# [Maxima] difficulty with solve

Paul Bowyer pbowyer at olynet.com
Mon May 11 11:55:20 CDT 2009

```Hello:

I am having difficulty trying to solve some expressions:

det1 :
((3*(x1-x)*(y0-y)-3*(x0-x)*(y1-y))*(-(x0-x)*(y3-y)-9*(x1-x)*(y2-y)+9*(x2-x)*(y1-y)+(x3-x)*(y0-y))-
(3*(x2-x)*(y0-y)-3*(x0-x)*(y2-y))^2)*(3*(x3-x)*(y2-y)-3*(x2-x)*(y3-y))-((3*(x1-x)*(y0-y)-3*(x0-x)*(y1-y))*
(3*(x3-x)*(y1-y)-3*(x1-x)*(y3-y))-(3*(x2-x)*(y0-y)-3*(x0-x)*(y2-y))*((x3-x)*(y0-y)-(x0-x)*(y3-y)))*
(3*(x3-x)*(y1-y)-3*(x1-x)*(y3-y))+((3*(x2-x)*(y0-y)-3*(x0-x)*(y2-y))*(3*(x3-x)*(y1-y)-3*(x1-x)*(y3-y))-
((x3-x)*(y0-y)-(x0-x)*(y3-y))*(-(x0-x)*(y3-y)-9*(x1-x)*(y2-y)+9*(x2-x)*(y1-y)+(x3-x)*(y0-y)))*
((x3-x)*(y0-y)-(x0-x)*(y3-y));

/*Will not solve symbolically*/
solve( det1, y);

The above entry just goes off to calculate and never comes back.

After entering numerical values for the subscripted variables,

det2 :
((3*(1-x)*(2-y)-3*(-x-3)*(1-y))*(3*(2-x)*(4-y)-3*(4-x)*(-y-1))-((1-x)*(4-y)-(4-x)*(1-y))*
((1-x)*(4-y)+9*(2-x)*(2-y)-(4-x)*(1-y)-9*(-x-3)*(-y-1)))*((1-x)*(4-y)-(4-x)*(1-y))-(
(3*(1-x)*(2-y)-3*(-x-3)*(1-y))*(3*(-x-3)*(4-y)-3*(4-x)*(2-y))-((1-x)*(4-y)-(4-x)*(1-y))*
(3*(2-x)*(4-y)-3*(4-x)*(-y-1)))*(3*(1-x)*(2-y)-3*(-x-3)*(1-y))+((3*(-x-3)*(4-y)-3*(4-x)*(2-y))*
((1-x)*(4-y)+9*(2-x)*(2-y)-(4-x)*(1-y)-9*(-x-3)*(-y-1))-(3*(2-x)*(4-y)-3*(4-x)*(-y-1))^2)*
(3*(1-x)*(-y-1)-3*(2-x)*(1-y));

solve( det2, y);

comes back with:

[y=(-(sqrt(3)*%i)/2-1/2)*((243*x^2-237*x+41)/216+((81*x-29)*sqrt(9*x^2-12*x+2))/216)^(1/3)+(((sqrt(3)*%i)/2-1/2)*(18*x-1))/(36*((243*x^2-237*x+41)/216+((81*x-29)*sqrt(9*x^2-12*x+2))/216)^(1/3))-(x-5)/3,
y=((sqrt(3)*%i)/2-1/2)*((243*x^2-237*x+41)/216+((81*x-29)*sqrt(9*x^2-12*x+2))/216)^(1/3)+((-(sqrt(3)*%i)/2-1/2)*(18*x-1))/(36*((243*x^2-237*x+41)/216+((81*x-29)*sqrt(9*x^2-12*x+2))/216)^(1/3))-(x-5)/3,y=
((243*x^2-237*x+41)/216+((81*x-29)*sqrt(9*x^2-12*x+2))/216)^(1/3)+(18*x-1)/(36*((243*x^2-237*x+41)/216+((81*x-29)*sqrt(9*x^2-12*x+2))/216)^(1/3))-(x-5)/3]

Another instance with a different expression:

det3  :
(a0*(d3*y-b3)-a3*(d0*y-b0)+(b3*d0-b0*d3)*x)*((a0*(d2*y-b2)-a2*(d0*y-b0)+(b2*d0-b0*d2)*x)*
(a1*(d3*y-b3)-a3*(d1*y-b1)+(b3*d1-b1*d3)*x)-(a0*(d3*y-b3)-a3*(d0*y-b0)+(b3*d0-b0*d3)*x)*
(a0*(d3*y-b3)+a1*(d2*y-b2)-a2*(d1*y-b1)-a3*(d0*y-b0)+(b3*d0-b0*d3)*x+(b2*d1-b1*d2)*x))-
(a1*(d3*y-b3)-a3*(d1*y-b1)+(b3*d1-b1*d3)*x)*((a0*(d1*y-b1)-a1*(d0*y-b0)+(b1*d0-b0*d1)*x)*
(a1*(d3*y-b3)-a3*(d1*y-b1)+(b3*d1-b1*d3)*x)-(a0*(d2*y-b2)-a2*(d0*y-b0)+(b2*d0-b0*d2)*x)*
(a0*(d3*y-b3)-a3*(d0*y-b0)+(b3*d0-b0*d3)*x))+(a2*(d3*y-b3)-a3*(d2*y-b2)+(b3*d2-b2*d3)*x)*(
(a0*(d1*y-b1)-a1*(d0*y-b0)+(b1*d0-b0*d1)*x)*
(a0*(d3*y-b3)+a1*(d2*y-b2)-a2*(d1*y-b1)-a3*(d0*y-b0)+(b3*d0-b0*d3)*x+(b2*d1-b1*d2)*x)-
(a0*(d2*y-b2)-a2*(d0*y-b0)+(b2*d0-b0*d2)*x)^2);

/*Will not solve symbolically*/
solve( det3, y);

The above entry also goes off to calculate and never comes back.

