# [Maxima] difficulty with solve

Stefano Ferri ferriste at gmail.com
Mon May 11 14:48:58 CDT 2009

```I had a look at your first problem, and it is linear in y. Instead of solve,
try linsolve. It solves your problem in less than a second.
But look how complicated is the solution, and simplifier cannot help you here.

(%i3) linsolve(det1,y);
(%o3) [y = -((x0^3-3*x*x0^2+3*x^2*x0-x^3)*y3^3
+(((-9*x0^2+18*x*x0-9*x^2)*x1+9*x*x0^2-18*x^2*x0+9*x^3)*y2
+((-18*x0^2+36*x*x0-18*x^2)*x2+(27*x0-27*x)*x1^2+(54*x^2-54*x*x0)*x1
+18*x*x0^2-9*x^2*x0-9*x^3)
*y1
+((-3*x0^2+6*x*x0-3*x^2)*x3+((27*x0-27*x)*x1-27*x*x0+27*x^2)*x2
-27*x1^3+81*x*x1^2+(-27*x*x0-54*x^2)*x1
+3*x*x0^2+21*x^2*x0+3*x^3)
*y0)
*y3^2
+(((27*x0^2-54*x*x0+27*x^2)*x2-27*x*x0^2+54*x^2*x0-27*x^3)*y2^2
+(((27*x0^2-54*x*x0+27*x^2)*x3+((81*x-81*x0)*x1+81*x*x0-81*x^2)*x2
+(81*x*x0-81*x^2)*x1-27*x*x0^2
-27*x^2*x0+54*x^3)
*y1
+(((9*x-9*x0)*x1+9*x*x0-9*x^2)*x3+(54*x-54*x0)*x2^2
+(81*x1^2-162*x*x1+108*x*x0
-27*x^2)
*x2-81*x*x1^2+(9*x*x0+153*x^2)*x1
-63*x^2*x0-18*x^3)
*y0)
*y2
+(((54*x-54*x0)*x1+54*x*x0-54*x^2)*x3
+(81*x0-81*x)*x2^2+(162*x^2-162*x*x0)*x2+(54*x*x0-54*x^2)*x1
+27*x^2*x0-27*x^3)
*y1^2
+(((9*x0-9*x)*x2+54*x1^2-108*x*x1-9*x*x0+63*x^2)*x3
+(81*x-81*x1)*x2^2+(162*x*x1-9*x*x0-153*x^2)*x2-54*x*x1^2+27*x^2*x1
+9*x^2*x0+18*x^3)
*y0*y1
+((3*x0-3*x)*x3^2+((27*x-27*x1)*x2+27*x*x1-6*x*x0-21*x^2)*x3+27*x2^3
-81*x*x2^2+(27*x*x1+54*x^2)*x2-27*x^2*x1+3*x^2*x0
-3*x^3)
*y0^2)
*y3+((-27*x0^2+54*x*x0-27*x^2)*x3+27*x*x0^2-54*x^2*x0+27*x^3)*y2^3
+((((81*x0-81*x)*x1-81*x*x0+81*x^2)*x3
+(81*x^2-81*x*x0)*x1+81*x^2*x0-81*x^3)
*y1
+(((54*x0-54*x)*x2-81*x1^2+162*x*x1-54*x*x0-27*x^2)*x3
+(54*x^2-54*x*x0)*x2+81*x*x1^2-162*x^2*x1+54*x^2*x0+27*x^3)
*y0)
*y2^2
+((((81*x-81*x0)*x2+81*x*x0-81*x^2)*x3
+(81*x*x0-81*x^2)*x2-81*x^2*x0+81*x^3)
*y1^2
+((27*x-27*x0)*x3^2+((81*x1-81*x)*x2-81*x*x1+54*x*x0+27*x^2)*x3
+(81*x^2-81*x*x1)*x2+81*x^2*x1-27*x^2*x0-54*x^3)
*y0*y1
+((18*x1-18*x)*x3^2+(-27*x2^2+54*x*x2-36*x*x1+9*x^2)*x3+27*x*x2^2
-54*x^2*x2+18*x^2*x1+9*x^3)
*y0^2)
*y2+((27*x0-27*x)*x3^2+(54*x^2-54*x*x0)*x3+27*x^2*x0-27*x^3)*y1^3
+((27*x-27*x1)*x3^2+(54*x*x1-54*x^2)*x3-27*x^2*x1+27*x^3)*y0*y1^2
+((9*x2-9*x)*x3^2+(18*x^2-18*x*x2)*x3+9*x^2*x2-9*x^3)*y0^2*y1
+(-x3^3+3*x*x3^2-3*x^2*x3+x^3)*y0^3)
/(((3*x0^2-6*x*x0+3*x^2)*x3+((27*x-27*x0)*x1+18*x0^2-9*x*x0-9*x^2)*x2
+27*x1^3+(-27*x0-54*x)*x1^2
