Kernel connection has been lost during solve(system of equations)

Posted on 2008-12-05 07:13 By gillesdebil (2)

Categories:

Maple Commons general technical discussions

While solving the following system of equations, i get the error message "Kernel connection has been lost". I believe it is a memory problem.

= u[1]*u[2]*(B[1]-B[2]) = xi*(u[2]*E-u[2]*v[1]*B[1]-u[1]*E+u[1]*v[2]*B[2]);

= rho[1]*u[1]-rho[2]*u[2] = xi*(rho[1]*v[1]-rho[2]*v[2]);

=1/2*(2*rho[1]*u[1]^4*u[2]^2+2*p[1]*u[1]^2*u[2]^2-B[1]^2*u[1]^2*u[2]^2+u[2]^2*E^2-2*u[2]^2*E*v[1]*B[1]+u[2]^2*v[1]^2*B[1]^2-2*rho[2]*u[2]^4* u[1]^2-2*p[2]*u[1]^2*u[2]^2+B[2]^2*u[1]^2*u[2]^2-u[1]^2*E^2+2*u[1]^2*E*v[2]*B[2]-u[1]^2*v[2]^2*B[2]^2) = u[1]*u[2]*xi* (rho[1]*u[1]^2*v[1]*u[2]-B[1]*u[2]*E+B[1]^2*u[2]*v[1]-rho[2]*u[2]^2*v[2]*u[1]+B[2]*u[1]*E-B[2]^2*u[1]*v[2]);

= u[1]*u[2]*(rho[1]*u[1]^2*v[1]*u[2]-B[1]*u[2]*E+B[1]^2*u[2]*v[1]-rho[2]*u[2]^2*v[2]*u[1]+B[2]*u[1]*E-B[2]^2*u[1]*v[2]) = -(1/2)*xi* (-2*rho[1]*v[1]^2*u[1]^2*u[2]^2-2*p[1]*u[1]^2*u[2]^2-B[1]^2*u[1]^2*u[2]^2+u[2]^2*E^2-2*u[2]^2*E*v[1]*B[1]+u[2]^2*v[1]^2*B[1]^2+2*rho[2]*v[2]^2*u[1]^2*u[2]^2 +2*p[2]*u[1]^2*u[2]^2+B[2]^2*u[1]^2*u[2]^2-u[1]^2*E^2+2*u[1]^2*E*v[2]*B[2]-u[1]^2*v[2]^2*B[2]^2);

solve({eqe, eqd, eqc, eqb, eqa}, [xi, u[1], v[1], p[1], B[1]]);

This is a simple non-linear 5*5 system and i believe maple should be able to solve it. If anybody has an idea, please let me know. Thanks,

Peter

Try Maple 9.5

Comment on 2008-12-05 10:15 from Alex Smith ( Maple Rating 3

300)

In Maple 9.5, the following results:

solve({eqe, eqd, eqc, eqb, eqa}, {xi, u[1], v[1], p[1], B[1]});

{p[1] = p[1], u[1] = 0, xi = xi, v[1] = -rho[2]*(-xi*v[2]+u[2])/(xi*rho[1]),
B[1] = -xi*E*rho[1]/(rho[2]*(-xi*v[2]+u[2]))}

Subsequent to Maple 9.5, the solve command lost some functionality. It has still not been revived.

copy and paste

Comment on 2008-12-05 16:28 from roman_pearce ( Maple Rating 4

508)

Is there some way to copy and paste these equations? Can you repost them as text?

copy and paste / displayed equations

Comment on 2008-12-05 16:59 from Axel Vogt ( Maple Rating 4

987)

usually one can save the page as html, then they appear as text

Five equations

Comment on 2008-12-05 19:13 from Alex Smith ( Maple Rating 3

300)

Here are the equations. I used Doug's method of digging to the alternate text which is a property of the graphic image.

eqa:= u[1]*u[2]*(B[1]-B[2]) = xi*(u[2]*E-u[2]*v[1]*B[1]-u[1]*E+u[1]*v[2]*B[2]);

eqb:= rho[1]*u[1]-rho[2]*u[2] = xi*(rho[1]*v[1]-rho[2]*v[2]);

eqc:=1/2*(2*rho[1]*u[1]^4*u[2]^2+2*p[1]*u[1]^2*u[2]^2-B[1]^2*u[1]^2*u[2]^2+u[2]^2*E^2-2*u[2]^2*E*v[1]*B[1]+u[2]^2*v[1]^2*B[1]^2-2*rho[2]*u[2]^4* u[1]^2-2*p[2]*u[1]^2*u[2]^2+B[2]^2*u[1]^2*u[2]^2-u[1]^2*E^2+2*u[1]^2*E*v[2]*B[2]-u[1]^2*v[2]^2*B[2]^2) = u[1]*u[2]*xi* (rho[1]*u[1]^2*v[1]*u[2]-B[1]*u[2]*E+B[1]^2*u[2]*v[1]-rho[2]*u[2]^2*v[2]*u[1]+B[2]*u[1]*E-B[2]^2*u[1]*v[2]);

