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FormalGroupLaws :: compositionInverse(FormalSeries)

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

Synopsis

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