Opened 4 years ago
Closed 3 years ago
#8943 closed enhancement (fixed)
RuntimeError with series
Reported by: | casamayou | Owned by: | burcin |
---|---|---|---|
Priority: | minor | Milestone: | sage-4.7.1 |
Component: | calculus | Keywords: | series, taylor |
Cc: | Merged in: | sage-4.7.1.alpha1 | |
Authors: | Alexei Sheplyakov, Burcin Erocal | Reviewers: | Karl-Dieter Crisman |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | #11317 | Stopgaps: |
Description (last modified by casamayou)
The function *series* can not give the power series expansion of f(x)=(1+arctan(x))(1/x) , while *taylor* succeeds. Note that the function f can be continuously extended at 0.
sage: taylor((1+arctan(x))**(1/x), x, 0, 3) 1/16*x^3*e + 1/8*x^2*e - 1/2*x*e + e sage: ((1+arctan(x))**(1/x)).series(x==0, 3) RuntimeError: power::eval(): division by zero
Subsidiary question: why the functions *taylor* and *series* perform similar tasks, but differently?
Attachments (1)
Change History (8)
comment:1 Changed 4 years ago by casamayou
- Description modified (diff)
comment:2 Changed 3 years ago by kcrisman
- Priority changed from trivial to minor
Changed 3 years ago by burcin
comment:3 Changed 3 years ago by burcin
This was fixed upstream in ginac. The changes will be in the next pynac release. Patch with doctest is attached.
comment:4 Changed 3 years ago by burcin
- Dependencies set to 11317
- Status changed from new to needs_review
New pynac package with the fix is at #11317.
comment:5 Changed 3 years ago by kcrisman
- Reviewers set to Karl-Dieter Crisman
- Status changed from needs_review to positive_review
This is nice, and the other examples given by the author also did not work before but now do:
sage: (cos(x)^(sin(x)/x)).series(x==0,9) 1 + (-1/2)*x^2 + 1/8*x^4 + (-1/30)*x^6 + 631/120960*x^8 + Order(x^9) sage: ((1+x)^(1/x)).series(x==0,9) (e) + (-1/2*e)*x + (11/24*e)*x^2 + (-7/16*e)*x^3 + (2447/5760*e)*x^4 + (-959/2304*e)*x^5 + (238043/580608*e)*x^6 + (-67223/165888*e)*x^7 + (559440199/1393459200*e)*x^8 + Order(x^9)
Also, the new series does correctly approximate the original function near x=0 :)
comment:6 Changed 3 years ago by jdemeyer
- Dependencies changed from 11317 to #11317
- Milestone changed from sage-4.7 to sage-4.7.1
comment:7 Changed 3 years ago by jdemeyer
- Merged in set to sage-4.7.1.alpha1
- Resolution set to fixed
- Status changed from positive_review to closed
Looks like this is in Ginac/Pynac?. But maybe it makes sense not to have an answer here? After all, the technical definition would imply that f doesn't have a Taylor series there, if it doesn't even exist. Probably Maxima is more lenient about such things.