Le lundi 8 octobre 2012 18:37:45 UTC+2, Pierre a écrit :
>
> Consider the functional equation
>
> (f*z + z * L(z,f)^2 + z * L(z,f+1) - L(z,f) == 0)
>
> This defines implicitly a bivariate function L(z,f). My goal is to find
> the Taylor development of L(z,0). I know from
>
> Bernhard Gittenberger Enumeration of generalized BCI λ terms -
> AofA'11
>
> that the result is
>
> z^2 + 2z^3 + 4z^4 + 13z^5 + 42z^6 + 139z^7 + 506z^8 +1915z^9 + 7558z^10 +
> · · ·
>
> How do I do that in SAGE?
>
> Thank you in advance.
>
> Pierre
Actually the idea (thanks to Bernhard and Philippe Flajolet) is to compute
a fix point:
zero(z,u) = 0
# nb of terms of size n with exactly m variables and |x| = 1
def Phi(L):
return z*L(z,u)^2 + z*u + z*L(z,u+1)
def iter(n):
result = zero
for i in [1..n]:
result(z,u) = Phi(result)
return result
L11 = iter(11)
taylor(L11(z,u=0), z, 0, 10)
Pierre
--
You received this message because you are subscribed to the Google Groups
"sage-support" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
Visit this group at http://groups.google.com/group/sage-support?hl=en.
