advanced symbolic series of Order any expression

[dkrenn]

sage: (x+1).sqrt().series(x,3)
1 + 1/2*x + (-1/8)*x^2 + Order(x^3)
sage: (x+1).sqrt().series(x,3).subs(x=1/x)
1/2/x - 1/8/x^2 + 1

Component: symbolics

Issue created by migration from https://trac.sagemath.org/ticket/19997

[rwst]

comment:1

The substitution is fine. To support other than power series would be a major enhancement.

[dkrenn]

comment:2

Replying to @rwst:

The substitution is fine. To support other than power series would be a major enhancement.

I'm not sure if I understand your comment. What I see (as someone having only little idea how power series are done in SR) is that in

sage: a = 1 + x/2 - x^2/8 + (x^3).Order()
sage: a
-1/8*x^2 + 1/2*x + Order(x^3) + 1
sage: a.subs(x=1/x)
1/2/x - 1/8/x^2 + Order(x^(-3)) + 1

substitution works (somehow at least), but in the example stated in the ticket not, the O-Term disappears.

[rwst]

comment:3

So, until that enhancement is implemented, a second ticket is needed for consistency, which throws an error. But note that the user won't even encounter this inconsistency if she creates symbolic series the way the documentation suggests it:

sage: (1/(1-x)).series(x,2)
1 + 1*x + Order(x^2)
sage: s=_
sage: s.subs(x==sin(x))
sin(x) + 1
sage: s.subs(x==exp(x))
e^x + 1
sage: s.subs(x==1/x)
1/x + 1
sage: s.subs(x=1/x)
1/x + 1