eqd:=u[1]*u[2]*(rho[1]*u[1]^2*v[1]*u[2]-B[1]*u[2]*E+B[1]^2*u[2]*v[1]-rho[2]*u[2]^2*v[2]*u[1]+B[2]*u[1]*E-B[2]^2*u[1]*v[2]) = -(1/2)*xi* (-2*rho[1]*v[1]^2*u[1]^2*u[2]^2-2*p[1]*u[1]^2*u[2]^2-B[1]^2*u[1]^2*u[2]^2+u[2]^2*E^2-2*u[2]^2*E*v[1]*B[1]+u[2]^2*v[1]^2*B[1]^2+2*rho[2]*v[2]^2*u[1]^2*u[2]^2 +2*p[2]*u[1]^2*u[2]^2+B[2]^2*u[1]^2*u[2]^2-u[1]^2*E^2+2*u[1]^2*E*v[2]*B[2]-u[1]^2*v[2]^2*B[2]^2);

eqe:=u[2]*rho[1]*u[1]^2*v[1]^2*gamma-6*u[2]*E*v[1]*B[1]*gamma-u[1]*rho[2]*u[2]^2*v[2]^2*gamma+6*u[1]*E*v[2]*B[2]*gamma-u[2]*rho[1]*u[1]^4 +2*u[2]*E^2*gamma-4*u[2]*v[1]^2*B[1]^2+u[1]*rho[2]*u[2]^4-2*u[1]*E^2*gamma+4*u[1]*v[2]^2*B[2]^2-2*u[2]*E^2+2*u[1]*E^2+u[2]*rho[1]*u[1]^4*gamma- u[2]*rho[1]*u[1]^2*v[1]^2+2*u[2]*gamma*p[1]*u[1]^2+6*u[2]*E*v[1]*B[1]+4*u[2]*v[1]^2*B[1]^2*gamma-u[1]*rho[2]*u[2]^4*gamma+u[1]*rho[2]*u[2]^2*v[2]^2- 2*u[1]*gamma*p[2]*u[2]^2-6*u[1]*E*v[2]*B[2]-4*u[1]*v[2]^2*B[2]^2*gamma = u[1]*u[2]*xi*(v[1]*rho[1]*u[1]^2*gamma-v[1]*rho[1]*u[1]^2 +rho[1]*v[1]^3*gamma-rho[1]*v[1]^3+2*v[1]*gamma*p[1]+4*v[1]*B[1]^2*gamma-4*v[1]*B[1]^2-2*B[1]*E*gamma+2*B[1]*E-v[2]*rho[2]*u[2]^2*gamma +v[2]*rho[2]*u[2]^2-rho[2]*v[2]^3*gamma+rho[2]*v[2]^3-2*v[2]*gamma*p[2]-4*v[2]*B[2]^2*gamma+4*v[2]*B[2]^2+2*B[2]*E*gamma-2*B[2]*E);

solve

Comment on 2008-12-05 22:14 from roman_pearce ( Maple Rating 4

508)

Try solving for all the variables (note, gamma is considered a constant).

#63

Comment on 2008-12-06 22:03 from Robert Israel ( Maple Rating 4

1554)

The result is 81 solutions, of which number 45 is equivalent to the single Maple 9.5 solution Alex quoted. But number 63 is strange, because it has an extra variable that looks like O but seems to be an escaped local (it's not the global O):

