Bonjour,
Je cherche une méthode éfficace pour résoudre le système d'équations polynomiales suivant :
with(SolveTools):
> PolynomialSystem({f0,f1,f2,f3,f4,f5,f6},{alpha,lambda,mu,nu});
# avec les fi ci-dessous :
f0:= (1+mu+nu+lambda)*alpha^3*(1+mu+nu)*(mu^2-2*mu*alpha+2*nu*alpha*mu+2*mu-2*nu*alpha+2*nu*alpha^2+alpha^2-2*alpha+1+alpha^2*nu^2)*(-lambda*alpha^3+3*mu*nu+alpha^2*lambda-lambda+3*nu*mu^2+3*nu*mu^2*lambda+lambda*alpha+nu+mu^2*alpha^3+nu^2+mu*alpha^3-nu*alpha-mu^3*alpha^2-2*mu^2*alpha^2+3*lambda*nu-4*alpha^2*lambda*mu+4*alpha^2*lambda*nu-3*lambda*mu-alpha^2*mu-4*nu*alpha*mu-4*nu*alpha^2*mu+4*lambda*mu*alpha+nu^2*mu^2-2*nu^3*alpha^2*mu+mu^3*nu-mu^3*lambda-2*nu^2*alpha+3*lambda*alpha^3*nu^2*mu+3*lambda*alpha^3*mu+6*lambda*alpha^3*mu*nu-3*lambda*alpha^3*nu^2-3*lambda*alpha^3*nu+nu^3*alpha^3*mu+2*mu^2*alpha^3*nu+mu^2*alpha^3*nu^2+3*mu*alpha^3*nu+3*mu*alpha^3*nu^2+5*nu^2*lambda*alpha^2-9*alpha^2*lambda*mu*nu+2*nu^3*alpha^2*lambda+2*nu^2*mu-nu^3*alpha+5*mu^2*alpha*lambda-4*lambda*alpha*nu-5*mu*alpha^2*nu^2+6*mu*nu*lambda+nu^3*alpha*mu-3*nu^2*alpha*mu+5*lambda*mu^2*alpha^2*nu-3*lambda*mu^2-nu^3*alpha^3*lambda-3*mu^2*nu*alpha^2-mu^2*alpha^2*nu^2-9*lambda*alpha*mu*nu-5*nu*alpha*lambda*mu^2-5*lambda*mu^2*alpha^2-5*nu^2*lambda*alpha^2*mu-5*nu*alpha*mu^2-5*nu^2*lambda*alpha+2*mu^3*lambda*alpha-mu^2*nu^2*alpha+5*nu^2*lambda*alpha*mu-2*mu^3*nu*alpha+mu^3*nu*alpha^2);
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f1:= -2*(1+mu+nu+lambda)*alpha^2*(1+mu+nu)*(mu^2-2*mu*alpha+2*nu*alpha*mu+2*mu-2*nu*alpha+2*nu*alpha^2+alpha^2-2*alpha+1+alpha^2*nu^2)*(-lambda*alpha^3+2*alpha^2*lambda+5*alpha^2*lambda*mu^3-7*lambda^2*nu*alpha+2*nu*mu^2*lambda-lambda*alpha-mu^2*alpha^3+nu^2-2*alpha^2*nu^2+mu*alpha^3+lambda^2+nu*alpha+mu^2*alpha^4-2*mu^3*alpha^3+lambda^2*alpha^3-mu^3*alpha^2-2*mu^2*alpha^2+2*lambda*nu+4*alpha^2*lambda*mu+4*alpha^2*lambda*nu+9*lambda^2*nu*alpha^2-alpha^2*mu+2*nu*alpha^4*lambda^2+nu^2*alpha^4*lambda^2-4*alpha^3*nu*lambda^2+4*nu*alpha*mu-12*nu*alpha^2*mu-4*lambda*mu*alpha+nu^2*mu^2-4*nu^3*alpha^2*mu+7*lambda^2*mu*alpha^3*nu-12*alpha^2*lambda^2*mu*nu-nu^2*alpha+3*lambda*alpha^3*nu^2*mu+9*lambda*alpha^3*mu^2*nu+2*lambda*alpha^4*mu*nu^2+4*lambda*alpha^4*mu*nu-2*lambda*alpha^3*mu-9*lambda*alpha^3*mu^2+lambda*alpha^3*mu*nu+2*lambda*alpha^4*mu-5*lambda*alpha^3*nu^2-4*lambda*alpha^3*nu+2*nu^3*alpha^3*mu-mu^2*alpha^3*nu+2*mu^2*alpha^4*nu+2*mu^3*alpha^3*nu+4*mu*alpha^3*nu+5*mu*alpha^3*nu^2+7*nu^2*lambda*alpha^2+9*alpha^2*lambda^2*mu-24*alpha^2*lambda*mu*nu+lambda^2*mu^2+5*nu^3*alpha^2*lambda+5*alpha^2*nu^2*lambda^2-5*nu^2*alpha^3*lambda^2+2*nu^2*mu-2*nu^3*alpha+7*lambda^2*nu*alpha*mu+lambda^2*alpha+lambda^2*alpha^4-5*mu^2*alpha*lambda-2*lambda*alpha*nu-15*mu*alpha^2*nu^2+4*mu*nu*lambda+5*lambda^2*mu^2*alpha^2-nu*alpha^2-7*lambda^2*mu*alpha^3+2*nu^3*alpha*mu-nu^2*alpha*mu-5*lambda*mu^2*alpha^2*nu-5*lambda^2*alpha*mu^2-2*nu^3*alpha^3*lambda-15*mu^2*nu*alpha^2-nu^3*alpha^2-2*mu^2*alpha^2*nu^2+lambda*alpha*mu*nu+3*nu*alpha*lambda*mu^2+mu^2*nu^2*alpha^4+7*lambda*mu^2*alpha^2-5*nu^2*lambda*alpha^2*mu+5*nu*alpha*mu^2-9*nu^2*lambda*alpha-2*mu^3*lambda*alpha-4*alpha^2*lambda^2-4*lambda^2*mu*alpha+9*nu^2*lambda*alpha*mu+2*mu^3*nu*alpha-4*mu^3*nu*alpha^2+2*lambda^2*mu);
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f2:= (1+mu+nu+lambda)*alpha*(-60*mu^4*alpha^3-14*alpha^2*lambda*mu^3+5*nu^6*mu*alpha^3+165*lambda^3*mu^2*alpha^3+103*nu^2*alpha^4*lambda^2*mu^3+15*lambda*alpha*nu^3*mu^2-15*alpha^5*lambda^2-19*lambda^2*nu*alpha+3*lambda^3*alpha^2*mu-10*nu^5*alpha^3*mu^2+21*lambda^3*alpha^2+6*nu^4*alpha*mu^3-4*alpha^7*lambda^3*nu-10*mu^6*alpha^3+25*nu^2*alpha^3+70*nu^3*alpha^3-10*mu^2*alpha^3-60*nu^4*alpha^4-40*nu^3*alpha^4-20*alpha^2*nu^2-10*nu^2*alpha^4-mu^4*lambda^3-lambda^3-4*lambda^3*mu^3+25*mu^2*alpha^4-40*mu^3*alpha^3-30*mu^3*alpha^5+10*lambda^2*alpha^3-20*mu^2*alpha^5-6*lambda^3*mu^2+nu^3-61*lambda*alpha^4*mu*nu^4-6*alpha^7*lambda^3*nu^2-10*nu^6*alpha^4*mu+39*lambda^3*alpha^5*mu-40*mu^5*alpha^3+70*mu^3*nu^2*lambda^2*alpha^5+118*lambda^3*alpha^3*mu^3+21*lambda^3*alpha^5+70*mu^3*alpha^4+15*mu^3*lambda*alpha*nu^3-66*lambda^3*nu*mu^3*alpha^3-15*lambda^3*alpha^4+10*mu^5*alpha^4+4*nu^3*mu^3-3*mu*alpha^6*nu*lambda^3+23*mu^3*nu^3*alpha^3*lambda+281*nu^3*lambda*mu*alpha^3+56*nu^5*lambda*mu*alpha^3+120*nu^4*lambda*mu*alpha^3-alpha^7*lambda^3+alpha^2*lambda*mu-7*alpha^2*lambda*nu-100*nu^3*alpha^2*mu*lambda^2-lambda^2*nu-46*lambda^3*alpha^4*mu^3+38*lambda^2*nu*alpha^2-15*lambda^3*alpha^3+12*lambda^2*alpha*mu^2*nu^2+12*lambda^2*alpha*mu^3*nu^2-3*lambda^3*alpha^6*mu+165*nu^2*alpha^4*lambda^3+22*nu*alpha^4*lambda^2+127*nu^2*alpha^4*lambda^2-15*alpha^3*nu*lambda^2-84*alpha^3*nu*lambda^3-95*nu^2*alpha^5*lambda^2-6*nu^4*alpha*mu-6*mu*alpha^7*lambda^2*nu^2-66*lambda^3*mu^2*alpha^3*nu+19*nu*mu^5*alpha^2-nu*alpha^2*mu-4*lambda^2*nu*mu^3+52*lambda^3*nu*alpha^4+118*lambda^3*nu^3*alpha^4-46*nu^3*alpha^3*lambda^3+3*lambda^3*alpha^5*nu+mu^4*nu^3-10*nu^6*alpha^4-92*mu^2*alpha^5*lambda*nu-7*mu*alpha^5*lambda+6*nu^4*alpha*mu^2+6*nu^3*alpha^6*mu^4-164*nu^3*alpha^2*mu+12*lambda^2*alpha^6*nu^3*mu^2-133*mu^3*nu*alpha^2*lambda^2+193*lambda^2*mu^4*alpha^3+27*lambda^3*alpha^5*nu*mu+97*lambda^2*nu*mu^4*alpha^4+4*nu^3*mu-36*lambda^3*alpha^5*nu*mu^2-32*lambda^2*mu*alpha^3*nu+57*alpha^2*lambda^2*mu*nu+3*lambda^3*nu*alpha*mu^2+12*lambda^2*alpha^6*nu^2*mu^2-5*lambda^3*alpha^6+3*lambda^3*alpha^6*nu^3*mu-66*nu^2*alpha^4*lambda^3*mu-104*mu^3*alpha^5*nu*lambda+5*lambda^2*alpha^6*nu^5+60*nu^4*alpha^3+5*nu^2*alpha+89*mu^3*nu*alpha*lambda^2-91*lambda*nu*mu^4*alpha^2+263*lambda*alpha^3*nu^2*mu-68*lambda*alpha^3*mu^2*nu-68*lambda*alpha^4*mu*nu^2+41*lambda*alpha^4*mu*nu-192*nu^3*alpha^4*lambda*mu-5*lambda*alpha^3*mu-10*lambda*alpha^3*mu^2+10*mu^2*alpha^4*lambda-63*mu^3*alpha^4*lambda+20*mu^3*alpha^3*lambda+nu*alpha^5*lambda+nu^2*lambda+41*lambda*alpha^3*mu*nu-190*nu^3*alpha^5*lambda*mu-174*nu^2*alpha^5*lambda*mu+281*mu^3*alpha^4*lambda*nu-nu^2*alpha^5*lambda-14*nu^3*alpha^5*lambda-26*nu^4*alpha^5*lambda-5*lambda*alpha^4*nu-10*lambda*alpha^4*nu^2+20*lambda*alpha^4*nu^3+9*lambda*alpha^4*mu+15*mu^2*alpha^5*lambda+70*mu^4*alpha^3*lambda+10*lambda*alpha^3*nu^2+9*lambda*alpha^3*nu-67*nu*alpha^5*lambda*mu+45*nu^2*alpha^4*lambda*mu^2+263*nu*alpha^4*lambda*mu^2-192*nu*alpha^3*lambda*mu^3+45*nu^2*alpha^3*lambda*mu^2-168*mu^2*alpha^5*lambda*nu^2-35*mu^2*nu^4*lambda*alpha^4-92*nu^2*alpha^3*mu^3+401*nu^3*alpha^3*mu-88*mu*alpha^4*nu^2-88*mu^2*alpha^3*nu+187*mu^2*alpha^3*nu^2-280*mu*alpha^4*nu^3+nu^2*alpha^5*mu+26*nu^4*alpha^5*mu-302*nu^4*alpha^4*mu+187*mu^2*alpha^4*nu+mu*alpha^4*nu-125*nu*alpha^5*mu^2+401*nu*alpha^4*mu^3+270*nu^3*alpha^3*mu^2-255*nu^2*alpha^5*mu^2-280*mu^3*alpha^3*nu+mu*alpha^3*nu+187*mu*alpha^3*nu^2+250*mu^4*alpha^4*nu-228*mu^3*alpha^5*nu^2-92*nu^3*alpha^4*mu^2-302*nu*alpha^3*mu^4-nu*alpha^5*mu+14*nu^3*alpha^5*mu-164*mu^3*alpha^5*nu+270*nu^2*alpha^4*mu^3-215*nu^3*alpha^5*mu^2-5*mu^3*nu^4*alpha^3-215*mu^3*nu^2*alpha^2-84*nu^3*mu^3*alpha^2+268*lambda^2*mu^3*alpha^3+15*nu^2*lambda*alpha^2-50*alpha^2*lambda^2*mu+10*nu^5*alpha^2-64*nu^2*alpha^5*mu^3*lambda+6*nu^2*mu^2*lambda+10*nu^4*alpha^5*mu^3+20*nu^4*alpha^4*lambda^3-5*mu^2*nu^4*alpha^3-67*alpha^2*lambda*mu*nu-9*alpha^2*nu^2*lambda^2*mu+119*nu^3*mu^2*lambda*alpha^3-6*nu^4*alpha+111*alpha^5*lambda^2*mu^2-35*nu^5*alpha^5*lambda^2+193*nu^4*alpha^4*lambda^2-25*lambda^2*nu*mu^4*alpha^3+103*lambda^2*mu^2*nu^3*alpha^3+27*lambda^3*alpha^2*mu*nu+70*nu^4*alpha^4*lambda+50*lambda^2*alpha^6*nu^2-3*lambda^3*alpha^6*nu+69*nu^3*alpha^6*mu^2*lambda-9*alpha^5*lambda^2*nu*mu^2-30*nu^4*alpha^5*lambda^3+70*nu^3*alpha^2*mu^2*lambda^2-15*mu^3*lambda*alpha^6+9*mu^3*alpha^6*nu^2+6*mu^3*alpha^7*nu^2+10*mu^5*alpha^5+mu^3*alpha^7-mu^3*alpha^6-6*mu^4*alpha^6+72*nu^3*alpha^2*lambda-253*nu^3*alpha^3*lambda^2+111*alpha^2*nu^2*lambda^2+50*lambda^2*alpha^6*nu^3-123*nu^2*alpha^3*lambda^3+268*nu^3*alpha^4*lambda^2-99*lambda^3*alpha^5*nu^3-181*nu^2*alpha^3*lambda^2-135*alpha^5*lambda^2*nu^3-4*alpha^7*lambda^3*nu^3+28*mu^4*lambda*alpha*nu^2-10*mu^6*alpha^3*nu+20*mu^6*lambda*alpha^3-133*alpha^5*lambda^2*nu^3*mu-4*lambda^2*alpha^7*nu^3*mu+4*mu^3*alpha^7*nu+72*mu^3*alpha^5*lambda-19*lambda*mu^5*alpha^2-6*mu^4*alpha^6*nu-104*nu^3*alpha^2*lambda*mu+51*lambda^2*nu*alpha*mu^2-190*alpha^2*lambda*mu^3*nu+39*nu^2*lambda*alpha*mu^2+30*alpha^2*nu^2*lambda^3-68*mu^4*nu*alpha^5+4*mu^4*nu^3*alpha^5-64*mu^4*nu^2*alpha^5-5*mu^4*nu^2*alpha^4-5*mu^4*nu^3*alpha^4-20*mu^4*nu^3*alpha^3-15*lambda*alpha*nu^3-122*mu^4*nu^2*alpha^3-120*mu^4*lambda*alpha^4+6*mu^4*alpha^6*nu^2+84*lambda*alpha^6*nu^2*mu+50*mu^4*alpha^5*lambda-nu^3*alpha+5*mu^6*nu*alpha^4+74*mu*lambda*nu^4*alpha^6-81*mu^3*nu^3*alpha^4-253*lambda^2*mu^3*alpha^4-26*mu^4*lambda*alpha^2+97*nu^4*mu*lambda^2*alpha^3-27*nu^2*alpha^4*lambda^3*mu^2+89*lambda^2*alpha^6*nu^3*mu-21*lambda^2*nu*alpha*mu-20*mu^3*nu^4*alpha^4-81*mu^3*nu^3*alpha^3+40*mu^5*lambda^2*alpha^3+4*nu^4*alpha^2*mu^3+20*mu^4*lambda^3*alpha^3+5*lambda^2*alpha-84*mu^3*nu^3*alpha^5+3*lambda^2*alpha^4*mu^2*nu+57*alpha^5*lambda^2*mu*nu+10*lambda^2*alpha^4-123*lambda^3*alpha^4*mu^2+39*nu*alpha^2*lambda^3-110*lambda^2*mu^4*alpha^2+mu^3*alpha^6*nu+4*mu^3*nu^4*alpha^6+mu^3*nu^4*alpha^7+2*lambda*alpha*nu+11*mu^3*nu^3*alpha^6+4*mu^3*nu^3*alpha^7-28*mu^5*nu*alpha^5+10*mu^5*nu^2*alpha^5-10*mu^5*nu^2*alpha^4+40*mu^5*nu*alpha^4-5*mu^5*nu^2*alpha^3-121*mu^5*alpha^3*nu-56*mu^5*lambda*alpha^4+65*mu^5*lambda*alpha^3+112*nu^3*mu^3*alpha^2*lambda+51*lambda^2*alpha^6*nu^2*mu-12*alpha^6*nu*lambda^2*mu^2+2*mu*lambda*alpha^6-122*mu^2*nu^4*alpha^4-15*mu^2*lambda*alpha^6+50*mu^2*alpha^6*nu^2-24*lambda^3*mu*alpha^3*nu-5*mu^6*alpha^4+116*lambda*nu^3*alpha^6*mu+4*lambda*mu*nu^2+19*mu*nu^5*alpha^5+5*mu^