Missing multiplication signs?

Preben Alsholm — Tue, 22 Nov 2011 20:22:16 Z

In the posted text several multiplication signs were missing.

eqns := {(x[1]+1)^2+y[1]^2 = (x[2]-1)^2+y[2]^2, (x[1]-c[1])^2+(y[1]-c[2])^2 = (x[3]-1)^2+y[3]^2, (x[2]-c[1])^2+(y[2]-c[2])^2 = (x[3]+1)^2+y[3]^2, y[1]*(x[3]+1) = y[3]*(x[1]+1), y[2]*(x[3]-1) = y[3]*(x[2]-1), (x[2]-c[1])*(y[1]-c[2]) = (x[1]-c[1])*(y[2]-c[2])};
vars := {x[1], x[2], x[3], y[1], y[2], y[3]};
#With my limited patience I didn't wait for a possible answer from 'solve', but proceeded to 'fsolve', which of course expects c[1] and c[2] to be of type numeric.
solve(eqns, vars);
fsolve(eval(eqns,{c[1]=1.234,c[2]=2.345}), vars);

Symbolic solution

Markiyan Hirnyk — Sat, 26 Nov 2011 00:38:13 Z

At least one symbolic solution of eqns union vars can be found:
>SolveTools[PolynomialSystem]({y[1]*(x[3]+1) = y[3]*(x[1]+1), y[2]*(x[3]-1) = y[3]*(x[2]-1),
(x[2]-c[1])*(y[1]-c[2]) = (x[1]-c[1])*(y[2]-c[2]), (x[1]+1)^2+y[1]^2 = (x[2]-1)^2+y[2]^2,
(x[1]-c[1])^2+(y[1]-c[2])^2 = (x[3]-1)^2+y[3]^2, (x[2]-c[1])^2+(y[2]-c[2])^2 = (x[3]+1)^2+y[3]^2},
{x[1], x[2], x[3], y[1], y[2], y[3]})

         { x[1] = 0, x[2] = 0, x[3] = 0, y[1] =(-1+c[1]^2+c[2]^2)/(2 c[2]),

y[2]=(-1+c[1]^2+c[2]^2)/(2 c[2]), y[3]=(-1+c[1]^2+c[2]^2)/(2 c[2])}

MaplePrimes - answers and comments on Question, How to solve this equations?

Missing multiplication signs?

Symbolic solution