Again after entering numerical values for the subscripted variables,

det4  :
(-y+2*(y-1)+2*x-1)*((4*(y-2)+3*(y-4)-2*x)*(-3*(y+1)-y+4*(y-1)-2*(y-2)-6*x+4)-(4*(y+1)-2*(y-4)-5*x)^2)-
(-y-3*(y-1)-x+2)*((4*(y-2)+3*(y-4)-2*x)*(-y-3*(y-1)-x+2)-(-y+4*(y-1)-3*x+4)*(4*(y+1)-2*(y-4)-5*x))+
(-y+4*(y-1)-3*x+4)*((-y-3*(y-1)-x+2)*(4*(y+1)-2*(y-4)-5*x)-(-y+4*(y-1)-3*x+4)*(-3*(y+1)-y+4*(y-1)-2*(y-2)-6*x+4));

solve( det4, y);

comes back with:

[y=(-(sqrt(3)*%i)/2-1/2)*(((143*x-131)*sqrt(4*x^4-52*x^3+311*x^2-476*x+212))/(600*sqrt(3))-(3294*x^3-56853*x^2+97947*x-44531)/27000)^(1/3)-
(((sqrt(3)*%i)/2-1/2)*(354*x^2-1182*x+779))/(900*(((143*x-131)*sqrt(4*x^4-52*x^3+311*x^2-476*x+212))/(600*sqrt(3))-(3294*x^3-56853*x^2+97947*x-44531)/27000)^(1/3))+(3*x+13)/15,y=((sqrt(3)*%i)/2-1/2)*
(((143*x-131)*sqrt(4*x^4-52*x^3+311*x^2-476*x+212))/(600*sqrt(3))-(3294*x^3-56853*x^2+97947*x-44531)/27000)^(1/3)-
((-(sqrt(3)*%i)/2-1/2)*(354*x^2-1182*x+779))/(900*(((143*x-131)*sqrt(4*x^4-52*x^3+311*x^2-476*x+212))/(600*sqrt(3))-(3294*x^3-56853*x^2+97947*x-44531)/27000)^(1/3))+(3*x+13)/15,y=
(((143*x-131)*sqrt(4*x^4-52*x^3+311*x^2-476*x+212))/(600*sqrt(3))-(3294*x^3-56853*x^2+97947*x-44531)/27000)^(1/3)-
(354*x^2-1182*x+779)/(900*(((143*x-131)*sqrt(4*x^4-52*x^3+311*x^2-476*x+212))/(600*sqrt(3))-(3294*x^3-56853*x^2+97947*x-44531)/27000)^(1/3))+(3*x+13)/15]

Yet another instance with yet a different expression:

det5 :
w0*w3*(x0*(y-y3)-x3*(y-y0)+(y3-y0)*x)*(9*w0*w1*w2*w3*(x0*(y-y2)-x2*(y-y0)+(y2-y0)*x)*
(x1*(y-y3)-x3*(y-y1)+(y3-y1)*x)-w0*w3*(x0*(y-y3)-x3*(y-y0)+(y3-y0)*x)*
(9*w1*w2*(x1*(y-y2)-x2*(y-y1)+(y2-y1)*x)+3*w0*w2*(x0*(y-y2)-x2*(y-y0)+(y2-y0)*x)))+3*w2*w3*
(x2*(y-y3)-x3*(y-y2)+(y3-y2)*x)*(3*w0*w1*(x0*(y-y1)-x1*(y-y0)+(y1-y0)*x)*
(9*w1*w2*(x1*(y-y2)-x2*(y-y1)+(y2-y1)*x)+3*w0*w2*(x0*(y-y2)-x2*(y-y0)+(y2-y0)*x))-9*w0^2*w2^2*
(x0*(y-y2)-x2*(y-y0)+(y2-y0)*x)^2)-3*w1*w3*(x1*(y-y3)-x3*(y-y1)+(y3-y1)*x)*(9*w0*w1^2*w3*(x0*(y-y1)-x1*(y-y0)+(y1-y0)*x)*
(x1*(y-y3)-x3*(y-y1)+(y3-y1)*x)-3*w0^2*w2*w3*(x0*(y-y2)-x2*(y-y0)+(y2-y0)*x)*(x0*(y-y3)-x3*(y-y0)+(y3-y0)*x));

/*Will not solve symbolically*/
solve( det5, y);

comes back after awhile with:

Quotient by a polynomial of higher degree
-- an error.  To debug this try debugmode(true);

Yet again after entering numerical values for the subscripted variables
and entering y : 1.6 :

det6 :
1.0*(1.09375-1.75*x)*(1.0*(1.75*x-4.15625)*(1.0*(1.75*x-3.10625)-2.0125)-1.0*(1.75*x-3.10625)^2)+1.05*
(1.0*(2.14375-1.75*x)*(1.75*x-3.10625)-1.05*(1.0*(1.75*x-3.10625)-2.0125))-1.0*(2.14375-1.75*x)*
(1.0*(2.14375-1.75*x)*(1.75*x-4.15625)-1.05*(1.75*x-3.10625));

solve( det6, x);

comes back with:

[x=-(sqrt(649)-60)/40,x=(sqrt(649)+60)/40,x=19/8]

Is there a problem with solve or am I just not doing something correctly?
If it is my error, would you please point me in a direction that leads
to a correct symbolic solution to these expressions, if there are any?

I'm using Maxima-5.17.1, clisp-2.47, and wxMaxima-0.8.1 which I built
from source on PCLinuxOS-2009.1.
I have just run the test suite and no unexpected errors were found.

Thanks,

Paul Bowyer
```