#8541: modular forms / linear algebra issue -- subspace not invariant
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Reporter: was | Owner: jason, was
Type: defect | Status: new
Priority: major | Milestone: sage-4.4
Component: linear algebra | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by davidloeffler):
* owner: craigcitro => jason, was
* component: modular forms => linear algebra
Comment:
The problem is in the multimodular algorithm that's used for computing
matrix multiplication over cyclotomic fields:
{{{
sage: K.<zeta4> = CyclotomicField(4)
sage: m = matrix(K, 1, 1, [186])
sage: n = matrix(K, 1, 2, [1, -6/125*zeta4 - 117/125])
sage: m * n
[ -23087/125 -1116/125*zeta4 - 21762/125]
}}}
According to the output of verbose, it works modulo a single prime (split
in K), in this case 46337; and the result is indeed correct modulo this
prime. But that's not enough, clearly. I'm very suspicious about the
method {{{sage.matrix.matrix_cyclo_dense.Matrix_cyclo_dense.height()}}}.
It returns the maximum absolute value of any entry (in any complex
embedding), so n has height 1. Shouldn't it return the maximum absolute
value of the numerator or denominator of any element, as with the
corresponding method for dense rational matrices? (What does this even
mean when K doesn't have class number 1?)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8541#comment:2>
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