Ask Your Question

Revision history [back]

click to hide/show revision 1
initial version

How can I compose 2 power series in one variable with their compositional inverse get a power series in two variables?

I would like to compose a power series $\ell$ defined in $x$ to get a power series $\ell^{-1}(\ell(x) + \ell(y))$ as a power series $f(x, y)$ in two variables, $x$ and $y$. In the code below I call l := $\ell$, and e := $\ell^{-1}$.

PREC = 20    
R.<x, y> = PowerSeriesRing( QQ, default_prec=PREC )
f = exp( 1/3 * log( 1-x^3 ) )
print f
w = 1/f
l = w.integral(x)
e = l.reverse() 
g = e(l(x) + l(y)) ??

I find immediately the following issue, let alone the issue of composing:

e = l.reverse()
AttributeError: 'MPowerSeriesRing_generic_with_category.element_class' object has no attribute 'reverse'

Once I have this two variable power series $f(x, y)$, I would like to output $f(x, (f(x, ..., f(x,x)))$, composed with itself $n$-times for a natural number $n$.