#15312: fix integer overflow (?) in conversion of powersums to Schur functions
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Reporter: zabrocki | Owner:
Type: defect | Status: new
Priority: critical | Milestone: sage-5.13
Component: combinatorics | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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The following bug seems to appear on Macs only (linux machines do not seem
to be effected).
To begin with, let's do a change of basis in a small degree:
{{{
sage: p = SymmetricFunctions(QQ).powersum()
sage: s = SymmetricFunctions(QQ).schur()
sage: s(p[2,2])
s[1, 1, 1, 1] - s[2, 1, 1] + 2*s[2, 2] - s[3, 1] + s[4]
}}}
Now let's do one in a larger degree:
{{{
sage: time g = s(p([1]*47))
Time: CPU 19.16 s, Wall: 20.91 s
}}}
Now let's do that first one again:
{{{
sage: s(p[2,2])
s[1, 1, 1, 1] - s[2, 1, 1] + 4571483302*s[2, 2] - s[3, 1] + s[4]
}}}
That's not the correct answer ! And the next time you ask Sage, it
gives different, still incorrect, answers:
{{{
sage: s(p[2,2])
s[1, 1, 1, 1] - s[2, 1, 1] + 4614252243*s[2, 2] - s[3, 1] + s[4]
sage: s(p[2,2])
s[1, 1, 1, 1] - s[2, 1, 1] + 4634718110*s[2, 2] - s[3, 1] + s[4]
sage: s(p[2,2])
s[1, 1, 1, 1] - s[2, 1, 1] + 4631047636*s[2, 2] - s[3, 1] + s[4]
}}}
In [https://groups.google.com/d/topic/sage-combinat-
devel/fWMuS4R5M9Q/discussion this discussion] on sage-combinat-devel, Anne
noticed that the problem is "not symmetrica per se, but some wrapper
functions around symmetrica, as the following example shows":
{{{
sage: f = eval('symmetrica.t_POWSYM_SCHUR')
sage: f({Partition([2,2]):Integer(1)})
s[1, 1, 1, 1] - s[2, 1, 1] + 2*s[2, 2] - s[3, 1] + s[4]
sage: time g = f({Partition([1]*47):Integer(1)})
Time: CPU 13.03 s, Wall: 13.04 s
sage: f({Partition([2,2]):Integer(1)})
s[1, 1, 1, 1] - s[2, 1, 1] + 2*s[2, 2] - s[3, 1] + s[4]
sage: Sym = SymmetricFunctions(QQ)
sage: p = Sym.power()
sage: s = Sym.schur()
sage: s(p[2,2])
s[1, 1, 1, 1] - s[2, 1, 1] + 4631790164*s[2, 2] - s[3, 1] + s[4]
sage: f({Partition([2,2]):Integer(1)})
s[1, 1, 1, 1] - s[2, 1, 1] + 2*s[2, 2] - s[3, 1] + s[4]
}}}
And Travis commented that:
> When (random) big numbers appear like that, it almost always is an
integer overflow. I suspect the communication with Symmetrica goes through
the native integer. Is this correct? If so, then that's where I'd say the
problem lies.
This is a bug which is carried over from #13413 . When we realized that
there are actually two bugs and one has been corrected, these tickets were
split.
--
Ticket URL: <http://trac.sagemath.org/ticket/15312>
Sage <http://www.sagemath.org>
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