2*nu^5*alpha^6-65*mu^2*nu^4*alpha^5-125*mu*alpha^2*nu^2+40*lambda^2*alpha^4*nu^5-68*nu^4*mu*alpha^2+38*alpha^5*lambda^2*mu+65*nu^5*alpha^4*lambda+12*lambda^2*alpha^3*mu^2*nu^2-214*lambda^2*mu^3*alpha^3*nu^2+170*nu^3*alpha^3*lambda^2*mu-35*mu^5*lambda^2*alpha^2+5*nu^6*alpha^5*mu-57*alpha^5*lambda^2*mu*nu^2+31*nu^5*alpha^4*lambda*mu-92*nu^4*mu*alpha^2*lambda+61*nu^2*mu^4*lambda*alpha^2+90*nu^2*mu*lambda^3*alpha^3+3*lambda^2*mu*alpha^3*nu^2+127*lambda^2*alpha^3*mu^2-19*lambda^2*alpha^6*mu+mu^2*lambda*alpha^7-65*nu^2*mu^4*alpha^2+10*mu^4*nu^3*alpha^2-5*nu^5*alpha^4*mu^2-95*lambda^2*mu^2*alpha^2+9*nu^3*mu^2*alpha-87*lambda^3*alpha^5*nu^2-19*nu^5*alpha^5*lambda+25*lambda^2*mu^4*alpha-15*lambda*alpha*nu^3*mu-168*nu^2*mu^2*lambda*alpha^2+30*lambda^2*alpha^4*mu*nu^2+46*lambda^3*nu^3*mu*alpha^3-66*lambda^3*nu^3*alpha^4*mu+170*lambda^2*nu*mu^3*alpha^4+22*lambda^2*nu*mu^3*alpha^3+90*lambda^3*nu*alpha^4*mu^2+25*mu^2*alpha^6*nu+25*mu^2*nu^4*alpha^6+50*mu^2*nu^3*alpha^6+5*mu^2*alpha^6+22*lambda^2*mu*alpha^3-12*nu^2*lambda^2*alpha+nu^3*alpha*mu-121*nu^5*alpha^4*mu+9*nu*alpha^2*lambda^3*mu^2+25*nu^2*alpha*mu+12*lambda^3*alpha^6*nu^4-228*nu^3*alpha^2*mu^2+12*mu^4*lambda^3*alpha-5*nu^6*lambda*alpha^5-5*mu^6*lambda*alpha^2+5*mu^5*lambda^2*alpha+30*lambda^3*alpha^5*nu^2*mu^2-15*nu^5*alpha^5*lambda*mu+9*lambda^3*alpha^5*nu^2*mu-15*nu*mu^5*lambda*alpha^2-56*nu^5*alpha^3*lambda+21*lambda^3*alpha^5*nu^3*mu+129*alpha^5*lambda^2*nu^3*mu^2-3*lambda^3*nu*alpha*mu-174*lambda*mu^2*alpha^2*nu+50*lambda^2*alpha*mu^2+50*lambda^2*alpha*mu^3+6*nu^3*mu^2-5*lambda^3*alpha-99*lambda^3*alpha^2*mu^3-63*nu^3*alpha^3*lambda-110*alpha^5*lambda^2*nu^4+70*lambda^2*mu^3*alpha^5-97*lambda^2*mu^4*alpha^4-lambda^2*nu*mu^4+52*lambda^3*mu*alpha^3-214*lambda^2*mu^2*nu^3*alpha^4+mu^2*nu*alpha^2+10*nu^5*alpha^3-3*lambda^3*alpha*mu-27*nu^2*alpha^3*lambda^3*mu^2+50*mu^2*nu^4*alpha^2*lambda+50*mu^3*nu^2*alpha-30*nu^3*alpha^2+30*alpha^2*nu^2*lambda^3*mu^2+9*mu^2*alpha^2*nu^2*lambda^2-36*alpha^2*nu^2*lambda^3*mu+129*mu^3*nu^2*alpha^2*lambda^2-64*nu^3*alpha^2*mu^2*lambda+mu^2*lambda*nu^4*alpha^7+28*mu^2*lambda*nu^4*alpha^6-17*mu^2*lambda*alpha^6*nu+39*mu^2*lambda*alpha^6*nu^2+6*mu^2*lambda*alpha^7*nu^2+4*mu^2*lambda*alpha^7*nu+4*mu^2*lambda*nu^3*alpha^7+61*mu^2*nu^4*alpha^5*lambda-243*mu^2*lambda*alpha^4*nu^3+5*lambda^2*alpha^6-91*mu*nu^4*alpha^5*lambda+112*mu^3*nu^3*alpha^5*lambda+119*mu^3*lambda*alpha^4*nu^2+23*mu^3*lambda*alpha^4*nu^3-243*mu^3*lambda*alpha^3*nu^2-15*mu^3*lambda*alpha^6*nu+15*mu^3*lambda*alpha^6*nu^2+15*mu^3*lambda*nu^3*alpha^6+56*mu^5*lambda*alpha^4*nu+31*mu^5*lambda*alpha^3*nu+30*lambda^3*alpha^5*mu^2-255*mu^2*alpha^2*nu^2+26*lambda*alpha*mu*nu+116*mu^3*alpha*lambda*nu+84*nu*alpha*lambda*mu^2+187*mu^2*nu^2*alpha^4+250*nu^4*alpha^3*mu-3*lambda^3*nu*alpha-lambda*mu^2*alpha^2+21*lambda^3*alpha*mu^2+3*lambda^3*alpha^6*nu^2*mu-92*nu^2*lambda*alpha^2*mu-87*lambda^3*alpha^2*mu^2-84*lambda^3*alpha^4*mu-135*alpha^2*lambda^2*mu^3-40*nu^5*alpha^4+40*nu^5*mu*alpha^3-28*nu^5*alpha^2*mu+70*lambda^2*nu^3*alpha^2-50*alpha^5*lambda^2*nu-97*nu^4*alpha^3*lambda^2-5*nu^6*alpha^3-15*lambda^2*alpha^4*mu-181*lambda^2*alpha^4*mu^2-120*nu^4*alpha^3*lambda+nu^2*mu^4*lambda+10*nu^5*alpha^2*mu^2+21*lambda^3*alpha^2*mu^3*nu-lambda^2*alpha^7*nu^4*mu-57*alpha^5*lambda^2*nu^4*mu+46*lambda^3*alpha^4*mu^3*nu-57*lambda^2*nu*mu^4*alpha^2-12*nu^2*lambda^2*alpha*mu+120*nu^4*alpha^3*lambda*mu^2+36*lambda^2*alpha^6*nu^4*mu+50*nu^4*lambda*alpha^2-15*nu^2*lambda*alpha+31*lambda^3*alpha^6*nu^3+26*mu^4*nu*alpha^2+25*nu^2*mu^4*alpha-4*lambda^3*mu+69*mu^3*lambda*alpha*nu^2-57*lambda^2*mu^2*alpha^2*nu-15*alpha^2*lambda^2+31*lambda^3*alpha*mu^3+25*lambda^2*mu*alpha+9*alpha^5*lambda^2*mu^2*nu^2+25*alpha^6*nu*lambda^2+21*lambda^3*alpha^6*nu^2+50*mu^2*nu^2*alpha+5*mu^6*nu*alpha^2+5*mu^5*nu^2*alpha+4*mu^3*nu^2*lambda-6*lambda^2*nu*mu^2-alpha^7*lambda^3*nu^4-mu*alpha^7*lambda^2-12*mu^2*alpha^6*lambda^2+30*lambda^2*alpha^3*mu^2*nu-32*lambda^2*alpha^4*mu*nu-17*nu^2*lambda*alpha*mu-25*nu^4*alpha^4*lambda^2*mu+26*mu*lambda*alpha^6*nu+18*mu*lambda*nu^5*alpha^6-100*mu^3*alpha^5*nu*lambda^2+4*mu^4*nu^3*alpha+60*mu^4*alpha^4+14*mu^3*nu*alpha^2-21*alpha^6*nu*lambda^2*mu-4*mu*alpha^7*lambda^2*nu-24*lambda^3*alpha^4*mu*nu+36*mu^4*nu*alpha*lambda^2+3*mu^3*nu*alpha*lambda^3-30*mu^4*lambda^3*alpha^2+22*nu^3*alpha^4*lambda^2*mu+12*lambda^2*alpha^4*mu^2*nu^2-4*lambda^2*mu*nu+18*mu^5*lambda*alpha*nu+74*mu^4*lambda*alpha*nu+11*nu^3*alpha*mu^3+20*nu^6*alpha^4*lambda+25*lambda^2*alpha^6*nu^4-64*mu^2*nu^4*alpha^2-92*mu^4*nu*alpha^5*lambda+50*mu^4*nu^2*alpha^5*lambda+120*mu^4*lambda*alpha^4*nu+120*mu^4*lambda*alpha^4*nu^2-35*mu^4*lambda*alpha^3*nu^2-61*mu^4*lambda*alpha^3*nu);
