. The problem is that
>>> the integral is being recomputed each time f is evaluated. What you
>>> would really want to do is to compute the integral once, as a symbolic
>>> facility is under development.
>>>
>>> Note that you can also use 'assume':
>>>
>>> (%i35) [ (map(forget,facts()), assume(k<-1),f(k)) , (forget(k<-1),
>>> assume(k>1),f(k)) , (forget(k>1), assume(k>-1,k<1),f(k)), f(-1), f(1) ];
>>> (%o35) [0,0,%pi,0,%pi]
>>>
>>> Leo
>>>
>>> --
>>> The University of Edinburgh is a charitable body, registered in
>>> Scotland, with registration number SC005336.
>>>
>>> _______________________________________________
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>>>
>>
>>
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