+(9*x0^2+63*x*x0+9*x^2)*x1-3*x0^3
-21*x*x0^2-3*x^2*x0)
*y3^2
+((((9*x0-9*x)*x1-27*x0^2+45*x*x0-18*x^2)*x3
+(54*x0-54*x)*x2^2
+(-81*x1^2+(81*x0+81*x)*x1-54*x0^2-81*x*x0+54*x^2)*x2+81*x*x1^2
+(18*x0^2-126*x*x0-54*x^2)*x1+63*x*x0^2+18*x^2*x0)
*y2
+(((9*x-9*x0)*x2-54*x1^2+108*x0*x1-27*x0^2-45*x*x0+18*x^2)*x3
+(81*x1-162*x0+81*x)*x2^2
+((81*x0-243*x)*x1+36*x0^2+180*x*x0-54*x^2)*x2+(108*x-54*x0)*x1^2
+(54*x^2-81*x*x0)*x1-9*x*x0^2-18*x^2*x0)
*y1
+((6*x-6*x0)*x3^2+((54*x1-9*x0-45*x)*x2-54*x1^2+(9*x0+45*x)*x1
+6*x0^2-6*x^2)
*x3-54*x2^3+(81*x1+54*x0+27*x)*x2^2
+(-81*x1^2-54*x0*x1-45*x*x0+18*x^2)*x2+54*x1^3
-27*x*x1^2+(45*x*x0-18*x^2)*x1-6*x*x0^2+6*x^2*x0)
*y0)
*y3
+(((54*x-54*x0)*x2+81*x1^2+(-81*x0-81*x)*x1+81*x0^2-27*x*x0+27*x^2)
*x3
+(-27*x0^2+108*x*x0-81*x^2)*x2-81*x*x1^2+(81*x*x0+81*x^2)*x1
-54*x*x0^2-27*x^2*x0)
*y2^2
+(((27*x0-27*x)*x3^2+((-81*x1+162*x0-81*x)*x2
+(243*x-162*x0)*x1-27*x0^2-54*x^2)
*x3+(81*x0*x1-243*x*x0+162*x^2)*x2
+(81*x*x0-162*x^2)*x1+27*x*x0^2+54*x^2*x0)
*y1
+((-36*x1+27*x0+9*x)*x3^2+(54*x2^2+(-81*x1-108*x0+81*x)*x2+162*x1^2
+(9*x0-180*x)*x1+45*x*x0+18*x^2)
*x3+(54*x0-108*x)*x2^2
+(-81*x1^2+243*x*x1-54*x^2)*x2-81*x*x1^2
+(54*x^2-9*x*x0)*x1-18*x^2*x0)
*y0)
*y2
+((27*x1-81*x0+54*x)*x3^2+((81*x0-81*x)*x2+(54*x0-108*x)*x1+27*x*x0
+27*x^2)
*x3+(81*x-81*x0)*x2^2+(81*x*x0-81*x^2)*x2
+(81*x^2-54*x*x0)*x1-27*x^2*x0)
*y1^2
+((-18*x2+54*x1+27*x0-63*x)*x3^2
+((-81*x1-9*x0+126*x)*x2-54*x1^2+81*x*x1-45*x*x0-18*x^2)*x3
+(81*x1-81*x)*x2^2+(-81*x*x1+9*x*x0+54*x^2)*x2+54*x*x1^2-54*x^2*x1
+18*x^2*x0)
*y0*y1
+(3*x3^3+(-9*x2-18*x1-3*x0+21*x)*x3^2
+(27*x2^2+(27*x1-63*x)*x2+9*x*x1+6*x*x0+3*x^2)*x3-27*x2^3
+54*x*x2^2+(-27*x*x1-9*x^2)*x2+9*x^2*x1-3*x^2*x0)
*y0^2)]

Stefano

In data lunedì 11 maggio 2009 18:55:20, Paul Bowyer ha scritto:
: > 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^4-5
>2*x^3+311*x^2-476*x+212))/(600*sqrt(3))-(3294*x^3-56853*x^2+97947*x-44531)/2
>7000)^(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)/1
>5]
>
>
> 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-y
>0)*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-y
>0)*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
> _______________________________________________
> Maxima mailing list
> Maxima at math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima

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