Before all, many thanks for your collective prompt-and-deep investigations.
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As far as I understand, you discard the discontinuities in the curve by avoiding the undefined value -2 and +1 and drawing on intervals [t,-20,-2.1] ,[t,-1.9,0.9],[t,1.1,20].
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The pain is when the undefined values aren?t so quite obvious and we have to trust Maxima to chase them away? I remember a very convenient Maple plot-option like ?discont=true? which masters all the stuff, but apparently it hasn?t be implemented in Maxima ?
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Concerning the asymptotes, your useful set of commands is close to the natural computation and works well. If anybody can dig up tricks about the ASYMPA package, the community will enjoy it.
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Warm regards from Bernie
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PS concerning the stability of m1, m2, m3, the unicity of limit principle shall suffice, shan?t it ? At the latest, testing MINUS infinity as well could comfort m3 and a3 coefficients :
m3: limit(g/f,t,minf)?; a3: m3*x + limit(g-m3*f,t,minf);
> Message du 31/10/12 12:27
> De : "Jaime Villate"
> A :
> Copie ? : "Maxima Mailing List" , "Bernard LUCE"
> Objet : Re: [Maxima] DISCONTINUITIES IN A CURVE
>
> Hi again,
> I would also like to show to Bernard another plot2d option that will
> make the plot nicer, and at the same time amend my last message by
> including the 3rd asymptote that Aleksas plotted:
>
> (%i1) display2d: false$
> (%i2) f: t^3/(t-1)/(t+2)$
> (%i3) g: (t^2-2*t)/(t-1)$
> (%i4) m1: limit(g/f,t,-2)$
> (%i5) m2: limit(g/f,t,1)$
> (%i6) m3: limit(g/f,t,inf)$
> (%i7) a1: m1*x + limit(g-m1*f,t,-2);
> (%o7) -8/3
> (%i8) a2: m2*x + limit(g-m2*f,t,1);
> (%o8) 8/3-3*x
> (%i9) a3: m3*x + limit(g-m3*f,t,inf);
> (%o9) x
> (%i10)
> plot2d([a1,a2,a3,[parametric,f,g,[t,-20,-2.1]],[parametric,f,g,[t,-1.9,0.9]],[parametric,f,g,[t,1.1,20]]],[x,-30,20],[y,-20,10],[nticks,200],[legend,false],[color,black,black,black,blue,blue,blue]);
>
> Of course, I made some attempts first to find some appropriate values
> for x and y, and I also checked that m1, m2, and m3 gave constant
> numbers, otherwise there would be no asymptotes.
>
> Regards,
> Jaime
>
>