Bug in solve? do not give me wanted effect.

You found a bug in 'solve.' Please file a bug report.  Here might be
a workaround -- at least it gives four real solutions. The assignments
algebraic : true and gcd : spmod aren't necessary -- other values
work.

(%i1) load("Grobner\\maxima-grobner.lisp");
Loading maxima-grobner $Revision: 1.2 $ $Date: 2003/05/03 11:40:00 $
Warning - you are redefining the MACSYMA function ODDP
Warning - you are redefining the MACSYMA function EVENP
(%o1) C:/PROGRA~1/MAXIMA~1.1/share/maxima/5.9.1
/share/contrib/Grobner/maxima-grobner.lisp
(%i2) algebraic : true$
(%i3) realonly : true$
(%i4) gcd : spmod$
(%i5) POLY_BUCHBERGER([x0+y0-x1-y1,2*x0^2+4*y0^2-3,2
*x1^2+4*y1^2-3,x0*x1+y0*y1]
,[x0,x1,y0,y1])$
(%i6) algsys(%,[x0,x1,y0,y1]);
(%o6) [[x0=-(sqrt(10)+4)/6,x1=(4*sqrt(10)-3
*sqrt(2)*sqrt(5)-4)/6,y0=(sqrt(2)*sqrt(5)-2)/6,Y1=-(sqrt(2)*sqrt(5)+2)/6],[x0=(sqrt(10)-4)/6,x1=-

(4*sqrt(10)-3
*sqrt(2)*sqrt(5)+4)/6,y0=-(sqrt(2)*sqrt(5)+2)/6,Y1=(sqrt(2)*sqrt(5)-2)/6],[x0=-(sqrt(10)-4)/6,x1=(4*sqrt(10)-3
*sqrt(2)*sqrt(5)+4)/6,y0=
(sqrt(2)*sqrt(5)+2)/6,Y1=-(sqrt(2)*sqrt(5)-2)/6],[x0=(sqrt(10)+4)/6,x1=-(4*sqrt(10)-3
*sqrt(2)*sqrt(5)-4)/6,y0=-(sqrt(2)*sqrt(5)-2)/6,Y1=(sqrt(2)*sqrt(5)+2)/6]]
(%i7)

Barton

-----maxima-admin@math.utexas.edu wrote: -----

>To: "maxima list"
>From:
>Sent by: maxima-admin@math.utexas.edu
>Date: 04/25/2005 10:03PM
>Subject: Bug in solve? do not give me
>wanted effect.
>
>
>
>
>I have met such a geometry problem:
>Suppose
>a line l: x+y-m=0 intersects an ellipse
>2*x^2+4*y^2=3 with
>A(x0,y0),B(x1,y1), and x0*x1+y0*y1=0, .i.e OA is
>vertical to OB, Solve
>the x0,x1,y0,y1.
>
> solve([x0+y0-x1-y1,2*x0^2+4*y0^2-3,2*x1^2+4*y1^2
>-3,x0*x1+y0*y1]);
> [[Y1 = - -------, y0 = - -------, x1 =
>----------, x0 = ------------],
>
>             SQRT(2)
>         SQRT(2)
>    SQRT(2)              2
>SQRT(3)
>        SQRT(3)
>         SQRT(3)
>       SQRT(3) %I
>  3 SQRT(2) %I
>[Y1 = - -------, y0 = - -------, x1 = -
>----------, x0 = - ------------],
>
>       SQRT(2)
>     SQRT(2)
>    SQRT(2)            2 SQRT(3)
>
>     SQRT(3)
> SQRT(3)          SQRT(3) %I
>        3 SQRT(2) %I
>[Y1 = -------, y0 = -------, x1 = ----------, x0
>= ------------],
>
>     SQRT(2)
> SQRT(2)           SQRT(2)
>       2 SQRT(3)
>      SQRT(3)
>           SQRT(3)
>     SQRT(3) %I
>    3 SQRT(2) %I
>[Y1 = -------, y0 = -------, x1 = - ----------,
>x0 = - ------------]]
>
>     SQRT(2)
> SQRT(2)             SQRT(2)
>             2 SQRT(3)
>Intuitionisticly,
>it should exists real x0,y0,x1,y1, but Maxima do
>not give the real
>solution. It should be pointed out that the real
>solution does exits.
>
>
>
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