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f3:= -4*(1+mu+nu+lambda)*alpha*(-15*mu^4*alpha^3+lambda^4+18*alpha^2*lambda*mu^3+33*lambda^3*mu^2*alpha^3+85*nu^2*alpha^4*lambda^2*mu^3-alpha^5*lambda^4-24*lambda*alpha*nu^3*mu^2+10*lambda^4*alpha^3-2*lambda^2*nu*alpha+13*lambda^3*alpha^2*mu+5*lambda^3*alpha^2-8*nu^5*alpha*mu-3*nu^2*mu^2*lambda^2-6*lambda^4*alpha^4*mu^2-nu^3*mu^2*lambda-5*mu^6*alpha^3-5*nu^3*alpha^3-lambda^3-lambda^3*mu^3-5*mu^3*alpha^3-6*mu^3*alpha^5-3*lambda^3*mu^2+nu^3-38*lambda*alpha^4*mu*nu^4-nu^3*lambda*mu^3+2*lambda^3*alpha^5*mu-15*mu^5*alpha^3+6*lambda^4*alpha^4*nu*mu^2+48*lambda^3*alpha^3*mu^3+lambda^3*alpha^5+lambda^4*mu+10*mu^3*alpha^4+lambda^4*alpha^6+14*mu^3*lambda*alpha*nu^3+4*lambda^3*nu*mu^3*alpha^3+12*nu*alpha^2*mu*lambda^4-4*nu*alpha*mu*lambda^4-10*nu^3*alpha^4*lambda^4+5*lambda^3*alpha^4+10*mu^5*alpha^4+nu^3*mu^3+3*mu*alpha^6*nu*lambda^3-44*nu^3*lambda*mu*alpha^3+26*nu^5*lambda*mu*alpha^3+58*nu^3*alpha^2*mu*lambda^2-lambda^2*nu-18*lambda^3*alpha^4*mu^3+12*lambda^2*nu*alpha^2-10*lambda^3*alpha^3+9*lambda^2*alpha*mu^2*nu^2+34*lambda^2*alpha*mu^3*nu^2-36*lambda^2*nu^3*alpha*mu+14*lambda^4*nu*alpha^3+3*lambda^3*alpha^6*mu-9*nu^2*alpha^4*lambda^3+5*nu*alpha^4*lambda^2+20*nu^2*alpha^4*lambda^2-14*alpha^3*nu*lambda^2-22*nu^4*alpha*mu+2*lambda^3*mu^2*alpha^3*nu-6*nu*mu^5*alpha^2-lambda^2*nu*mu^3+13*lambda^3*nu*alpha^4-37*lambda^3*nu^3*alpha^4+5*nu^6*alpha^3*lambda+15*nu^5*alpha^3*lambda^2-18*nu^4*alpha^2*lambda^2+48*nu^3*alpha^3*lambda^3-6*nu^5*alpha^2*lambda-2*lambda^3*alpha^5*nu+3*nu^2*lambda^2-26*mu^2*alpha^5*lambda*nu-16*nu^4*alpha*mu^2+41*nu^3*alpha^2*mu-3*lambda^2*alpha^6*nu^3*mu^2-87*mu^3*nu*alpha^2*lambda^2+34*lambda^2*mu^4*alpha^3+2*lambda^3*alpha^5*nu*mu+18*lambda^2*nu*mu^4*alpha^4+3*nu^3*mu-20*lambda^3*alpha^5*nu*mu^2-5*lambda^4*alpha^2-28*lambda^2*mu*alpha^3*nu+19*alpha^2*lambda^2*mu*nu+26*lambda^3*nu*alpha*mu^2-3*lambda^2*alpha^6*nu^2*mu^2-lambda^3*alpha^6-11*lambda^4*nu*alpha^3*mu^2-3*lambda^3*alpha^6*nu^3*mu-47*nu^2*alpha^4*lambda^3*mu-46*mu^3*alpha^5*nu*lambda-15*nu^4*alpha^3+46*mu^3*nu*alpha*lambda^2-38*lambda*nu*mu^4*alpha^2-lambda^4*mu^2-2*lambda*alpha^3*nu^2*mu-2*lambda*alpha^3*mu^2*nu-42*lambda*alpha^4*mu*nu^2-12*lambda*alpha^4*mu*nu-58*nu^3*alpha^4*lambda*mu-19*lambda*alpha^3*mu^2+21*mu^2*alpha^4*lambda+37*mu^3*alpha^4*lambda-48*mu^3*alpha^3*lambda+nu^2*lambda+16*lambda*alpha^3*mu*nu-lambda^4*alpha+36*nu^3*alpha^5*lambda*mu+20*nu^2*alpha^5*lambda*mu+87*mu^3*alpha^4*lambda*nu+6*lambda*alpha^4*nu^2+18*lambda*alpha^4*nu^3-9*mu^2*alpha^5*lambda-34*mu^4*alpha^3*lambda-19*lambda*alpha^3*nu^2+4*nu*alpha^5*lambda*mu-21*nu^2*alpha^4*lambda*mu^2+47*nu*alpha^4*lambda*mu^2-44*nu*alpha^3*lambda*mu^3+18*nu^2*alpha^3*lambda*mu^2-9*mu^2*alpha^5*lambda*nu^2+8*mu^2*nu^4*lambda*alpha^4+72*nu^2*alpha^3*mu^3-4*nu^3*alpha^3*mu-6*mu*alpha^4*nu^2+11*mu^2*alpha^3*nu+94*mu^2*alpha^3*nu^2-18*mu*alpha^4*nu^3-18*nu^4*alpha^4*mu-5*mu^2*alpha^4*nu+41*nu*alpha^4*mu^3+72*nu^3*alpha^3*mu^2-4*mu^3*alpha^3*nu+11*mu*alpha^3*nu^2+56*mu^4*alpha^4*nu-34*mu^3*alpha^5*nu^2-85*nu^3*alpha^4*mu^2-41*nu*alpha^3*mu^4-26*mu^3*alpha^5*nu-6*nu^2*alpha^4*mu^3-85*mu^3*nu^2*alpha^2-37*nu^3*mu^3*alpha^2-10*lambda^4*mu^3*alpha^2+21*nu^2*lambda*alpha^2-20*nu^2*alpha*lambda^3*mu+5*alpha^2*lambda^2*mu+10*nu^5*alpha^2-24*nu^2*alpha^5*mu^3*lambda+3*nu^2*mu^2*lambda-20*nu^4*alpha^4*lambda^3-11*mu^2*nu^4*alpha^3-4*alpha^5*lambda^4*mu*nu+6*nu^5*alpha^2*lambda*mu-12*alpha^2*lambda*mu*nu+24*alpha^2*nu^2*lambda^2*mu-6*nu^4*alpha-3*mu^3*nu^2*lambda^2+alpha^5*lambda^2*mu^2-10*nu^4*alpha^4*lambda^2+41*lambda^2*nu*mu^4*alpha^3-72*lambda^2*mu^2*nu^3*alpha^3-19*lambda^3*alpha^2*mu*nu-3*nu*mu^2*lambda^3+18*nu^4*alpha^4*lambda-3*lambda^3*alpha^6*nu-11*lambda^4*mu*alpha^3*nu^2-16*lambda^4*mu*alpha^3*nu-28*nu^4*alpha*mu*lambda+18*lambda^3*nu^3*mu*alpha^2+nu^3*alpha^6*mu^2*lambda+20*nu^4*alpha^2-24*alpha^5*lambda^2*nu*mu^2+6*nu^4*alpha^5*lambda^3-5*lambda^4*alpha^4+85*nu^3*alpha^2*mu^2*lambda^2+mu^3*lambda*alpha^6+3*mu^3*alpha^6*nu^2+mu^3*alpha^6-6*mu^4*alpha^5+14*lambda^4*mu*alpha^3+37*nu^3*alpha^2*lambda+9*alpha^2*nu^2*lambda^2+33*nu^2*alpha^3*lambda^3+15*nu^3*alpha^4*lambda^2+8*lambda^3*alpha^5*nu^3-33*nu^2*alpha^3*lambda^2+16*mu^4*lambda*alpha*nu^2+5*mu^6*lambda*alpha^3+46*alpha^5*lambda^2*nu^3*mu+3*nu^2*mu*lambda^2-8*mu^3*alpha^5*lambda+6*lambda*mu^5*alpha^2+87*nu^3*alpha^2*lambda*mu+24*lambda^2*nu*alpha*mu^2-58*alpha^2*lambda*mu^3*nu-9*nu^2*lambda*alpha*mu^2-20*alpha^2*nu^2*lambda^3-22*mu^4*nu*alpha^5-16*mu^4*nu^2*alpha^5-8*mu^4*nu^2*alpha^4-8*lambda*alpha*nu^3-11*mu^4*nu^2*alpha^3+10*mu^4*lambda*alpha^4-6*nu^3*alpha-37*mu^3*nu^3*alpha^4-15*lambda^2*mu^3*alpha^4+18*mu^4*lambda*alpha^2+41*nu^4*mu*lambda^2*alpha^3+18*nu^4*mu*lambda^2*alpha^2+50*nu^2*alpha^4*lambda^3*mu^2-lambda^2*alpha^6*nu^3*mu-2*lambda^2*nu*alpha*mu-12*lambda^4*alpha^2*mu+15*mu^5*lambda^2*alpha^3+15*mu^4*lambda^3*alpha^3-14*mu^3*nu^3*alpha^5+24*lambda^2*alpha^4*mu^2*nu-2*alpha^5*lambda^2*mu*nu+6*alpha^5*lambda^4*nu^3-20