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 Post subject: How to solve this algebraic system
PostPosted: Fri May 23, 2014 6:43 pm 
Hello,
How to solve the following algebraic system (f1=0,f2=0,f3=0,f4=0); where (lambda+mu+nu+1)*alpha*lambda*mu*nu*(alpha-1)<>0;

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f1:=(1+mu+nu)*(mu^2-2*mu*alpha+2*mu+2*mu*alpha*nu+2*nu*alpha^2+alpha^2+1+alpha^2*nu^2-2*alpha-2*nu*alpha)*(-lambda*alpha^3-nu*alpha+3*mu*alpha^3*nu^2+2*mu^2*alpha^3*nu+3*mu^2*nu-mu^2*alpha*nu^2+2*lambda*alpha^2*nu^3-mu*alpha^2-lambda*alpha^3*nu^3-9*lambda*alpha*mu*nu+3*lambda*alpha^3*mu+nu+6*lambda*mu*nu+3*lambda*mu^2*nu+nu^3*alpha*mu+mu^2*alpha^3*nu^2+nu^3*alpha^3*mu+alpha^3*mu^2+alpha^3*mu+6*lambda*alpha^3*nu*mu+3*lambda*alpha^3*mu*nu^2-mu^2*alpha^2*nu^2+mu^3*alpha^2*nu-4*nu*alpha^2*mu-5*mu*alpha^2*nu^2-3*mu^2*alpha^2*nu-4*lambda*alpha*nu+2*lambda*mu^3*alpha+3*nu*alpha^3*mu-mu^3*alpha^2-3*mu^2*lambda-5*nu^2*alpha*lambda+4*lambda*alpha^2*nu-5*mu^2*lambda*alpha^2-nu^3*alpha+mu^3*nu-4*mu*alpha*nu+5*lambda*alpha^2*nu*mu^2-5*mu^2*alpha*nu+lambda*alpha^2-5*lambda*mu^2*alpha*nu-2*mu^2*alpha^2-2*mu^3*alpha*nu-3*mu*lambda-4*lambda*alpha^2*mu-3*nu^2*alpha*mu-2*mu*alpha^2*nu^3+5*alpha^2*nu^2*lambda-5*lambda*alpha^2*mu*nu^2+3*lambda*nu+4*mu*lambda*alpha+5*mu^2*lambda*alpha+lambda*alpha-3*lambda*alpha^3*nu-3*lambda*alpha^3*nu^2+nu^2-lambda*mu^3-2*nu^2*alpha-9*lambda*alpha^2*mu*nu+5*nu^2*alpha*mu*lambda+3*mu*nu+mu^2*nu^2+2*mu*nu^2-lambda);

====================================================================

f2:=(1+nu+lambda)*(alpha^2*nu^2-2*nu^2*alpha+nu^2-2*nu*alpha+2*nu*alpha^2-2*lambda*alpha*nu+2*lambda*nu+lambda^2+alpha^2+2*lambda*alpha)*(5*lambda^2*alpha*mu-3*lambda^2*nu-lambda*alpha^3+nu*alpha+3*mu*alpha^3*nu^2+lambda*alpha^2*nu^3-2*mu*alpha^2-lambda*alpha^3*nu^3-lambda^2*alpha^3*nu^2+9*lambda*alpha*mu*nu-3*lambda*alpha^3*mu-6*lambda*mu*nu-5*nu*lambda^2*alpha*mu+5*nu*lambda^2*alpha-nu^3*alpha*mu+nu^3*alpha^3*mu+alpha^3*mu-6*lambda*alpha^3*nu*mu-3*lambda*alpha^3*mu*nu^2-2*lambda^2*alpha^3*nu-5*nu*alpha^2*mu-4*mu*alpha^2*nu^2+3*lambda*alpha*nu+mu*lambda^3+3*nu*alpha^3*mu+4*nu^2*alpha*lambda+3*lambda^2*alpha^2*nu+5*lambda*alpha^2*nu+lambda^3*alpha^2*nu+2*lambda^2*alpha^2*nu^2+nu^3*alpha+5*mu*alpha*nu-2*mu*lambda^3*alpha+5*lambda^2*alpha^2*nu*mu-lambda^3*alpha^2+lambda^2*alpha+2*lambda*alpha^2-5*mu*lambda^2*alpha^2-3*nu^2*lambda+5*lambda*alpha^2*mu+4*nu^2*alpha*mu-mu*alpha^2*nu^3+4*alpha^2*nu^2*lambda+4*lambda*alpha^2*mu*nu^2-2*lambda*nu-5*mu*lambda*alpha-lambda*alpha-3*mu*lambda^2-lambda^2*alpha^3+3*mu*nu^2*lambda-3*lambda*alpha^3*nu-3*lambda*alpha^3*nu^2-nu^3-nu^2-lambda^3+lambda^2*alpha^2+2*lambda^3*alpha-lambda^2+3*lambda^2*nu*mu+2*nu^2*alpha+9*lambda*alpha^2*mu*nu-4*nu^2*alpha*mu*lambda+mu*nu^3-3*mu*nu^2);

