#12561: Factoring padic polynomials
---------------------------------------------------+------------------------
Reporter: bsinclai | Owner: roed
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.8
Component: padics | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Brian Sinclair, Sebastian Pauli | Merged in:
Dependencies: | Stopgaps:
---------------------------------------------------+------------------------
Comment (by roed):
Replying to [comment:3 spice]:
> Patch applies correctly on 7.5 and all doctests written so far pass.
However:
>
> In the doctest from `pfactortree()`:
> {{{
> sage: from sage.rings.polynomial.padics.factor.factoring import
jorder4,pfactortree
> sage: f = ZpFM(2,24,'terse')['x']( (x^32+16)*(x^32+16+2^16*x^2)+2^34 )
> sage: pfactortree(f) # long (3.8s)
> [(1 + O(2^24))*x^64 + (65536 + O(2^24))*x^34 + (32 + O(2^24))*x^32 +
(1048576 + O(2^24))*x^2 + (256 + O(2^24))]
> }}}
> This is just returning the polynomial unfactored, so demonstrably the
factoring isn't working here. We should get:
> {{{
> sage: f = ZpFM(2,24,'terse')['x']( (x^32+16)*(x^32+16+2^16*x^2)+2^34 )
> sage: f.factor()
> ((1 + O(2^24))*x^32 + (65536 + O(2^24))*x^2 + (16 + O(2^24))) * ((1 +
O(2^24))*x^32 + (16 + O(2^24)))
> }}}
> Also, we should rework this code so that a sage Factorization object is
returned, and that pfactortree is called by the `.factor()` method
attached to p-adic polynomials.
Note that increasing the precision yields a factorization:
{{{
sage: f = ZpFM(2,44,'terse')['x']( (x^32+16)*(x^32+16+2^16*x^2) + 2^34)
sage: pfactortree(f)
[(1 + O(2^44))*x^32 + (7242791239680 + O(2^44))*x^30 + (13194407968768 +
O(2^44))*x^28 + (7902202888192 + O(2^44))*x^26 + (2147483648 +
O(2^44))*x^24 + (442381107200 + O(2^44))*x^22 + (21474836480 +
O(2^44))*x^20 + (6193337597952 + O(2^44))*x^18 + (240518168576 +
O(2^44))*x^16 + (2405122965504 + O(2^44))*x^14 + (2886218022912 +
O(2^44))*x^12 + (16766847680512 + O(2^44))*x^10 + (1099511627776 +
O(2^44))*x^8 + (2190164885504 + O(2^44))*x^6 + (14293651161088 +
O(2^44))*x^4 + (14178492350464 + O(2^44))*x^2 + (8796093022224 + O(2^44)),
(1 + O(2^44))*x^32 + (10349394804736 + O(2^44))*x^30 + (8796093022208 +
O(2^44))*x^28 + (5291936645120 + O(2^44))*x^26 + (17149804937216 +
O(2^44))*x^22 + (11398848446464 + O(2^44))*x^18 + (15187063078912 +
O(2^44))*x^14 + (825338363904 + O(2^44))*x^10 + (15402021158912 +
O(2^44))*x^6 + (3413693759488 + O(2^44))*x^2 + (8797166764048 + O(2^44))]
}}}
In the case Simon pointed out, adding `2^34` doesn't do anything since the
precision cap of the base ring is 24, so we have an actual example of a
reducible polynomial being claimed to be irreducible.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12561#comment:4>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac?hl=en.
For more options, visit https://groups.google.com/groups/opt_out.