*lambda^3*alpha^4*mu^2-13*nu*alpha^2*lambda^3-5*lambda^4*alpha^4*mu-10*lambda^2*mu^4*alpha^2-alpha^6*nu^2*lambda^4+3*mu^3*alpha^6*nu+mu^3*nu^3*alpha^6-8*mu^5*nu*alpha^5+10*mu^5*nu*alpha^4-26*mu^5*alpha^3*nu-6*mu^5*lambda*alpha^4-39*mu^3*nu^2*alpha^2*lambda+37*nu^3*mu^3*alpha^2*lambda-3*lambda^2*alpha^6*nu^2*mu+3*alpha^6*nu*lambda^2*mu^2-40*mu^2*nu^4*alpha^4+mu^2*lambda*alpha^6+28*lambda^3*mu*alpha^3*nu+3*lambda*mu*nu^2-5*mu*alpha^2*nu^2-10*lambda^2*alpha^4*nu^5+56*nu^4*mu*alpha^2-2*alpha^5*lambda^2*mu+6*nu^5*alpha^4*lambda-18*lambda^2*alpha^3*mu^2*nu^2-72*lambda^2*mu^3*alpha^3*nu^2+44*nu^3*alpha^3*lambda^2*mu-10*mu^5*lambda^2*alpha^2+24*alpha^5*lambda^2*mu*nu^2-10*nu^5*alpha^4*lambda*mu+38*nu^4*mu*alpha^2*lambda+8*nu^2*mu^4*lambda*alpha^2+2*nu^2*mu*lambda^3*alpha^3-33*lambda^2*alpha^3*mu^2-lambda^2*alpha^6*mu-40*nu^2*mu^4*alpha^2+20*lambda^2*mu^2*alpha^2-34*nu^3*mu^2*alpha-lambda^3*alpha^5*nu^2-46*lambda*alpha*nu^3*mu-21*nu^2*mu^2*lambda*alpha^2-24*lambda^2*alpha^4*mu*nu^2+4*lambda^3*nu^3*mu*alpha^3-41*lambda^3*nu^3*alpha^4*mu+5*mu^2*nu*alpha^2*lambda^4+58*lambda^2*nu*mu^3*alpha^4+44*lambda^2*nu*mu^3*alpha^3+42*lambda^3*nu*alpha^4*mu^2-14*lambda^2*mu*alpha^3+nu^2*lambda^2*alpha-26*nu^3*alpha*mu-6*nu^5*alpha^4*mu-47*nu*alpha^2*lambda^3*mu^2-6*nu^3*alpha^2*mu^2-6*alpha^2*nu^2*lambda^4-21*lambda^4*alpha^4*nu^2+2*alpha^5*lambda^4*nu+6*mu^4*lambda^3*alpha+8*nu^5*alpha^5*lambda*mu+26*lambda^3*alpha^5*nu^2*mu+15*nu^4*alpha^3*lambda^3-10*nu*mu^5*lambda*alpha^2+3*mu*nu*lambda^3+26*lambda^3*alpha^5*nu^3*mu+34*alpha^5*lambda^2*nu^3*mu^2+2*lambda^3*nu*alpha*mu-42*lambda*mu^2*alpha^2*nu+nu^3*lambda+6*lambda^4*alpha*mu^3+3*nu^3*mu^2+lambda^3*alpha+nu^3*lambda*mu-37*lambda^3*alpha^2*mu^3-48*nu^3*alpha^3*lambda-18*lambda^2*mu^4*alpha^4+lambda^4*alpha^6*nu+6*lambda^2*mu^2*nu^3*alpha^4-6*mu^2*nu*alpha^2-15*nu^5*alpha^3-2*lambda^3*alpha*mu-94*nu^2*alpha^3*lambda^3*mu^2+40*mu^2*nu^4*alpha^2*lambda+5*lambda^4*alpha^4*mu*nu^2+10*nu^3*alpha^2+50*alpha^2*nu^2*lambda^3*mu^2+21*mu^2*alpha^2*nu^2*lambda^2+6*alpha^2*nu^2*lambda^4*mu+42*alpha^2*nu^2*lambda^3*mu+6*mu^3*nu^2*alpha^2*lambda^2+39*nu^3*alpha^2*mu^2*lambda+3*mu^2*lambda*alpha^6*nu+3*mu^2*lambda*alpha^6*nu^2+24*mu^2*nu^3*alpha^5*lambda+16*mu^2*nu^4*alpha^5*lambda-39*mu^2*lambda*alpha^4*nu^3+28*mu*nu^4*alpha^5*lambda+14*mu^3*nu^3*alpha^5*lambda+39*mu^3*lambda*alpha^4*nu^2+37*mu^3*lambda*alpha^4*nu^3+mu^3*lambda*alpha^6*nu-mu^3*lambda*alpha^6*nu^2-mu^3*lambda*nu^3*alpha^6+6*mu^5*lambda*alpha^4*nu+26*mu^5*lambda*alpha^3*nu-50*mu^2*alpha^2*nu^2+4*lambda*alpha*mu*nu+36*mu^3*alpha*lambda*nu+20*nu*alpha*lambda*mu^2-50*mu^2*nu^2*alpha^4-41*nu^4*alpha^3*mu+2*lambda^3*nu*alpha+6*lambda*mu^2*alpha^2-lambda^3*alpha*mu^2-21*lambda^4*mu^2*alpha^2-3*lambda^3*alpha^6*nu^2*mu+47*nu^2*lambda*alpha^2*mu+2*lambda^4*alpha*mu-9*lambda^3*alpha^2*mu^2-13*lambda^3*alpha^4*mu+15*alpha^2*lambda^2*mu^3-26*nu^5*mu*alpha^3-5*nu*alpha^2*lambda^4+10*nu^5*alpha^2*mu-15*lambda^2*nu^3*alpha^2+5*lambda^4*mu^3*alpha^3+34*nu^4*alpha^3*lambda^2-5*nu^6*alpha^3+12*lambda^2*alpha^4*mu+9*lambda^2*alpha^4*mu^2-34*nu^4*alpha^3*lambda+9*nu^2*alpha^5*lambda^4-41*lambda^3*alpha^2*mu^3*nu+22*alpha^5*lambda^2*nu^4*mu+18*lambda^3*alpha^4*mu^3*nu-56*lambda^2*nu*mu^4*alpha^2-24*nu^2*lambda^2*alpha*mu+11*nu^4*alpha^3*lambda*mu^2+10*nu^4*lambda*alpha^2-9*nu^2*lambda*alpha-nu^3*alpha^6*lambda^4+5*nu^3*alpha^3*lambda^4-18*nu^3*alpha^2*lambda^3-3*lambda^3*nu*mu^3-lambda^3*alpha^6*nu^3-18*mu^4*nu*alpha^2-3*lambda^3*mu+24*mu^3*lambda*alpha*nu^2-24*lambda^2*mu^2*alpha^2*nu+8*lambda^3*alpha*mu^3+9*lambda^4*alpha*mu^2-lambda^4*mu^3+9*alpha^5*lambda^2*mu^2*nu^2-3*lambda^3*alpha^6*nu^2+3*lambda^3*nu+mu^3*nu^2*lambda-3*lambda^2*nu*mu^2+3*mu^2*alpha^6*lambda^2+19*lambda^2*alpha^4*mu*nu-26*nu^2*lambda*alpha*mu-12*lambda^4*alpha^4*nu+19*nu^2*alpha^3*lambda^4-56*nu^4*alpha^4*lambda^2*mu-36*mu^3*alpha^5*nu*lambda^2+20*mu^4*alpha^4-18*mu^3*nu*alpha^2+12*lambda^4*alpha^4*nu*mu-3*alpha^6*nu*lambda^2*mu-19*lambda^3*alpha^4*mu*nu+22*mu^4*nu*alpha*lambda^2+26*mu^3*nu*alpha*lambda^3-20*mu^4*lambda^3*alpha^2-87*nu^3*alpha^4*lambda^2*mu+21*lambda^2*alpha^4*mu^2*nu^2-3*lambda^2*mu*nu+8*mu^5*lambda*alpha*nu+28*mu^4*lambda*alpha*nu-14*nu^3*alpha*mu^3-8*mu^2*nu^4*alpha^2+19*lambda^4*alpha^3*mu^2-28*mu^4*nu*alpha^5*lambda+38*mu^4*lambda*alpha^4*nu+40*mu^4*lambda*alpha^4*nu^2+11*mu^4*lambda*alpha^3*nu^2);