${E = E, xi = RootOf(_Z^2+1), B[1] = B[1], B[2] = -(u[2]^2*B[1]-u[2]*B[1]*RootOf(_Z^2+1)*v[2]-2*u[1]*u[2]*B[1]+RootOf(_Z^2+1)*u[2]*E-RootOf(_Z^2+1)*u[1]*E)/u[1]/(u[2]+RootOf(_Z^2+1)*v[2]), p[1] = p[1], p[2] = -(-2*v[2]*u[2]^2*E^2*RootOf(_Z^2+1)+2*v[2]^3*RootOf(_Z^2+1)*u[2]^2*B[1]^2+4*u[1]^3*u[2]^2*O*B[1]^2-4*v[2]*u[2]^3*B[1]*E+2*u[2]^4*B[1]^2*O*u[1]-4*u[1]*B[1]^2*v[2]^2*u[2]^2-v[2]^3*RootOf(_Z^2+1)*p[1]*u[1]^2-6*u[2]^3*O*B[1]^2*u[1]^2-2*u[2]^3*O*B[1]^2*v[2]^2+2*v[2]*u[2]^4*B[1]^2*RootOf(_Z^2+1)+6*v[2]^3*RootOf(_Z^2+1)*u[1]^2*B[1]^2-2*v[2]^2*u[2]*E^2*O+2*v[2]^2*u[1]*E^2*O-4*v[2]^2*u[1]^3*O*B[1]^2-2*v[2]^2*u[2]*B[1]^2*u[1]^2+4*v[2]^3*E*u[1]*B[1]-v[2]^2*p[1]*u[1]^2*u[2]-6*v[2]^2*RootOf(_Z^2+1)*u[2]*O*E*B[1]*u[1]+6*v[2]^2*RootOf(_Z^2+1)*u[1]*u[2]*B[1]*E-6*v[2]^3*RootOf(_Z^2+1)*O*u[1]^2*B[1]^2-2*v[2]^3*RootOf(_Z^2+1)*O*u[2]^2*B[1]^2-6*v[2]^2*u[1]^2*B[1]*RootOf(_Z^2+1)*E+8*v[2]^3*RootOf(_Z^2+1)*O*u[2]*u[1]*B[1]^2-4*v[2]^3*B[1]*u[2]*E+6*v[2]^2*RootOf(_Z^2+1)*u[1]^2*E*O*B[1]+2*u[1]^2*u[2]^2*B[1]*RootOf(_Z^2+1)*E-2*v[2]^4*u[2]*O*B[1]^2-2*u[2]^4*u[1]*B[1]^2+6*u[2]^3*B[1]^2*u[1]^2-2*v[2]*RootOf(_Z^2+1)*u[1]*u[2]*E^2*O+8*v[2]*u[1]^3*u[2]*O*B[1]^2*RootOf(_Z^2+1)+2*v[2]^2*u[2]^3*B[1]^2-p[1]*u[1]^2*u[2]^3+2*v[2]*RootOf(_Z^2+1)*u[2]^2*E^2*O-8*v[2]*u[1]^3*u[2]*B[1]^2*RootOf(_Z^2+1)-8*v[2]*u[2]^3*B[1]^2*RootOf(_Z^2+1)*u[1]-4*v[2]^3*O*E*B[1]*u[1]+4*v[2]^3*u[2]*O*E*B[1]+2*v[2]^2*u[2]*O*B[1]^2*u[1]^2+4*u[2]^3*O*v[2]*E*B[1]-12*O*v[2]*E*B[1]*u[1]*u[2]^2+2*v[2]^4*u[1]*O*B[1]^2+2*v[2]*u[1]*E^2*RootOf(_Z^2+1)*u[2]+4*u[1]*O*B[1]^2*v[2]^2*u[2]^2+12*u[1]*B[1]*E*v[2]*u[2]^2-2*v[2]*u[2]^4*O*B[1]^2*RootOf(_Z^2+1)+14*v[2]*B[1]^2*u[1]^2*u[2]^2*RootOf(_Z^2+1)-v[2]*p[1]*u[1]^2*u[2]^2*RootOf(_Z^2+1)-4*u[1]^3*u[2]^2*B[1]^2-14*v[2]*u[1]^2*u[2]^2*O*B[1]^2*RootOf(_Z^2+1)+8*v[2]*u[2]^3*u[1]*O*B[1]^2*RootOf(_Z^2+1)+4*v[2]^2*u[1]^3*B[1]^2+2*v[2]^4*u[2]*B[1]^2-2*v[2]^4*B[1]^2*u[1]-2*v[2]^2*u[1]*E^2+2*v[2]^2*u[2]*E^2-2*RootOf(_Z^2+1)*u[1]*u[2]^3*B[1]*E-8*v[2]^3*RootOf(_Z^2+1)*u[2]*u[1]*B[1]^2-2*u[1]^2*u[2]^2*O*E*B[1]*RootOf(_Z^2+1)+2*u[2]^3*O*E*B[1]*u[1]*RootOf(_Z^2+1)+8*v[2]*u[1]^2*u[2]*O*E*B[1]-8*v[2]*u[1]^2*E*u[2]*B[1])/(RootOf(_Z^2+1)*v[2]^3+u[2]*v[2]^2+RootOf(_Z^2+1)*u[2]^2*v[2]+u[2]^3)/u[1]^2, rho[1] = -2*(3*u[1]*B[1]*E*v[2]-2*v[2]*u[2]*B[1]*E+u[2]^2*B[1]^2*O*u[