compute asymptotic expansion to some rational directly

[dkrenn]

Currently we have

sage: A.<y> = AsymptoticRing(growth_group='y^ZZ', coefficient_ring=QQ)
sage: (y^2 + O(y))^(1/2)  # not tested
y + O(1)

It is not tested, since the current implementation rewrites it to exp(log(...)) which is not possible in A. There is a workaround:

sage: B.<z> = AsymptoticRing(growth_group='z^QQ * log(z)^QQ', coefficient_ring=QQ)
sage: (z^2 + O(z))^(1/2)
z + O(1)

The aim of this ticket is to make such things possible directly.

[dkrenn]

Last 10 new commits:

​84568cf	Trac #19423: two code simplifications
​342af12	Trac #19316: write __pow_number__
​a3b66af	Trac #19316: extend existing __pow__ to use new method
​1028b95	Trac #19316: rewrite error message
​37c6115	Merge Trac #19850 into asy/pow_rational
​d122786	Trac #19316: restructure doctests of pow (add section EXAMPLES)
​ef717b0	Trac #19316: allow symbolic constants
​6844299	Trac #19316: fix ReST doc
​6837874	Trac #19423: fix ReST doc
​58d1f28	Merge branch 'asy/exploginv_taylor' into asy/pow_rational

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​f87be85	Merge commit '8f7195f7f8875ea81bd8b9026a138e269f719a4d' of git://trac.sagemath.org/sage into asy/pow_rational
​10b2a64	Trac #19316: fix doctest

[cheuberg]

Merged #20000 due to a merge conflict (both tickets introduce a new method at the same position of the file).

My comments on #19423 also apply here.

---

New commits:

​ffc1bf5	write .sqrt() for asymptotic expansions
​1441b31	additional doctest (comparing with power series result)
​310780a	Trac #20000: remove redundant pair of parentheses
​b38d602	Trac #19316: Merge #20000 due to merge conflict

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​3ac3044	Trac #19423: rename _taylor_ to _power_series_
​4c5edd6	Trac #19423: new method _main_term_relative_error_
​c3aeae8	Trac #19423: refactor log to use _main_term_relative_error_
​2a76cd7	Trac #19423: refactor __invert__ to use _main_term_relative_error_
​1a526b7	Trac #19423: Merge #19946 to fix merge conflict
​9a58142	Trac #19423: document parameter precision
​c56a095	Trac #19423: doctests for precision
​eb10a2a	Trac #19316: merge latest version of #19423
​a7d28ba	Trac #19316: use _main_term_relative_error_

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​6d44199

Trac #19316: fix 0^0

[cheuberg]

I reviewed your code, merged latest version of #19423 and adapted to use main_term_relative_error. This now needs review.

[dkrenn]

Replying to cheuberg:

I reviewed your code, merged latest version of #19423 and adapted to use main_term_relative_error. This now needs review.

LGTM, merged in #19423 again and removed two code lines (were already commented out), which were used for testing purposes.

---

New commits:

​1b44d48	Trac #19423: change ZeroDivisionError message
​ecbeb26	Trac #19423: rephrase OUTPUT-block of _main_term_relative_error_
​f21ea78	Trac #19423: new parameter to return inverse of main term in _main_term_relative_error_
​7974666	Trac #19423: use new parameter of previous commit
​b091009	Trac #19423: minor code rewrite to improve readability
​96f1ea6	Trac #19423: correct parent in __invert__
​a61913c	Merge branch 'u/dkrenn/asy/exploginv_taylor' of trac.sagemath.org:sage into t/19316/asy/pow_rational
​44e314c	Trac #19316: remove two commented code lines

[cheuberg]

I think that while merging the latest version of #19423, you inadvertently reverted commit ​1b44d48 Trac #19423: change ZeroDivisionError message.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​37917b2

Trac #19316: change ZeroDivisonError message again (after merge; something went wrong earlier)

[dkrenn]

Replying to cheuberg:

I think that while merging the latest version of #19423, you inadvertently reverted commit ​1b44d48 Trac #19423: change ZeroDivisionError message.

Changed.