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f4:=-(1+mu+nu+lambda)*(-lambda^4-10*nu^6*mu*alpha^3-181*lambda^3*mu^2*alpha^3-92*nu^2*alpha^4*lambda^2*mu^3+21*alpha^5*lambda^4+69*lambda*alpha*nu^3*mu^2-15*lambda^4*alpha^3+39*lambda^3*alpha^2*mu-5*nu^5*alpha^3*mu^2+4*nu^4*alpha*mu^3+18*nu^5*alpha*mu+5*nu^5*alpha*mu^2+50*nu^2*alpha*lambda^3+50*nu^2*alpha*lambda^3*mu^2+6*nu^2*mu^2*lambda^2-60*lambda^3*alpha^4*mu^4-10*lambda^4*alpha^4*mu^2+4*nu^3*mu^2*lambda-nu^4+120*lambda*alpha^4*mu*nu^4-15*lambda^5*alpha^5+4*nu^3*lambda*mu^3+5*nu^6*alpha^4*mu+3*lambda^3*alpha^5*mu-215*mu^3*nu^2*lambda^2*alpha^5-88*lambda^4*alpha^4*nu*mu^2-63*lambda^3*alpha^3*mu^3-lambda^4*mu-5*lambda^4*alpha^6+11*mu^3*lambda*alpha*nu^3+401*lambda^3*nu*mu^3*alpha^3-67*nu*alpha^2*mu*lambda^4+26*nu*alpha*mu*lambda^4+5*alpha^6*lambda^5+70*nu^3*alpha^4*lambda^4-lambda^5*alpha^5*mu*nu+40*mu^5*alpha^4+5*lambda^5*alpha-21*mu*alpha^6*nu*lambda^3+14*lambda^3*alpha^5*nu*mu^3-81*mu^3*nu^3*alpha^3*lambda+22*nu^3*lambda*mu*alpha^3-121*nu^5*lambda*mu*alpha^3-61*nu^4*lambda*mu*alpha^3-5*lambda^5*alpha^4*mu-190*nu^3*alpha^2*mu*lambda^2-14*lambda^3*alpha^5*mu^3+20*lambda^3*alpha^4*mu^3+50*lambda^2*nu^3*alpha*mu^2+39*lambda^2*alpha*mu^2*nu^2+9*lambda^2*alpha*mu^3*nu^2+116*lambda^2*nu^3*alpha*mu+mu^3*nu^4+22*lambda^4*nu*alpha^3+50*mu^3*alpha^6*lambda^2-3*lambda^3*alpha^6*mu-181*nu^2*alpha^4*lambda^3-123*nu^2*alpha^4*lambda^2+52*alpha^3*nu*lambda^3+30*nu^2*alpha^5*lambda^2+36*nu^4*alpha*mu+263*lambda^3*mu^2*alpha^3*nu-4*alpha^7*lambda^3*mu*nu-84*lambda^3*nu*alpha^4-63*lambda^3*nu^3*alpha^4-6*mu^2*alpha^7*lambda^2-50*alpha^5*lambda^4*mu-10*nu^6*alpha^3*lambda-40*nu^5*alpha^3*lambda^2-26*nu^4*alpha^2*lambda^2+20*nu^3*alpha^3*lambda^3-19*nu^5*alpha^2*lambda+39*lambda^3*alpha^5*nu-6*nu^2*lambda^2+9*mu^2*alpha^5*lambda*nu+28*nu^4*alpha*mu^2+2*alpha^6*lambda^5*nu+5*alpha^6*lambda^5*nu^2-20*lambda^5*alpha^5*nu^2-4*alpha^7*lambda^3*mu+50*lambda^3*alpha^6*mu^2+5*nu^5*alpha+5*nu^6*alpha^2*mu+4*nu^3*alpha^6*mu^4+21*nu^3*alpha^2*mu+9*lambda^2*alpha^6*nu^3*mu^2-104*mu^3*nu*alpha^2*lambda^2-120*lambda^2*mu^4*alpha^3+57*lambda^3*alpha^5*nu*mu-302*lambda^2*nu*mu^4*alpha^4-5*nu^6*alpha^2-174*lambda^3*alpha^5*nu*mu^2+21*lambda^4*alpha^2-24*lambda^2*mu*alpha^3*nu+27*alpha^2*lambda^2*mu*nu-17*lambda^3*nu*alpha*mu^2+25*nu^4*alpha*mu^2*lambda+84*lambda^3*alpha^6*nu*mu^2+39*lambda^2*alpha^6*nu^2*mu^2+187*lambda^4*nu*alpha^3*mu^2+lambda^5*mu*alpha^3*nu+lambda^3*alpha^6*nu^3*mu+263*nu^2*alpha^4*lambda^3*mu-133*mu^3*alpha^5*nu*lambda+25*nu^4*lambda*alpha+25*lambda^4*nu*alpha+20*nu^4*alpha^3-15*mu^3*nu*alpha*lambda^2-92*lambda*nu*mu^4*alpha^2+lambda^4*mu^2-66*lambda*alpha^3*nu^2*mu+90*lambda*alpha^3*mu^2*nu+90*lambda*alpha^4*mu*nu^2+170*nu^3*alpha^4*lambda*mu+118*mu^3*alpha^4*lambda-46*mu^3*alpha^3*lambda-5*lambda^4*alpha-100*nu^3*alpha^5*lambda*mu-36*nu^2*alpha^5*lambda*mu+22*mu^3*alpha^4*lambda*nu-46*lambda*alpha^4*nu^3-97*mu^4*alpha^3*lambda+12*nu^2*alpha^4*lambda*mu^2-66*nu*alpha^4*lambda*mu^2+170*nu*alpha^3*lambda*mu^3+12*nu^2*alpha^3*lambda*mu^2+9*mu^2*alpha^5*lambda*nu^2-5*mu^2*nu^4*lambda*alpha^4+103*nu^2*alpha^3*mu^3-66*nu^3*alpha^3*mu-27*mu^2*alpha^3*nu^2+46*mu*alpha^4*nu^3+97*nu^4*alpha^4*mu-66*nu*alpha^4*mu^3-214*nu^3*alpha^3*mu^2+30*nu^2*alpha^5*mu^2+46*mu^3*alpha^3*nu-25*mu^4*alpha^4*nu+129*mu^3*alpha^5*nu^2+103*nu^3*alpha^4*mu^2+97*nu*alpha^3*mu^4+21*mu^3*alpha^5*nu-214*nu^2*alpha^4*mu^3+70*nu^3*alpha^5*mu^2-20*mu^3*nu^4*alpha^3+70*mu^3*nu^2*alpha^2+112*nu^3*mu^3*alpha^2-30*lambda^4*mu^3*alpha^2-253*lambda^2*mu^3*alpha^3+10*nu^2*mu^5*alpha^2+84*nu^2*alpha*lambda^3*mu-35*nu^5*alpha^2-alpha^5*lambda^4*mu^2-40*lambda^4*alpha^4*mu^3+4*nu^4*alpha^5*mu^3+60*nu^4*alpha^4*lambda^3-35*mu^2*nu^4*alpha^3+6*mu^2*alpha^7*lambda^2*nu^3-67*alpha^5*lambda^4*mu*nu-125*alpha^5*lambda^4*mu*nu^2+19*nu^5*alpha^2*lambda*mu-57*alpha^2*nu^2*lambda^2*mu-243*nu^3*mu^2*lambda*alpha^3+12*nu^4*alpha+6*mu^3*nu^2*lambda^2+25*nu*alpha*mu^2*lambda^4-87*alpha^5*lambda^2*mu^2+10*nu^5*alpha^5*lambda^2-120*nu^4*alpha^4*lambda^2+lambda^5*alpha^5*mu+250*lambda^2*nu*mu^4*alpha^3-92*lambda^2*mu^2*nu^3*alpha^3+57*lambda^3*alpha^2*mu*nu+4*nu*mu^2*lambda^3-97*nu^4*alpha^4*lambda-3*lambda^3*alpha^6*nu-88*lambda^4*mu*alpha^3*nu^2+41*lambda^4*mu*alpha^3*nu+74*nu^4*alpha*mu*lambda+14*lambda^3*nu^3*mu*alpha^2+15*nu^3*alpha^6*mu^2*lambda-30*nu^4*alpha^2-57*alpha^5*lambda^2*nu*mu^2-15*lambda^4*alpha^4-215*nu^3*alpha^2*mu^2*lambda^2+25*lambda^5*mu^2*alpha^3+31*mu^3*lambda*alpha^6+12*mu^3*alpha^6*nu^2+5*mu^5*alpha^6-35*mu^5*alpha^5-mu^4*alpha^7+12*mu^4*alpha^6-30*mu^4*alpha^5-5*mu^6*alpha^5-15*lambda^4*mu*alpha^3-99*nu^3*alpha^2*lambda+268*nu^3*alpha^3*lambda^2-87*alpha^2*nu^2*lambda^2+127*nu^2*alpha^3*lambda^3-253*nu^3*alpha^4*lambda^2+72*lambda^3*alpha^5*nu^3+9*lambda^5*mu*alpha^3+165*nu^2*alpha^3*lambda^2-26*alpha^5*lambda^2*mu^4+70*alpha^5*lambda^2*nu^3+10*lambda^5*alpha^4+6*mu^4*lambda*alpha*nu^2+5*mu^6*alpha^3*nu-10*mu^6*lambda*alpha^4-5*mu^6*lambda*alpha^3-lambda^5*nu*alpha^2*mu-104*alpha^5*lambda^2*nu^3*mu-6*nu^2*mu*lambda^2-99*mu^3*alpha^5*lambda+36*mu^4*alpha^6*nu+mu^4*nu^3*alpha^7-133*nu^3*alpha^2*lambda*mu-12*lambda^2*nu*alpha*mu^2-100*alpha^2*lambda*mu^3*nu+12*nu^2*lambda*alpha*mu^2-95*alpha^2*nu^2*lambda^3-57*mu^4*nu*alpha^5+10*mu^4*nu^3*alpha^5+61*mu^4*nu^2*alpha^5-35*mu^4*nu^2