# compositionInverse(FormalSeries) -- inverse for composition of formal series

## Description

The FormalSeries s must be in one variable and have a zero constant coefficient and a coefficient +1 or -1 in degree 1. Then, compositionInverse computes the inverse of s for the composition of formal series, up to the precision of s.

 i1 : ZZ[x] o1 = ZZ[x] o1 : PolynomialRing i2 : s = series(x+x^2+2*x^3-5*x^4,4) 4 3 2 o2 = FormalSeries{- 5x + 2x + x + x, 4} o2 : FormalSeries i3 : t = compositionInverse(s) 4 2 o3 = FormalSeries{10x - x + x, 4} o3 : FormalSeries i4 : substitute(s,{t}) o4 = FormalSeries{x, 4} o4 : FormalSeries i5 : substitute(t,{s}) o5 = FormalSeries{x, 4} o5 : FormalSeries