 LIB "grobcov.lib";
// Steiner Deltoid
// 1. Consider the circle x1^2+y1^21=0, and a mover point M(x1,y1) on it.
// 2. Consider the triangle A(0,1), B(1,0), C(1,0).
// 3. Consider lines passing through M perpendicular to two sides of ABC triangle.
// 4. Obtain the envelop of the lines above.
ring R=(0,x,y),(x1,y1,x2,y2),lp;
ideal C=(x1)^2+(y1)^21,
x2+y21,
x2y2x1+y1;
matrix M[3][3]=x,y,1,x2,y2,1,x1,0,1;
poly F=det(M);
short=0;
// Curves Family F=
F;
==> x1*y2+(y)*x1+(y)*x2+(x)*y2
// Conditions C=
C;
==> C[1]=x1^2+y1^21
==> C[2]=x2+y21
==> C[3]=x1+y1+x2y2
def Env=envelop(F,C);
Env;
==> [1]:
==> [1]:
==> _[1]=(x^4+2*x^2*y^2+10*x^2*yx^2+y^46*y^3+12*y^28*y)
==> [2]:
==> [1]:
==> _[1]=1
==> [3]:
==> Normal
==> [4]:
==> 1
==> [2]:
==> [1]:
==> _[1]=(x+y1)
==> [2]:
==> [1]:
==> _[1]=1
==> [3]:
==> [1]:
==> Special
==> [2]:
==> y2,x21,y1,x11
==> [3]:
==> 0
==> [4]:
==> 1
