Opened 7 years ago

Last modified 7 years ago

## #19997 new enhancement

# advanced symbolic series of Order any expression

Reported by: | Daniel Krenn | Owned by: | |
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Priority: | major | Milestone: | sage-7.1 |

Component: | symbolics | Keywords: | |

Cc: | Merged in: | ||

Authors: | Reviewers: | ||

Report Upstream: | N/A | Work issues: | |

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description

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

### Change History (3)

### comment:1 follow-up: 2 Changed 7 years ago by

Summary: | substitution in symbolic series: losing Order → advanced symbolic series of Order any expression |
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Type: | defect → enhancement |

### comment:2 Changed 7 years ago by

Replying to rws:

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.

### comment:3 Changed 7 years ago by

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

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