> (67) -> series(sin(y+x), x=0)
>
> (67)
> sin(y) 2 cos(y) 3 sin(y) 4 cos(y) 5
> sin(y) + cos(y)x - ------ x - ------ x + ------ x + ------ x
> 2 6 24 120
> +
> sin(y) 6 cos(y) 7 sin(y) 8 cos(y) 9 sin(y) 10 11
> - ------ x - ------ x + ------ x + ------ x - ------- x + O(x )
> 720 5040 40320 362880 3628800
> Type: UnivariatePuiseuxSeries(Expression Integer,x,0)
Looking at this thing I would say that if you take
R = Q[s,c] -- polynomial ring in two variables over rationals
I = (s^2+c^2-1)R -- ideal in R
A = R/I -- factor structure
S = A[[x]] -- formal power series
then S would be a perfect candidate for the result type of the above
expression. And there is no "Expression Integer".
While constructing the result of "series", Axiom should try hard to get
a reasonable (in some sense minimal) type for the result.