Solve three non linear equations.

I want to solve the following equations in MAXIMA, but my system runs out of memory. Is it possible to solve these symbolic equations.

exp1=(2*beta4^2+2*beta3^2+2*beta2^2)*d^2*z1^2+( (4*alpha4*beta4+4*alpha3*beta3+4*alpha2*beta2)*d^2*y1+4*beta4*d^2*gamma4+4*beta3*d^2*gamma3+4* beta2*d^2*gamma2)*z1+(2*alpha4^2+2*alpha3^2+2*alpha2^2)*d^2*y1^2+ (4*alpha4*d^2*gamma4+4*alpha3*d^2*gamma3+4*alpha2*d^2*gamma2)*y1+l2^2-l1^2+2*d^2*gamma4^2+2*d^2* gamma3^2+2*d^2*gamma2^2

exp2=zp^2-2*z1*zp+(beta1^2+1)*z1^2+(2*alpha1*beta1*y1-2*beta1*xp+2*beta1*gamma1)*z1+yp^2 -2*y1*yp+(alpha1^2+1)*y1^2+(2*alpha1*gamma1-2*alpha1*xp)*y1+xp^2-2*gamma1*xp-l1^2+gamma1^2

exp3=(-4*beta4*d*z1-4*alpha4*d*y1-4*d*gamma4)*zp+(4*beta4+4*beta1*beta2)*d*z1^2+(-4* beta3*d*yp+(4*beta3+4*alpha1*beta2+4*alpha2*beta1+4*alpha4)*d*y1-4*beta2*d*xp+4*d*gamma4+4* beta1*d*gamma2+4*beta2*d*gamma1)*z1+(-4*alpha3*d*y1-4*d*gamma3)*yp+(4*alpha3+4*alpha1*alpha2)* d*y1^2+(-4*alpha2*d*xp+4*d*gamma3+4*alpha1*d*gamma2+4*alpha2*d*gamma1)*y1-4*d*gamma2*xp-3*l2^2+ 3*l1^2+4*d*gamma1*gamma2

Can anyone please help solve them to get an expression for y1 and z1?

Answer 1

[Walter Roberson]

It is not clear to me whether exp1, exp2, and exp3 are known values, or if the those are labels being used for the three equations and each is implicitly equal to 0 ?

In Maple, trying to solve 3 equations for 2 variables usually fails. Which additional variable would you like to be solved for?

[Walter Roberson]

I can solve the first two expressions for y1 and z1 without undue difficulty, but the expression for y1 involves the solution to a quartic (order 4 equation), and the expression for z1 is over 1 million characters long. Are you sure there isn't a better way to approach this?

[Walter Roberson]

Maple was taking over 25 minutes just to _format_ a fraction of the second term of z1. I gave up and killed it off.

Answer 2

[Sourabh Bajaj]

I solved the problem using eliminations in Maxima using some eliminations. Thank you for your response though.