I got the following message from Andrej Vodopivec: You can solve this system in maxima with to_poly_solve:
(%i2) to_poly_solve([(x-5)^2+y^2-16, (y-3)^2+x^2-9], [x,y], use_grobner=true); (%o2) %union([x=-(9*sqrt(55)-135)/68,y=-(3*5^(3/2)*sqrt(11)-123)/68], [x=(9*sqrt(55)+135)/68,y=(3*5^(3/2)*sqrt(11)+123)/68]) HTH, Andrej On 9 bře, 12:02, "[email protected]" <[email protected]> wrote: > No, it is because Maxima (which solves equations for Sage) cannot > solve this system. My suggestions: > > 1. (better but long term) - improve Maxima's solver > > 2. (shorter) - help Maxima and write your simstem in simpler form like > this > > sage: x,y=var('x y') > sage: c1(x,y)=(x-5)^2+y^2-16; c2(x,y)=(y-3)^2+x^2-9 > sage: c2b(x,y) = expand(c2(x,y)-c1(x,y)) > sage: solve([c1(x,y)==0,c2b(x,y)==0],[x,y]) > [[x == -9/68*sqrt(55) + 135/68, y == -15/68*sqrt(5)*sqrt(11) + > 123/68], [x == 9/68*sqrt(55) + 135/68, y == 15/68*sqrt(5)*sqrt(11) + > 123/68]] > > And we can doublecheck the answer > > sage: sol=_ > sage: c1(sol[0][0].rhs(),sol[0][1].rhs()).expand().simplify_full() > 0 > sage: c2(sol[0][0].rhs(),sol[0][1].rhs()).expand().simplify_full() > 0 > sage: c1(sol[1][0].rhs(),sol[1][1].rhs()).expand().simplify_full() > 0 > sage: c2(sol[1][0].rhs(),sol[1][1].rhs()).expand().simplify_full() > 0 > > Robert > > On 9 bře, 05:26, Markus <[email protected]> wrote: > > > Hi, > > > when trying to compute the intersection points of 2 circles i got > > strange results. > > > Example 1: > > > c1(x,y)=(x-5)^2+y^2-25; c2(x,y)=(y-3)^2+x^2-9 > > solve([c1(x,y)==0,c2(x,y)==0],x,y) > > > produces the expected result: > > > [[x == (45/17), y == (75/17)], [x == 0, y == 0]] > > > Example 2: > > (circle 1 smaller) > > > c1(x,y)=(x-5)^2+y^2-16; c2(x,y)=(y-3)^2+x^2-9 > > solve([c1(x,y)==0,c2(x,y)==0],x,y) > > > produces the unexpected result: > > > [] > > > whereas intersection points do exist, e.g. > > x=(-9(sqrt(55)-15)/68, y=(-3(sqrt(55)-41)/68 > > > Is it because Example 1 has a rational result, whereas Examples 2 has > > an irrational one? > > > Thanks for any help. > > > Markus -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
