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
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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
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i3 : t = compositionInverse(s)
4 2
o3 = FormalSeries{10x - x + x, 4}
o3 : FormalSeries
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i4 : substitute(s,{t})
o4 = FormalSeries{x, 4}
o4 : FormalSeries
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i5 : substitute(t,{s})
o5 = FormalSeries{x, 4}
o5 : FormalSeries
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