solution of system of quadratic eqns.



On 06/24/2012 06:27 AM, Barton Willis wrote:
> Oh...the square root denesting trick fixes a few cases, but it doesn't allow algsys to solve
> [x^2+y^2-a, (x-1/2)^2 + (y-1/2)^2-b] for x & y, for example.
>
> ...

For the more general problem, below, solve() actually executes for a 
very long time before coming back with a  null solution, using your 
current definition of ebaksubst :

--
(%i1) load(sqdnst);
(%o1)      /usr/share/maxima/5.24.0/share/simplification/sqdnst.mac
(%i2) :lisp (defun ebaksubst (solnl lhsl) (mapcar #'(lambda (s) (cadr 
(ratf ($radcan (mfuncall '$sqrtdenest ($substitute (cons '(mlist) solnl) 
(pdis s))))))) lhsl))

EBAKSUBST
(%i2) e1: (x-a)^2 + (y-b)^2 = r1^2;
                                   2          2     2
(%o2)                      (y - b)  + (x - a)  = r1
(%i3) e2: (x-c)^2 + (y-d)^2 = r2^2;
                                   2          2     2
(%o3)                      (y - d)  + (x - c)  = r2
(%i4) solve( [e1,e2], [x,y] );
--


Krishna