source: CGBLisp/examples/euler.macsyma@ 1

/* Unfinished !! */
if get('geometry2, 'version)=false then load(geometry2);
A:[u1,u2]; B:[u3,u4]; C:[u5,u6]; /* Vertices */
H1:[x1,x2]; H2: [x3,x4]; H3: [x5,x6]; /* Feet of altitudes */
M1:[x7,x8]; M2: [x9,x10]; M3: [x11,x12]; /* Midpoints */
O1:[x13,x14]; /* Centroid */
O2:[x15,x16]; /* Orthocenter */
O3:[x17,x18]; /* Intersection point of altitudes */

vars:listofvars([H1,H2,H3,M1,M2,M3,O1,O2,O3,v]);
params:listofvars([A,B,C]);

eqns:append(
        midpoint(M1,B,C),
        midpoint(M2,A,C),
        midpoint(M3,A,B),
        [
                /* Hi are on the sides */
                collinear(B,C,H1),
                collinear(A,C,H2),
                collinear(A,B,H3),
                /* O3 is intersection of altitudes */
                perpendicular(A,O3,B,C),
                perpendicular(B,O3,A,C),
                perpendicular(C,O3,A,B),
                /* O2 is orthocenter */
                perpendicular(O2,M1,B,C),
                perpendicular(O2,M2,A,C),
                perpendicular(O2,M3,A,B),
                /* O1 is the centroid */
                collinear(O1,M1,A),
                collinear(O1,M2,B),
                /* collinear(O1,M3,C),  */
                /* Conclusion */
                1-v*collinear(O1,O2,O3)
        ]
);

cover:[[[],[]]];

eqns:expand(eqns);
cover:expand(cover);
stringout("euler.out",eqns,vars,params,cover);