How can I recurse a power series in two variables?
I would like very much to express, for example,
R.<x, y> = PowerSeriesRing(QQ, default_prec = 20)
g(x, g(x, g(x, x)))
Or,
f(x, f(x, f(x, f(x, f(x, f(x, f(x, f(x, f(x, f(x, f(x, f(x, (f(x, (f(x, f(x,y))))))))))))))))).expand()
In a more elegant way, for a specified number of self-compositions in one variable. I have only been able to find the sage function of composition for one variable polynomials, not for nesting two variable power series.
Could you provide a definition of
f
andg
that one could use to explore your question?Note: with
R
as in the question,R.random_element()
gave a starting point for exploration.In general though, providing a working example helps other Ask Sage users to explore a question. This question had
g(x, g(x, g(x, x)))
but no definition ofg
to make that work.