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asked 7 years ago

tzeentch gravatar image

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 defined in x to get a power series 1((x)+(y)) as a power series f(x,y) in two variables, x and y. In the code below I call l := , and e := 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.