The case q=3 and nu=0 : asymptotics (Theorem 25)
Expression of M(1)
> | M0c; |
> | algS; |
> | implicitplot(algS,t=0..0.1,S=0..1,numpoints=10000); |
> | factor(discrim(algS,S)); |
> | solve(%); |
> | evalf(%); |
The radius is 0.07...
> | tc:=33/50-6/25*6^(1/2); evalf (tc); |
The value of mu
> | rationalize(1/tc); |
> | factor(subs(t=tc,algS)); |
> | Sc:=solve(2*S+2-6^(1/2));evalf(Sc); |
> | algeqtoseries(subs(t=tc*(1-x),algS),x,S,2,true); |
> |
Equation for M0=M(1)
> | algM0:=collect(factor(1/320*resultant(numer(M-M0c),algS,S)),M,factor); |
> | factor(discrim(algM0,M)); |
> | fsolve(2700*z^2-404*z+23,z,complex); |
> | fsolve((100*z^2-132*z+9),z,complex); |
> | fsolve(108*z^2-28*z+3,z,complex); |
> | with(plots): |
> | implicitplot(algM0,t=0..0.08,M=0..1.3,numpoints=10000); |
Expansion of M0 near its singularity
> | op(2,algeqtoseries(subs(t=tc*(1-x), algM0),x, M,3)); |
> |
> |