Re: [Maxima-discuss] trying to solve for intersection of 2 circles

[Barton W. <wi...@un...>]

Hi Randall,

You did nothing wrong---the problem is that solve just isn’t powerful enough to solve these equations.  A workaround is to use Maxima’s Grobner basis code to triangularize the equations before solving. Maybe the easiest way to do this is to use an alternative solve package.

(%i1)   load("to_poly_solve")$

(%i2)  %solve([(x-1)^2+y^2-a^2=0,x^2+(y-1)^2-b^2=0],[x,y], 'use_grobner = true);
(%o2) %union([x=\-(sqrt(\-b^4+(2*a^2+4)*b^2\-a^4+4*a^2\-4)\-b^2+a^2\-2)/4,y=\-(sqrt(\-b^4+(2*a^2+4)*b^2\-a^4+4*a^2\-4)+b^2\-a^2\-2)/4],
[x=(sqrt(\-b^4+(2*a^2+4)*b^2\-a^4+4*a^2\-4)+b^2\-a^2+2)/4,y=(sqrt(\-b^4+(2*a^2+4)*b^2\-a^4+4*a^2\-4)\-b^2+a^2+2)/4])

There are other approaches—maybe others can comment.

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Subject: [Maxima-discuss] trying to solve for intersection of 2 circles

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I have two circles, first is centered at [1,0] with radius a and the second is at [0,1] with radius b

(1)    (x-1)^2 + y^2 = a^2

(2)    x^2 + (y-1)^2 = b^2

I used some known points, with p = [16/9, 28/15] thus giving a = 91/45 and b = 89/45 for the two circles passing through point p.

When I use maxima to solve for the general case

(%i1) solve([(x-1)^2+y^2-a^2=0,x^2+(y-1)^2-b^2=0],[x,y]);
(%o1)                                 []

Maxima says that the solution is the empty set. However the example showed that we do have a rational solution for known values.

What did I do wrong? If I used the values, Maxima finds 2 intersection points [ -13/15, -7/9] and p = [16/9, 28/15] but it refuses to solve for distances a,b for the general case.

Randall