Algsys Not Solving A Simultaneous Polynomial I Would Expect It To
Subject: Algsys Not Solving A Simultaneous Polynomial I Would Expect It To
From: Barton Willis
Date: Thu, 2 Nov 2006 18:56:50 -0600
-----maxima-bounces at math.utexas.edu wrote: -----
>I am a big fan of Maxima, but I have stumbled
>across a simultaneous
>polynomial which algsys (and hence solve) doesn't
>seem to be able to
>resolve, and I'm wondering if anyone can tell me
>what the problem is,
>please. Here's the original command:
>
>(%i7) assume (s>0)$
>(%i8)
>algsys([x^2+y^2=4,(s-x)^2+y^2=16,x^2+(s-y)^2=25],
>[s,x,y]);
>(%o8) []
>
>I then tried rewriting the 3 polynomials with
>their factors expanded:
>
>(%i9) e1: y^2+x^2-4$
>(%i10) e2: y^2+x^2-2*s*x+s^2-16$
>(%i11) e3: y^2-2*s*y+x^2+s^2-25$
>(%i12) algsys([e1, e2, e3], [s,x,y]);
>(%o12) []
(1) I think that algsys isn't as sturdy as it should be.
(2) algsys (and I think the other solvers) do not consult the
fact database. So assume (s>0) doesn't in change the way algsys
works (or doesn't work!).
(3) A workaround:
(%i294) load("grobner.lisp")$
Loading maxima-grobner $Revision: 1.1 $ $Date: 2006/02/07 04:49:49 $
(%i295) eqs : [x^2+y^2=4,(s-x)^2+y^2=16,x^2+(s-y)^2=25]$
(%i296) eqs : map(rhs,eqs)-map(lhs,eqs);
(%o296) [-y^2-x^2+4,-y^2-(s-x)^2+16,-(s-y)^2-x^2+25]
(%i297) poly_reduced_grobner(eqs,[s,x,y]);
(%o297) [-520*y^3+2191*y-935*x,-2080*y^4+9784*y^2-7225,-7280
*y^3+23194*y-2805*s]
(%i298) algsys(%,[s,x,y]);
(%o298)
[[s=(sqrt(1223-33*sqrt(7)*sqrt(73))*(7*sqrt(2)*sqrt(5)*sqrt(7)*sqrt(13)*sqrt(73)+92*sqrt(2)*sqrt(5)*sqrt(13)))/11050,x=
<deleted junk>
(a) You might need to give a full path to grobner.lisp (it's in
/share/contrib/Grobner).
(b) You'll need to filter the solution by hand to pick out the solution(s)
with s > 0.
Barton