*alpha^4-20*mu^4*nu^3*alpha^4-5*mu^4*nu^3*alpha^3+31*lambda*alpha*nu^3+120*mu^4*nu^2*alpha^3+193*mu^4*lambda*alpha^4+25*mu^4*lambda*alpha^6+28*mu^4*alpha^6*nu^2+mu^4*alpha^7*nu^2-mu^4*alpha^7*nu-110*mu^4*alpha^5*lambda+5*mu^6*nu*alpha^5-10*mu^6*nu*alpha^4+23*mu^3*nu^3*alpha^4+268*lambda^2*mu^3*alpha^4+9*lambda^5*alpha^4*nu-302*nu^4*mu*lambda^2*alpha^3+26*nu^4*mu*lambda^2*alpha^2+187*nu^2*alpha^4*lambda^3*mu^2-15*lambda^2*alpha^6*nu^3*mu+alpha^5*lambda^4*nu*mu^2-alpha^7*lambda^4-3*lambda^2*nu*alpha*mu-5*mu^3*nu^4*alpha^4+23*mu^3*nu^3*alpha^3+38*lambda^4*alpha^2*mu+10*mu^5*lambda^2*alpha^3+10*nu^4*alpha^2*mu^3+60*mu^4*lambda^3*alpha^3+112*mu^3*nu^3*alpha^5+30*lambda^2*alpha^4*mu^2*nu+27*alpha^5*lambda^2*mu*nu-30*alpha^5*lambda^4*nu^3+127*lambda^3*alpha^4*mu^2+3*nu*alpha^2*lambda^3+22*lambda^4*alpha^4*mu+50*lambda^2*mu^4*alpha^2-15*alpha^6*nu^2*lambda^4+3*mu^3*alpha^6*nu-10*lambda^5*mu^2*alpha^4+6*mu^3*nu^4*alpha^6+15*mu^3*nu^3*alpha^6-4*mu^3*lambda*alpha^7-15*mu^5*nu*alpha^5-5*mu^5*nu^2*alpha^4+31*mu^5*nu*alpha^4-10*mu^5*nu^2*alpha^3+56*mu^5*alpha^3*nu+65*mu^5*lambda*alpha^4+5*mu^5*alpha^6*nu^2-56*mu^5*lambda*alpha^3-19*mu^5*alpha^5*lambda-64*mu^3*nu^2*alpha^2*lambda-84*nu^3*mu^3*alpha^2*lambda-12*lambda^2*alpha^6*nu^2*mu+51*alpha^6*nu*lambda^2*mu^2+18*mu^5*alpha^6*nu+120*mu^2*nu^4*alpha^4-32*lambda^3*mu*alpha^3*nu+20*mu^6*alpha^4+25*mu*alpha^6*lambda^4*nu^2+50*mu^2*nu^4*alpha^5+10*mu^2*nu^5*alpha^5-5*lambda^5*alpha^3*nu+10*lambda^2*alpha^4*nu^5-57*nu^4*mu*alpha^2-56*nu^5*alpha^4*lambda+45*lambda^2*alpha^3*mu^2*nu^2+270*lambda^2*mu^3*alpha^3*nu^2-192*nu^3*alpha^3*lambda^2*mu+25*mu*alpha^6*lambda^4+alpha^7*lambda^4*nu^3+10*mu^5*lambda^2*alpha^2-40*mu^5*lambda^2*alpha^4-9*alpha^5*lambda^2*mu*nu^2+40*nu^5*alpha^4*lambda*mu-91*nu^4*mu*alpha^2*lambda-64*nu^2*mu^4*lambda*alpha^2-68*nu^2*mu*lambda^3*alpha^3+30*lambda^2*mu*alpha^3*nu^2-123*lambda^2*alpha^3*mu^2+50*nu^2*mu^4*alpha^2+4*mu^4*nu^3*alpha^2-10*nu^5*alpha^4*mu^2+30*lambda^2*mu^2*alpha^2+12*nu^3*mu^2*alpha+111*lambda^3*alpha^5*nu^2+89*lambda*alpha*nu^3*mu+9*nu^2*mu^2*lambda*alpha^2+3*lambda^2*alpha^4*mu*nu^2+116*mu^3*alpha^6*lambda^2*nu-280*lambda^3*nu^3*mu*alpha^3+401*lambda^3*nu^3*alpha^4*mu-125*mu^2*nu*alpha^2*lambda^4-192*lambda^2*nu*mu^3*alpha^4+281*lambda^2*nu*mu^3*alpha^3-68*lambda^3*nu*alpha^4*mu^2+21*nu^2*lambda^2*alpha+3*nu^3*alpha*mu+56*nu^5*alpha^4*mu-92*nu*alpha^2*lambda^3*mu^2-6*lambda^3*alpha^6*nu^4+129*nu^3*alpha^2*mu^2-10*nu^2*alpha^3*lambda^5-alpha^2*nu^2*lambda^4+10*lambda^4*alpha^4*nu^2+38*alpha^5*lambda^4*nu-6*mu^4*lambda^3*alpha-255*lambda^3*alpha^5*nu^2*mu^2-28*nu^5*alpha^5*lambda*mu+50*lambda^3*alpha^6*nu^2*mu^2-92*lambda^3*alpha^5*nu^2*mu+50*mu^3*alpha^6*lambda^2*nu^2-60*nu^4*alpha^3*lambda^3-20*lambda^5*alpha^2*mu^2-28*nu*mu^5*lambda*alpha^2-4*mu*nu*lambda^3+65*nu^5*alpha^3*lambda-164*lambda^3*alpha^5*nu^3*mu+26*alpha^5*lambda^2*mu^4*nu-228*alpha^5*lambda^2*nu^3*mu^2+4*alpha^7*lambda^3*nu^3*mu-21*lambda^3*nu*alpha*mu-36*lambda*mu^2*alpha^2*nu-4*nu^3*lambda-lambda^4*alpha*mu^3+2*lambda^5*alpha*mu+5*lambda^5*alpha*mu^2+10*lambda^5*alpha^3-4*nu^3*lambda*mu+72*lambda^3*alpha^2*mu^3-alpha^7*lambda^4*nu+alpha^7*lambda^4*nu^2+118*nu^3*alpha^3*lambda+50*alpha^5*lambda^2*nu^4-135*lambda^2*mu^3*alpha^5+70*lambda^2*mu^4*alpha^4+26*lambda^4*alpha^6*nu*mu-84*lambda^3*mu*alpha^3-7*lambda^5*mu*alpha^2+25*lambda^5*alpha^4*nu^2-19*lambda^4*alpha^6*nu-7*lambda^5*alpha^5*nu+270*lambda^2*mu^2*nu^3*alpha^4+40*nu^5*alpha^3-3*lambda^3*alpha*mu+187*nu^2*alpha^3*lambda^3*mu^2-6*lambda^2*alpha^7*nu*mu^2-65*mu^2*nu^4*alpha^2*lambda+187*lambda^4*alpha^4*mu*nu^2-255*alpha^2*nu^2*lambda^3*mu^2-168*mu^2*alpha^2*nu^2*lambda^2+alpha^2*nu^2*lambda^4*mu-174*alpha^2*nu^2*lambda^3*mu-228*mu^3*nu^2*alpha^2*lambda^2+6*mu^2*lambda*nu^4*alpha^6+3*mu^2*lambda*alpha^6*nu+12*mu^2*lambda*alpha^6*nu^2-64*mu^2*nu^3*alpha^5*lambda-64*mu^2*nu^4*alpha^5*lambda+119*mu^2*lambda*alpha^4*nu^3-92*mu*nu^4*alpha^5*lambda-84*mu^3*nu^3*alpha^5*lambda-243*mu^3*lambda*alpha^4*nu^2-81*mu^3*lambda*alpha^4*nu^3+119*mu^3*lambda*alpha^3*nu^2+89*mu^3*lambda*alpha^6*nu+69*mu^3*lambda*alpha^6*nu^2+4*mu^3*lambda*alpha^7*nu^2-4*mu^3*lambda*alpha^7*nu+11*mu^3*lambda*nu^3*alpha^6+4*mu^3*lambda*nu^3*alpha^7+19*mu^5*nu*alpha^5*lambda-121*mu^5*lambda*alpha^4*nu+40*mu^5*lambda*alpha^3*nu-95*lambda^3*alpha^5*mu^2+30*mu^2*alpha^2*nu^2-27*mu^2*nu^2*alpha^4-25*nu^4*alpha^3*mu-3*lambda^3*nu*alpha-12*lambda^3*alpha*mu^2+15*lambda^4*mu^2*alpha^2-17*lambda^3*alpha^6*nu^2*mu+9*nu^2*lambda*alpha^2*mu-19*lambda^4*alpha*mu+111*lambda^3*alpha^2*mu^2+52*lambda^3*alpha^4*mu+70*alpha^2*lambda^2*mu^3-nu^4*mu+31*nu^5*mu*alpha^3-50*nu*alpha^2*lambda^4-15*nu^5*alpha^2*mu-135*lambda^2*nu^3*alpha^2+70*lambda^4*mu^3*alpha^3+70*nu^4*alpha^3*lambda^2+20*nu^6*alpha^3+165*lambda^2*alpha^4*mu^2+lambda^5*alpha^4*nu*mu+193*nu^4*alpha^3*lambda+15*