1]+2*RootOf(_Z^2+1)*E*B[1]*v[2]^2+RootOf(_Z^2+1)*E^2*O*v[2]+RootOf(_Z^2+1)*O*B[1]^2*v[2]^3+2*RootOf(_Z^2+1)*u[1]^2*B[1]^2*v[2]+RootOf(_Z^2+1)*u[2]^2*B[1]^2*v[2]-2*u[2]*O*B[1]^2*u[1]^2-2*u[2]*O*B[1]^2*v[2]^2+3*u[1]*O*B[1]^2*v[2]^2-RootOf(_Z^2+1)*u[1]*u[2]*B[1]*E+2*u[2]*B[1]^2*u[1]^2-RootOf(_Z^2+1)*O*u[2]^2*B[1]^2*v[2]+2*RootOf(_Z^2+1)*O*u[2]*u[1]*B[1]^2*v[2]+RootOf(_Z^2+1)*u[2]*O*E*B[1]*u[1]-2*RootOf(_Z^2+1)*O*u[1]^2*B[1]^2*v[2]+2*u[2]*O*v[2]*E*B[1]-3*O*v[2]*E*B[1]*u[1]-2*RootOf(_Z^2+1)*u[2]*u[1]*B[1]^2*v[2]-2*RootOf(_Z^2+1)*E*O*B[1]*v[2]^2-RootOf(_Z^2+1)*E^2*v[2]-RootOf(_Z^2+1)*B[1]^2*v[2]^3-u[2]^2*u[1]*B[1]^2-3*u[1]*B[1]^2*v[2]^2+2*v[2]^2*u[2]*B[1]^2)/(-u[2]^3-u[2]*v[2]^2+RootOf(_Z^2+1)*v[2]^3+RootOf(_Z^2+1)*u[2]^2*v[2])/u[1]^2, rho[2] = -2*(3*u[1]*B[1]*E*v[2]-2*v[2]*u[2]*B[1]*E+u[2]^2*B[1]^2*O*u[1]+2*RootOf(_Z^2+1)*E*B[1]*v[2]^2+RootOf(_Z^2+1)*E^2*O*v[2]+RootOf(_Z^2+1)*O*B[1]^2*v[2]^3+2*RootOf(_Z^2+1)*u[1]^2*B[1]^2*v[2]+RootOf(_Z^2+1)*u[2]^2*B[1]^2*v[2]-2*u[2]*O*B[1]^2*u[1]^2-2*u[2]*O*B[1]^2*v[2]^2+3*u[1]*O*B[1]^2*v[2]^2-RootOf(_Z^2+1)*u[1]*u[2]*B[1]*E+2*u[2]*B[1]^2*u[1]^2-RootOf(_Z^2+1)*O*u[2]^2*B[1]^2*v[2]+2*RootOf(_Z^2+1)*O*u[2]*u[1]*B[1]^2*v[2]+RootOf(_Z^2+1)*u[2]*O*E*B[1]*u[1]-2*RootOf(_Z^2+1)*O*u[1]^2*B[1]^2*v[2]+2*u[2]*O*v[2]*E*B[1]-3*O*v[2]*E*B[1]*u[1]-2*RootOf(_Z^2+1)*u[2]*u[1]*B[1]^2*v[2]-2*RootOf(_Z^2+1)*E*O*B[1]*v[2]^2-RootOf(_Z^2+1)*E^2*v[2]-RootOf(_Z^2+1)*B[1]^2*v[2]^3-u[2]^2*u[1]*B[1]^2-3*u[1]*B[1]^2*v[2]^2+2*v[2]^2*u[2]*B[1]^2)/(-u[2]^3-u[2]*v[2]^2+RootOf(_Z^2+1)*v[2]^3+RootOf(_Z^2+1)*u[2]^2*v[2])/u[1]^2, u[1] = u[1], u[2] = u[2], v[1] = RootOf(_Z^2+1)*u[2]-u[1]*RootOf(_Z^2+1)+v[2], v[2] = v[2]}$

more variables

Comment on 2008-12-07 11:09 from gillesdebil (2)

Thanks for the hint, i am running it right now. Actually, not only gamma is a constant, all the variables with index 2 are constant. I solve for xi and the variables with index 1. Since i solve these exautions iterativally, i can pick one of those 6 variables, leaving a 5*5 system to solve. The reason why i pick rho_1 as being constant, and thus iterationg on it, is physical, it really is the only possibility. Therefore, i solve the system that i posted. I will keep you informed. Could you send the complete solution you got to me?

thanks,

peter