#8541: Cyclotomic matrix multiplication bug
------------------------------+---------------------------------------------
Reporter: was | Owner: jason, was
Type: defect | Status: new
Priority: critical | Milestone: sage-4.4
Component: linear algebra | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by davidloeffler):
* priority: major => critical
Old description:
> {{{
> sage: f = CuspForms(DirichletGroup(5).0,5).0
> sage: f[15]
> Boom!
>
> ArithmeticError: subspace is not invariant under matrix (vector is not in
> free module)
> }}}
>
> This was reported by Paul Nelson, a grad student at Caltech.
New description:
Multiplying matrices over cyclotomic fields sometimes returns wrong
answers:
{{{
sage: sage: K.<zeta4> = CyclotomicField(4)
sage: sage: m = matrix(K, [186])
sage: sage: n = matrix(K, [125])
sage: m * n
[-23087]
}}}
Similar errors occur with other cyclotomic fields. Experiments with random
1 x 1 matrices with integer entries up to 10^5^, coerced into the
cyclotomic field of order 4, suggest that the answer is wrong about 15-20%
of the time. The problem also occurs (less often) for certain examples of
multiplying a 2x2 matrix by a 2x2 matrix, and I also found an error in one
case of a 1 x 3 multiplied by a 3 x 1.
(This bug first manifested itself in the modular forms code, as was
reported by Paul Nelson, a grad student at Caltech:
{{{
sage: f = CuspForms(DirichletGroup(5).0,5).0
sage: f[15] # Boom!
ArithmeticError: subspace is not invariant under matrix (vector is not in
free module)
}}}
)
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8541#comment:4>
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