Polynomgleichungen von W. Haager

Programmcode:

load(draw);
p1:y^3+4*y^2+2*x*y+2*y+x^2+2*x=2;
p2:13*x^2-3*y^2-20*x*y+20*y-26*x=-11;
res:solve([p1,p2],[x,y]),realonly=true;
punkte:matrixmap(rhs,res);
draw2d(color=black,implicit(p1,x,-20,7,y,-10,2),color=blue,
implicit(p2,x,-20,7,y,-10,2),color=red,point_type=7,
point_size=2,points(punkte),grid=true,xrange=[-20,7],
yrange=[-10,2]);

Link zu Maxima-Online: http://maxima-online.org/?inc=r-1641098279
Eine Variante für Kreis und Hyperbel: http://maxima-online.org/?inc=r69798870

(%i1) load(draw);
(%o1) /usr/share/maxima/5.21.1/share/draw/draw.lisp
(%i2) p1:y^3+4*y^2+2*x*y+2*y+x^2+2*x=2;
                     3      2                  2
(%o2)               y  + 4 y  + 2 x y + 2 y + x  + 2 x = 2
(%i3) p2:13*x^2-3*y^2-20*x*y+20*y-26*x=-11;
                      2                       2
(%o3)            - 3 y  - 20 x y + 20 y + 13 x  - 26 x = - 11
(%i4) res:solve([p1,p2],[x,y]),realonly=true;
(%o4) [[x = - 14.07510729613734, y = - 8.988313856427379],
[x = 1.38261253309797, y = - 2.538024164889837],
[x = - 0.85062789160608, y = - 1.058122915674131],
[x = 0.65693482761082, y = 0.070681797873291]]
(%i5) punkte:matrixmap(rhs,res);
(%o5) [[- 14.07510729613734, - 8.988313856427379],
[1.38261253309797, - 2.538024164889837],
[- 0.85062789160608, - 1.058122915674131],
[0.65693482761082, 0.070681797873291]]
(%i6) draw2d(color=black,implicit(p1,x,-20,7,y,-10,2),
color=blue,implicit(p2,x,-20,7,y,-10,2),
color=red,point_type=7,point_size=2,points(punkte),
grid=true,xrange=[-20,7],yrange=[-10,2]);
(%o6)                 [gr2d(implicit, implicit, points)]
(%i7) draw2d(color=black,implicit(p1,x,-20,7,y,-10,2),         color=blue,implicit(p2,x,-20,7,y,-10,2),         color=red,point_type=7,point_size=2,points(punkte),grid=true,xrange=[-20,7],yrange=[-10,2]);;