Hi David:
I understand the complexity, but I do actually need the symbolic
solutions, if there are any. So, I'm looking for a response from someone
who is a Maxima expert that can tell me if there is a problem in solve,
especially when it just goes off and never returns, or returns with an
error message. For other expressions I've tried solve returns an empty
solution rather than an error message and does not seem to compute forever.
Thanks for your assistance,
Paul Bowyer
David Chappaz wrote:
> Hi Paul,
>
> I'm no Maxima expert, but I think you're just slightly too ambitious
> there....
>
> Just try this:
> solve(a*y^3 + b*y^2 + c*y + d, y);
>
> and look how complicated the answer is.
> Now you can expand e.g. det1 to express a, b, c, d in terms of your
> variables, and substitute in the above... I don't think the answer is going
> to be very helpful (symbolic, though).
>
> In fact your original expression is complex enough to cause problems:
>
> (%i6) facsum(det1, y);
> << Expression too long to display! >> (I'm using wxMaxima 0.8.2)
>
> det1 is so long, it seems there is pretty much nothing I can do with it...
> No big surprise "solve" throws the towel !
>
> I'm afraid you can't expect miracles... As the name says, symbolic tools are
> just.... tools. The user in the first place has to make simplifications, or
> assumptions. Getting a symbolic result just for the sake of it doesn't lead
> anywhere if it is several pages long...
>
> Hope that helps a bit !!
> David.
>
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu]
> On Behalf Of Paul Bowyer
> Sent: 11 May 2009 17:55
> To: maxima at math.utexas.edu
> Subject: Re: [Maxima] difficulty with solve
>
> 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*d
> 0-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*d
> 0-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)/27
> 000)^(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^4-5
> 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=
> (((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)+(y
> 2-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
> _______________________________________________
> Maxima mailing list
> Maxima at math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima
>
>
>
>