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sb572

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These are answers submitted by sb572

Thanks for your...

sb572 52
August 18 2008
0 1

Thanks for your comments,

replacing the sqrt(3) by the variable s3 and adding the equation s3^2-3 worked using the function Isolate. So thanks for that suggestion.

Does anyone know why this might be the case? i.e. why the computation is easier if we add an extra equation and variable but make all of the coefficients integers?

Also, I'm interested in exactly how the "Isolate" function works - in particular how would I use the Groebner bases functions to reproduce the results? For example if I call Groebner[bases] and use the tdeg ordering Maple doesn't finish the computation even after 24 hours (compared to the 1min it takes using the Isolate function).

Steve

 Hi, the problem is to find...

sb572 52
August 14 2008
0 0

 Hi,

the problem is to find all solutions to the following set of 10 equations in the 10 real variables x[1]...x[5] and y[1]...y[5] 

 x[k]^2+y[k]^2-1 for k=1..5 and the following (rather messy) 5 equations equations

x[1]*x[2]+x[1]*x[3]+y[1]*y[3]+y[1]*y[5]+x[2]*x[5]+x[1]*x[5]+x[3]*x[4]+y[3]*y[5]+y[2]*y[3]+x[3]+x[4]+x[1]*x[4]+x[3]*x[5]+y[1]*y[4]+y[1]*y[2]+x[4]*x[5]+x[5]+y[3]*y[4]+y[2]*y[4]+x[1]+x[2]*x[4]+x[2]+x[2]*x[3]+y[2]*y[5]+y[4]*y[5]

 -y[3]*sqrt(3)*x[4]+2*x[1]*y[3]*sqrt(3)-2*y[1]*x[3]*sqrt(3)+x[3]*y[4]*sqrt(3)+y[1]*x[5]*sqrt(3)-2*y[2]*sqrt(3)*x[5]+y[4]*sqrt(3)*x[5]+y[2]*sqrt(3)*x[3]-x[2]*y[3]*sqrt(3)+y[1]*sqrt(3)+3*y[1]*y[5]+3*x[1]*x[5]-x[4]*y[5]*sqrt(3)+3*x[3]*x[4]+3*y[2]*y[3]+2*x[2]*y[5]*sqrt(3)-2*y[4]*sqrt(3)+3*x[4]*x[5]+3*y[3]*y[4]+3*x[1]-x[1]*y[5]*sqrt(3)+3*x[2]+y[2]*sqrt(3)+3*x[2]*x[3]+3*y[4]*y[5]

-y[3]*sqrt(3)*x[4]+x[3]*y[4]*sqrt(3)+y[1]*x[5]*sqrt(3)-y[2]*sqrt(3)*x[5]-y[4]*sqrt(3)*x[5]+y[2]*sqrt(3)*x[3]-y[1]*x[2]*sqrt(3)-x[3]*y[5]*sqrt(3)+x[1]*y[2]*sqrt(3)-x[2]*y[3]*sqrt(3)+y[1]*sqrt(3)+x[4]*y[5]*sqrt(3)-3*x[1]*x[3]+x[2]*y[5]*sqrt(3)-y[4]*sqrt(3)+y[3]*sqrt(3)-3*x[5]-3*y[1]*y[3]-3*y[2]*y[4]+x[1]*y[4]*sqrt(3)-x[1]*y[5]*sqrt(3)-y[2]*sqrt(3)-3*x[2]*x[4]+y[3]*sqrt(3)*x[5]-y[1]*x[4]*sqrt(3)

y[2]*sqrt(3)*x[4]-x[1]*y[3]*sqrt(3)+y[1]*x[3]*sqrt(3)-y[4]*sqrt(3)*x[5]+y[2]*sqrt(3)*x[3]-2*x[3]*y[5]*sqrt(3)-x[2]*y[3]*sqrt(3)+y[1]*sqrt(3)+y[5]*sqrt(3)+x[4]*y[5]*sqrt(3)-3*y[2]*y[3]-3*y[4]*y[5]-3*x[1]*x[3]-3*x[2]*x[3]-x[2]*y[4]*sqrt(3)-3*x[5]-3*y[1]*y[3]-3*x[1]-3*y[2]*y[4]+2*x[1]*y[4]*sqrt(3)-2*y[2]*sqrt(3)-3*x[4]*x[5]-3*x[2]*x[4]+2*y[3]*sqrt(3)*x[5]-2*y[1]*x[4]*sqrt(3)

y[2]*sqrt(3)*x[4]+x[1]*y[3]*sqrt(3)-y[1]*x[3]*sqrt(3)+2*y[4]*sqrt(3)*x[5]+y[5]*sqrt(3)-2*x[4]*y[5]*sqrt(3)-3*y[2]*y[3]-3*y[4]*y[5]-3*y[3]*y[5]-3*y[2]*y[5]-3*x[3]-2*y[3]*sqrt(3)-3*x[4]-3*x[2]*x[3]-x[2]*y[4]*sqrt(3)-2*x[1]*y[2]*sqrt(3)-3*y[1]*y[4]-3*x[1]-3*x[1]*x[2]+2*y[1]*x[2]*sqrt(3)+y[3]*sqrt(3)*x[4]-3*x[3]*x[5]+y[2]*sqrt(3)-3*x[1]*x[4]-3*x[4]*x[5]-3*x[2]*x[5]+x[1]*y[5]*sqrt(3)-y[1]*x[5]*sqrt(3)-x[3]*y[4]*sqrt(3)-3*y[1]*y[2]

thanks

 

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