Opened 12 years ago
Last modified 4 years ago
#5075 new defect
Polynomials over inexact rings should not truncate inexact leading zeroes
Reported by: | kedlaya | Owned by: | roed |
---|---|---|---|
Priority: | major | Milestone: | sage-6.4 |
Component: | algebra | Keywords: | polynomials, power series, inexact rings |
Cc: | dmharvey, niles, wuthrich | Merged in: | |
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: | todo |
Description
The generic polynomial class truncates leading zeroes, and this can cause problems when working over an inexact ring in which is_zero can return True even for an inexact zero (e.g., see #2943). Here is a simple example:
sage: C.<t> = PowerSeriesRing(Integers()) sage: D.<s> = PolynomialRing(C) sage: y = O(t) sage: y O(t^1) sage: z = y*s sage: z 0 sage: z.list() []
This was recognized earlier for p-adics and fixed (I'm not sure which ticket this was):
sage: C = pAdicField(11) sage: D.<s> = PolynomialRing(C) sage: y = O(11) sage: y O(11) sage: z = y*s sage: z (O(11))*s
The other main class of inexact rings are interval fields, but I believe for those is_zero returns False for an inexact zero, so this doesn't come up.
Attachments (2)
Change History (13)
comment:1 Changed 12 years ago by
- Cc dmharvey added
comment:2 Changed 12 years ago by
Changed 12 years ago by
In progress. I think it fixes the problem, but I'm working on a larger project for p-adic polynomials that this is part of.
comment:3 Changed 10 years ago by
- Report Upstream set to N/A
I tried to apply this against 4.7.1.rc1 and got a bunch of merge failures in power_series_poly.pyx. Probably another trivial rebase is needed.
comment:4 Changed 8 years ago by
- Milestone changed from sage-5.11 to sage-5.12
comment:5 Changed 7 years ago by
- Milestone changed from sage-6.1 to sage-6.2
comment:6 Changed 7 years ago by
- Cc niles wuthrich added
David, could you give us a rebase for sage 6.1? I know you're doing a lot of other work for padics, but we're trying to solve a more basic issue with power series comparison at #9457. Power series over padics are a confusing obstacle there, and we wanted to see if the patch here would help.
Here's the specific bug we're trying to track down (in sage 6.1): Power series over p-adics are changing inexact zeros to exact zeros -- this looks similar to the problem with polynomials on this ticket, but notice that the problem happens even for p-adics:
sage: Ct.<t> = PowerSeriesRing(Qp(11)) sage: O(11^2) # inexact zero O(11^2) sage: Ct(O(11^2)) # coercing to power series ring looses finite precision 0 sage: Ct(1+O(11^2)) # finite precision is retained for non-zero elements 1 + O(11^2)
There is a problem with multiplication of a p-adic by an element of the power series ring, which might be caused by the problem above:
sage: 1+O(11^2)*t # finite precision is retained 1 + O(11^20) + O(11^2)*t sage: O(11^2)*t # finite precision is lost 0
Note that there is a similar problem for more general power series ring over power series ring:
sage: D.<x> = PowerSeriesRing(QQ) sage: Ds.<s> = PowerSeriesRing(D) sage: O(x) # inexact zero O(x^1) sage: Ds(O(x)) # finite precision is lost 0 sage: Ds(1+O(x)) # finite precision is retained 1 + O(x) sage: 1+O(x)*s # !! this is different from behavior of power series over padic ring 1
My hope is that starting with a rebase of this patch would be a step toward solving this problem. Perhaps it will have to be extended to power series over inexact rings too. Unfortunately I don't understand the current status of padics well enough to do this rebase myself.
comment:7 Changed 7 years ago by
- Milestone changed from sage-6.2 to sage-6.3
comment:8 Changed 7 years ago by
- Milestone changed from sage-6.3 to sage-6.4
comment:9 Changed 6 years ago by
- Stopgaps set to todo
comment:10 Changed 5 years ago by
Ping. Is this issue due to be resolved by other developments on p-adics?
comment:11 Changed 4 years ago by
Ping again. The original example still behaves the same way in Sage 8.0.
A closely related issue is #3979.