if get('geometry2,'version)=false then load(geometry2);
/* Pappus theorem;
9 points and 9 lines
Points: a0, a1, a2, b0, b1, b2, c0, c1, c2
line		contains points
l0		a0 b1 c0
l1		a0 b2 c1
l2		a1 b0 c0
l3		a1 b2 c2
l4		a2 b0 c1
l5		a2 b1 c2
l6		a0 a1 a2
l7		b0 b1 b2
l8		c0 c1 c2
*/
/* Specs */
a00:a10:0; a20:1;
a01:1; a11:0; a21:1;
a12:0; a22:1; /* a02 # 0 */
l06:0; l16:1; l26:0;

for i:0 thru 2 do (
	a[i]:[concat('a0,i),concat('a1,i),concat('a2,i)],
	b[i]:[concat('b0,i),concat('b1,i),concat('b2,i)],		
	c[i]:[concat('c0,i),concat('c1,i),concat('c2,i)]
);		

for i:0 thru 8 do 
	l[i]:[concat('l0,i),concat('l1,i),concat('l2,i)];

rel(l,a,b,c):=[l.a,l.b,l.c];

eqns:append(
[1-v*collinear(c[0], c[1], c[2])],
rel(l[0],a[0], b[1], c[0]),
rel(l[1],a[0], b[2], c[1]),
rel(l[2],a[1], b[0], c[0]),
rel(l[3],a[1], b[2], c[2]),
rel(l[4],a[2], b[0], c[1]),
rel(l[5],a[2], b[1], c[2]),
rel(l[6],a[0], a[1], a[2]),
rel(l[7],b[0], b[1], b[2]));


vars:append(makelist(l[j],j,0,7),
	makelist([c[i]],i,0,2),[a[2],b[2]]);
params:makelist([a[i],b[i]],i,0,1);
vars:''vars;
params:''params;
vars:listofvars(vars);
params:listofvars(params);
cover:expand([[[],[]]]);
eqns:expand(''eqns);
cover:expand(''cover);
stringout("pappus4.out",eqns,vars,params,cover);