#13958: number of generators of number field ideal blows up under multiplication
-----------------------------+----------------------------------------------
Reporter: mstreng | Owner: davidloeffler
Type: defect | Status: new
Priority: major | Milestone: sage-5.7
Component: number fields | Keywords: number field ideal
multiplication power
Work issues: | Report Upstream: N/A
Reviewers: | Authors:
Merged in: | Dependencies:
Stopgaps: |
-----------------------------+----------------------------------------------
With
{{{
K = QQ[sqrt(2)]
I = K.ideal(2).factor()[0][0]
I = I*I; I.ngens()
4
I = I*I; I.ngens()
16
I = I*I; I.ngens()
256
I = I*I; I.ngens()
65536
}}}
the first three squarings are fast, the fourth starts to be a bit slower,
and if you try a fifth, it will take up all your memory.
The reason is that that the number of generators is multiplied with every
multiplication and never reduced back to 1 or 2 with gens_reduced or
gens_two, as you can see from the output.
Addition suffers from the same problem, but the result is less dramatic
{{{
sage: I = K.ideal(2).factor()[0][0]
sage: I = I+I; I.ngens()
4
sage: I = I+I; I.ngens()
8
sage: I = I+I; I.ngens()
16
sage: I = I+I; I.ngens()
32
sage: I = I+I; I.ngens()
64
sage: I = I+I; I.ngens()
128
sage: I = I+I; I.ngens()
256
}}}
Solution: implement {{{__mul__}}} for {{{NumberFieldFractionalIdeal}}}
(instead of inheriting the function from Ideal) and use gens_two or
gens_reduced before giving the output. Or wrap functions from pari.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13958>
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 post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
