RE : How to graph an expression involving sum?

> -----Message d'origine-----
> De?: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu] De la part de
> dlakelan
> Envoy??: vendredi 9 septembre 2011 21:28
> ??: maxima at math.utexas.edu
> Objet?: Re: [Maxima] How to graph an expression involving sum?
> 
> On 09/08/2011 09:09 PM, Mario Rodriguez wrote:
> > On 09/05/2011 04:08 PM, dlakelan wrote:
> >> I have a solution of a differential equation in terms of some fourier
> >> series. I would like to graph one of the spatially varying coefficients,
> >> so I tried something like:
> >>
> >> draw2d(explicit(subst(avals,coefseries),z,0,1));
> >>
> >> Where coefseries is something like a[0] + sum(a[i]*cos(...),i,1,17) and
> >> avals are the values for a[0]...a[17] in a list of the form
> >> [a[0]=...,a[1]=..., ...]
> >>
> >> but what the subst gives me is still in the form 1.234 +
> >> sum(a[i]*cos(...)...), that is, subst substituted the constant
> >> coefficient but of course not the individual coefficients in the sum
> >> (since they only appear as a[i]).
> > This is what I get:
> >
> >
> > (%i12) display2d:false$
> >
> > (%i13) avals: makelist(a[i]=random(10)-5,i,0,17);
> >
> > (%o13) [a[0] = -2,a[1] = -2,a[2] = 2,a[3] = 3,a[4] = -1,a[5] = 1,a[6] = 0,
> >         a[7] = -5,a[8] = 2,a[9] = 1,a[10] = 0,a[11] = -1,a[12] = 2,a[13]
> > = -3,
> >         a[14] = 3,a[15] = -2,a[16] = -5,a[17] = 1]
> > (%i14) coefseries: a[0] + sum(a[i]*cos(z*i*%pi),i,1,17);
> >
> > (%o14) a[17]*cos(17*%pi*z)+a[16]*cos(16*%pi*z)+a[15]*cos(15*%pi*z)
> >                           +a[14]*cos(14*%pi*z)+a[13]*cos(13*%pi*z)
> >                           +a[12]*cos(12*%pi*z)+a[11]*cos(11*%pi*z)
> >                           +a[10]*cos(10*%pi*z)+a[9]*cos(9*%pi*z)
> >                           +a[8]*cos(8*%pi*z)+a[7]*cos(7*%pi*z)
> >                           +a[6]*cos(6*%pi*z)+a[5]*cos(5*%pi*z)
> >                           +a[4]*cos(4*%pi*z)+a[3]*cos(3*%pi*z)
> >                           +a[2]*cos(2*%pi*z)+a[1]*cos(%pi*z)+a[0]
> >
> > Don't you get this expanded expression? Perhaps I misunderstood your
> > problem.
> 
> coefseries variable contains the noun form of the sum, I seem to have
> quoted it when I created it so that it wouldn't expand. If I force it to
> evaluate with the flag "nouns" i can get it expanded. Is that the right
> way to go about it, or is there a way where I don't have to expand the
> expression but can still get numerical evaluation? in other words, where
> maxima will calculate the numerical sum without constructing and
> carrying around a potentially long symbolic expression?
> 

Hi,

If I understand well your problem you want sum command to evaluate the a[i] "Just In Time".
If so, if your expressions don't need sum's specific simplification, then you can write your
own sum command. That will be just a loop and a method to read the value of the a[i] from your
list and maybe some call to ratsimp or trigsimp or so.

Just an idea...

Best.

Laurent.


  
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