#8972: Inversion and fraction fields for power series rings
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Reporter: SimonKing | Owner: AlexGhitza
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.4.2
Component: algebra | Keywords: power series ring, fraction field
Author: Simon King | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by SimonKing):
Replying to [comment:13 robertwb]:
> Do you have any timings for power series sqrt()?
Tentatively.
Without the patch:
{{{
sage: P.<t> = QQ[[]]
sage: p = 9 - 33*t - 13*t^2 - 155*t^3 - 429*t^4 - 137*t^5 + 170*t^6 +
81*t^7 - 132*t^8 + 179*t^9 + O(t^10)
sage: p.sqrt()
3 - 11/2*t - 173/24*t^2 - 5623/144*t^3 - 174815/1152*t^4 -
8187925/20736*t^5 - 12112939/9216*t^6 - 7942852751/1492992*t^7 -
1570233970141/71663616*t^8 - 12900142229635/143327232*t^9 + O(t^10)
sage: timeit('q = p.sqrt()')
25 loops, best of 3: 13.3 ms per loop
sage: timeit('q = (p^2).sqrt()')
25 loops, best of 3: 13.6 ms per loop
sage: timeit('q = (p^4).sqrt()')
25 loops, best of 3: 14.5 ms per loop
sage: PZ = ZZ[['t']]
sage: timeit('q = (PZ(p)^2).sqrt()')
ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (27, 0))
...
TypeError: no conversion of this rational to integer
sage: p = 9 - 33*t - 13*t^2 - 155*t^3 - 429*t^4 - 137*t^5 + 170*t^6 +
81*t^7 - 132*t^8 + 179*t^9
sage: timeit('q = p.sqrt()')
25 loops, best of 3: 20.7 ms per loop
sage: timeit('q = (p^2).sqrt()')
25 loops, best of 3: 21.9 ms per loop
}}}
With the patch:
{{{
sage: P.<t> = QQ[[]]
sage: p = 9 - 33*t - 13*t^2 - 155*t^3 - 429*t^4 - 137*t^5 + 170*t^6 +
81*t^7 - 132*t^8 + 179*t^9 + O(t^10)
sage: p.sqrt()
3 - 11/2*t - 173/24*t^2 - 5623/144*t^3 - 174815/1152*t^4 -
8187925/20736*t^5 - 12112939/9216*t^6 - 7942852751/1492992*t^7 -
1570233970141/71663616*t^8 - 12900142229635/143327232*t^9 + O(t^10)
sage: timeit('q = p.sqrt()')
25 loops, best of 3: 15.5 ms per loop
sage: timeit('q = (p^2).sqrt()')
25 loops, best of 3: 15.7 ms per loop
sage: timeit('q = (p^4).sqrt()')
25 loops, best of 3: 16.6 ms per loop
sage: PZ = ZZ[['t']]
sage: timeit('q = (PZ(p)^2).sqrt()')
25 loops, best of 3: 19.2 ms per loop
sage: p = 9 - 33*t - 13*t^2 - 155*t^3 - 429*t^4 - 137*t^5 + 170*t^6 +
81*t^7 - 132*t^8 + 179*t^9
sage: timeit('q = p.sqrt()')
25 loops, best of 3: 23.8 ms per loop
sage: timeit('q = (p^2).sqrt()')
25 loops, best of 3: 24.5 ms per loop
}}}
So, over QQ, there is a slight regression (both with exact and inexact
input). Over ZZ, it only works with my patch, even for a polynomial that
is quadratic by definition.
I will have a closer look at sqrt - perhaps I'll find something.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8972#comment:14>
Sage <http://www.sagemath.org>
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