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
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