nu^2*alpha^5*lambda^4-164*lambda^3*alpha^2*mu^3*nu-68*alpha^5*lambda^2*nu^4*mu-280*lambda^3*alpha^4*mu^3*nu-68*lambda^2*nu*mu^4*alpha^2+51*nu^2*lambda^2*alpha*mu-122*nu^4*alpha^3*lambda*mu^2-6*lambda^2*alpha^6*nu^4*mu-110*nu^4*lambda*alpha^2-nu^3*alpha^6*lambda^4-40*nu^3*alpha^3*lambda^4-14*nu^3*alpha^2*lambda^3+4*lambda^3*nu*mu^3-15*lambda^3*alpha^6*nu^3+15*mu^3*lambda*alpha*nu^2+mu^2*nu^4-9*lambda^2*mu^2*alpha^2*nu-15*lambda^3*alpha*mu^3-15*lambda^4*alpha*mu^2+lambda^4*mu^3-168*alpha^5*lambda^2*mu^2*nu^2-12*lambda^3*alpha^6*nu^2-4*lambda^3*nu+21*mu^2*alpha^6*lambda^2+3*lambda^2*alpha^3*mu^2*nu-24*lambda^2*alpha^4*mu*nu+3*nu^2*lambda*alpha*mu+50*lambda^2*nu^3*alpha-15*lambda^5*alpha^2-15*lambda^4*alpha^4*nu-10*nu^2*alpha^3*lambda^4+250*nu^4*alpha^4*lambda^2*mu-190*mu^3*alpha^5*nu*lambda^2+6*mu^4*nu^3*alpha+20*mu^4*alpha^4+4*alpha^7*lambda^3*nu^2*mu+6*mu^2*alpha^7*lambda^2*nu^2+41*lambda^4*alpha^4*nu*mu-3*alpha^6*nu*lambda^2*mu-32*lambda^3*alpha^4*mu*nu-6*mu^4*nu*alpha*lambda^2+mu^3*nu*alpha*lambda^3+281*nu^3*alpha^4*lambda^2*mu+45*lambda^2*alpha^4*mu^2*nu^2+15*nu^3*alpha*mu^3-5*nu^6*alpha^4*lambda+25*mu^4*lambda*alpha^6*nu^2+61*mu^2*nu^4*alpha^2+lambda^5*nu*alpha^2+10*lambda^4*alpha^3*mu^2-91*mu^4*nu*alpha^5*lambda-65*mu^4*nu^2*alpha^5*lambda-61*mu^4*lambda*alpha^4*nu-122*mu^4*lambda*alpha^4*nu^2-5*mu^4*lambda*alpha^3*nu^2+120*mu^4*lambda*alpha^3*nu+74*mu^4*lambda*alpha^6*nu);
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f5:= 2*(1+mu+nu+lambda)*(lambda+mu+nu)*(nu^2+2*nu*alpha*mu+mu^2*alpha^2+2*lambda*nu-2*lambda*alpha*nu-2*lambda*mu*alpha+2*alpha^2*lambda*mu-2*lambda^2*alpha+alpha^2*lambda^2+lambda^2)*(-alpha^2*lambda*mu^3-4*lambda^2*nu*alpha-lambda^3*alpha^2*mu+2*lambda^3*alpha^2+2*nu*mu^2*lambda-5*mu^2*alpha^3+nu^2+5*alpha^2*nu^2+lambda^2+mu^2*alpha^4-2*mu^3*alpha^3+lambda^2*alpha^3+5*mu^3*alpha^2+5*mu^2*alpha^2+2*lambda*nu+9*alpha^2*lambda*mu+9*alpha^2*lambda*nu+4*lambda^2*nu*alpha^2-lambda^3*alpha^3+2*nu*alpha^4*lambda^2+nu^2*alpha^4*lambda^2-2*alpha^3*nu*lambda^2+alpha^3*nu*lambda^3+7*nu*alpha*mu-12*nu*alpha^2*mu-7*lambda*mu*alpha+nu^2*mu^2-4*nu^3*alpha^2*mu+4*lambda^2*mu*alpha^3*nu-12*alpha^2*lambda^2*mu*nu-5*nu^2*alpha-lambda*alpha^3*nu^2*mu+5*lambda*alpha^3*mu^2*nu+2*lambda*alpha^4*mu*nu^2+4*lambda*alpha^4*mu*nu-4*lambda*alpha^3*mu-5*lambda*alpha^3*mu^2+lambda*alpha^3*mu*nu+2*lambda*alpha^4*mu-9*lambda*alpha^3*nu^2-7*lambda*alpha^3*nu+2*nu^3*alpha^3*mu+3*mu^2*alpha^3*nu+2*mu^2*alpha^4*nu+2*mu^3*alpha^3*nu+7*mu*alpha^3*nu+9*mu*alpha^3*nu^2+7*nu^2*lambda*alpha^2+4*alpha^2*lambda^2*mu-24*alpha^2*lambda*mu*nu+lambda^2*mu^2-nu^3*alpha^2*lambda-2*alpha^2*nu^2*lambda^2-nu^2*alpha^3*lambda^2+2*nu^2*mu-2*nu^3*alpha+4*lambda^2*nu*alpha*mu+lambda^2*alpha+lambda^2*alpha^4-nu*alpha^2*lambda^3-9*mu^2*alpha*lambda-4*lambda*alpha*nu-5*mu*alpha^2*nu^2+4*mu*nu*lambda-2*lambda^2*mu^2*alpha^2-4*lambda^2*mu*alpha^3+2*nu^3*alpha*mu+3*nu^2*alpha*mu-15*lambda*mu^2*alpha^2*nu-lambda^2*alpha*mu^2-lambda^3*alpha-2*nu^3*alpha^3*lambda-5*mu^2*nu*alpha^2+lambda^3*alpha*mu+5*nu^3*alpha^2-2*mu^2*alpha^2*nu^2+lambda*alpha*mu*nu-nu*alpha*lambda*mu^2+mu^2*nu^2*alpha^4+7*lambda*mu^2*alpha^2-15*nu^2*lambda*alpha^2*mu+9*nu*alpha*mu^2-5*nu^2*lambda*alpha-2*mu^3*lambda*alpha-4*alpha^2*lambda^2-2*lambda^2*mu*alpha+5*nu^2*lambda*alpha*mu+2*mu^3*nu*alpha-4*mu^3*nu*alpha^2+2*lambda^2*mu);
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f6:=-(1+mu+nu+lambda)*(lambda+mu+nu)*(4*lambda^2*nu*alpha+lambda^3*alpha^2+2*nu*mu^2*lambda-lambda^3-mu^3*alpha^3-nu^3+2*mu^3*alpha^2-3*lambda^2*nu-4*lambda^2*nu*alpha^2-lambda^3*alpha^3+3*alpha^3*nu*lambda^2+alpha^3*nu*lambda^3+nu^2*mu^2+nu^3*alpha^2*mu+nu^3*mu+3*lambda^2*mu*alpha^3*nu-4*alpha^2*lambda^2*mu*nu+2*lambda*alpha^3*nu^2*mu+3*lambda*alpha^3*mu^2*nu-3*lambda*alpha^3*mu^2-3*nu^2*lambda+6*lambda*alpha^3*mu*nu+3*mu^2*alpha^3*nu+mu^2*alpha^3*nu^2+mu^3*alpha^3*nu-5*nu^2*lambda*alpha^2+4*alpha^2*lambda^2*mu-9*alpha^2*lambda*mu*nu+lambda^2*mu^2-nu^3*alpha^2*lambda-2*alpha^2*nu^2*lambda^2+nu^2*alpha^3*lambda^2+3*nu^2*mu+2*nu^3*alpha-4*lambda^2*nu*alpha*mu-nu*alpha^2*lambda^3-5*mu^2*alpha*lambda+3*lambda*mu*nu^2+5*mu*alpha^2*nu^2+6*mu*nu*lambda-3*lambda^2*mu*alpha^3-2*nu^3*alpha*mu-5*nu^2*alpha*mu-5*lambda*mu^2*alpha^2*nu-2*lambda^2*alpha*mu^2+lambda^3*alpha-5*mu^2*nu*alpha^2-lambda^3*alpha*mu-mu^2*alpha^2*nu^2-9*lambda*alpha*mu*nu-3*nu*alpha*lambda*mu^2+5*lambda*mu^2*alpha^2-3*nu^2*lambda*alpha^2*mu+5*nu*alpha*mu^2+5*nu^2*lambda*alpha-mu^3*lambda*alpha+lambda^3*mu-4*lambda^2*mu*alpha-mu^2*nu^2*alpha-5*nu^2*lambda*alpha*mu+mu^3*nu*alpha-2*mu^3*nu*alpha^2+3*lambda^2*mu*nu+3*lambda^2*mu)*(nu^2+2*nu*alpha*mu+mu^2*alpha^2+2*lambda*nu-2*lambda*alpha*nu-2*lambda*mu*alpha+2*alpha^2*lambda*mu-2*lambda^2*alpha+alpha^2*lambda^2+lambda^2);
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Merci d'avance
Gérard.