====================================================================

f3:=(1+mu+lambda)*(mu^2*alpha^2-2*mu^2*alpha+mu^2+2*lambda*alpha^2*mu-2*mu*lambda*alpha-2*mu*alpha+2*mu+1+lambda^2*alpha^2+2*lambda*alpha)*(3*lambda^2*alpha*mu+2*lambda^2*alpha*mu^2-lambda^2*mu^2-2*nu*alpha-3*mu^2*alpha^3*nu+3*mu^2*nu+mu*alpha^2-3*lambda^2*alpha^3*mu+9*lambda*alpha*mu*nu-3*lambda*alpha^3*mu^2-2*lambda*alpha^3*mu+nu-6*lambda*mu*nu-3*lambda*mu^2*nu+5*nu*lambda^2*alpha*mu-5*nu*lambda^2*alpha-alpha^3*mu^2+lambda^3*alpha^3*nu-6*lambda*alpha^3*nu*mu+3*lambda*alpha^3*mu^2*nu-mu^3*alpha^2*nu-3*lambda^2*alpha^3*nu+5*nu*alpha^2*mu+4*mu^2*alpha^2*nu+3*lambda^2*alpha^3*mu*nu+5*lambda*alpha*nu+lambda*mu^3*alpha+mu^3*alpha^2-3*mu^2*lambda+5*lambda^2*alpha^2*nu-5*lambda*alpha^2*nu-2*lambda^3*alpha^2*nu+4*mu^2*lambda*alpha^2+mu^3*nu-5*mu*alpha*nu+mu*lambda^3*alpha-5*lambda^2*alpha^2*nu*mu-4*lambda*alpha^2*nu*mu^2-4*mu^2*alpha*nu+2*lambda^3*alpha^2+lambda^2*alpha-lambda*alpha^2+4*lambda*mu^2*alpha*nu+2*mu^2*alpha^2-mu^3*alpha*nu-3*mu*lambda+5*mu*lambda^2*alpha^2+mu^3*alpha^3*nu+3*lambda*alpha^2*mu-3*lambda*nu+5*mu*lambda*alpha+4*mu^2*lambda*alpha+2*lambda*alpha-2*mu*lambda^2-lambda^3*alpha^3-lambda^2*alpha^3-lambda*mu^3+lambda^2*alpha^2-lambda^3*alpha-lambda^2+9*lambda*alpha^2*mu*nu+3*mu*nu-mu^3*alpha^3-lambda);

====================================================================

f4:=(lambda+mu+nu)*(nu^2+2*mu*alpha*nu+mu^2*alpha^2+2*lambda*nu-2*lambda*alpha*nu-2*mu*lambda*alpha+2*lambda*alpha^2*mu+lambda^2-2*lambda^2*alpha+lambda^2*alpha^2)*(-4*lambda^2*alpha*mu-2*lambda^2*alpha*mu^2-3*lambda^2*nu+lambda^2*mu^2+3*mu^2*alpha^3*nu-mu^2*alpha*nu^2-lambda*alpha^2*nu^3-3*lambda^2*alpha^3*mu+lambda^2*alpha^3*nu^2-9*lambda*alpha*mu*nu-3*lambda*alpha^3*mu^2+6*lambda*mu*nu+2*lambda*mu^2*nu-4*nu*lambda^2*alpha*mu+4*nu*lambda^2*alpha-2*nu^3*alpha*mu+mu^2*alpha^3*nu^2+lambda^3*alpha^3*nu+6*lambda*alpha^3*nu*mu+2*lambda*alpha^3*mu*nu^2+3*lambda*alpha^3*mu^2*nu-mu^2*alpha^2*nu^2-2*mu^3*alpha^2*nu+3*lambda^2*alpha^3*nu+5*mu*alpha^2*nu^2-5*mu^2*alpha^2*nu+3*lambda^2*alpha^3*mu*nu+mu*lambda^3-lambda*mu^3*alpha+2*mu^3*alpha^2+5*nu^2*alpha*lambda-4*lambda^2*alpha^2*nu-lambda^3*alpha^2*nu-2*lambda^2*alpha^2*nu^2+5*mu^2*lambda*alpha^2+2*nu^3*alpha-mu*lambda^3*alpha-4*lambda^2*alpha^2*nu*mu-5*lambda*alpha^2*nu*mu^2+5*mu^2*alpha*nu+lambda^3*alpha^2-3*lambda*mu^2*alpha*nu+mu^3*alpha*nu+4*mu*lambda^2*alpha^2+mu^3*alpha^3*nu-3*nu^2*lambda-5*nu^2*alpha*mu+mu*alpha^2*nu^3-5*alpha^2*nu^2*lambda-3*lambda*alpha^2*mu*nu^2-5*mu^2*lambda*alpha+3*mu*lambda^2-lambda^3*alpha^3+3*mu*nu^2*lambda-nu^3-lambda^3+lambda^3*alpha+3*lambda^2*nu*mu-9*lambda*alpha^2*mu*nu-5*nu^2*alpha*mu*lambda+mu*nu^3+mu^2*nu^2+3*mu*nu^2-mu^3*alpha^3);

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thank you,
GERARD.


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