It is sometimes better to be more specific with the types.
Behind the scenes in assignment (2) a conversion happens.
Ralf
(1) -> a := series (sin x, x=0)
1 3 1 5 1 7 1 9 1 11 12
(1) x - - x + --- x - ---- x + ------ x - -------- x + O(x )
6 120 5040 362880 39916800
Type: UnivariatePuiseuxSeries(Expression(Integer),x,0)
(2) -> b: UnivariateTaylorSeries(Fraction Integer,x,0) := a
1 3 1 5 1 7 1 9 11
(2) x - - x + --- x - ---- x + ------ x + O(x )
6 120 5040 362880
Type: UnivariateTaylorSeries(Fraction(Integer),x,0)
(3) -> univariatePolynomial(b, 9)
1 9 1 7 1 5 1 3
(3) ------ x - ---- x + --- x - - x + x
362880 5040 120 6
Type: UnivariatePolynomial(x,Fraction(Integer))
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