From
http://www.math.utexas.edu/pipermail/maxima/2012/030338.html
Hi all,
Bernard Luce was having some trouble posting a question to the list. I'm
including the contents here.
Rupert
-----
DISCONTINUITIES IN A CURVE
A parametric curve displays 2 cases of discontinuity in the interval
chosen (t= 1 and t = - 2) (see command below). However the infinite
branches are unexpectedly linked. So, two questions :
1? is there any option to draw properly the curve and display the
discontinuities ?
2? Might you provide the main commands in the ASYMPA package to compute
the asymptotes and draw them together with the graph as well ?
THANKS BEFOREHAND
plot2d([parametric,t^3/(t-1)/(t+2),(t^2-2*t)/(t-1),[t,-20,20],[nticks,200]]);
****************************************************
Problem. Compute asymptotes of parametric curve
x=t^3/(t-1)/(t+2),(t^2-2*t)/(t-1)
y=(t^2-2*t)/(t-1)
and draw them together with the curve.
Solution. We compute asymptotes as1, as2, as3 and draw
(%i1) xt:t^3/(t-1)/(t+2)$
(%i2) yt:(t^2-2*t)/(t-1)$
(%i3) k1:limit(yt/xt,t,inf);
(%o3) 1
(%i4) b1:limit(yt-k1*xt,t,inf);
(%o4) 0
(%i5) as1:k1*x+b1;
(%o5) x
(%i6) k2:limit(yt/xt,t,1);
(%o6) -3
(%i7) b2:limit(yt-k2*xt,t,1);
(%o7) 8/3
(%i8) as2:k2*x+b2;
(%o8) 8/3-3*x
(%i9) k3:limit(yt/xt,t,-2);
(%o9) 0
(%i10) b3:limit(yt-k3*xt,t,-2);
(%o10) -8/3
(%i11) as3:k3*x+b3;
(%o11) -8/3
(%i12)
plot2d([[parametric,xt,yt,[t,-20,20],[nticks,200]],as1,as2,as3],[x,-10,10]);
(%o12)
Best,
Aleksas