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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | )abbrev domain NOTTING NottinghamGroup
++ Author: Mark Botch
++ Description:
++ This is an implmenentation of the Nottingham Group
NottinghamGroup(F) : SIG == CODE where
F : FiniteFieldCategory
SIG ==> Group with
retract : UnivariateFormalPowerSeries F -> %
CODE ==> add
Rep:=UnivariateFormalPowerSeries F
coerce f == coerce(f::Rep)$UnivariateFormalPowerSeries(F)
retract f ==
if zero? coefficient(f,0) and one? coefficient(f,1)
then f::Rep
else error"The leading term must be x"
1 == monomial(1,1)
f*g == f.g
inv f == revert f
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