#17272: Use pivoting for Gaussian elimination on matrices over p-adics
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Reporter: roed | Owner:
Type: defect | Status: new
Priority: critical | Milestone: sage-6.4
Component: linear algebra | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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{{{
sage: R = ZpCA(5,5,print_mode='val-unit')
sage: A = matrix(R,3,3,[250,2369,1147,106,927,362,90,398,2483])
sage: A
[5^3 * 2 + O(5^5) 2369 + O(5^5) 1147 + O(5^5)]
[ 106 + O(5^5) 927 + O(5^5) 362 + O(5^5)]
[ 5 * 18 + O(5^5) 398 + O(5^5) 2483 + O(5^5)]
sage: A.det()
2634 + O(5^5)
sage: ~A
Traceback (most recent call last):
...
ZeroDivisionError: input matrix must be nonsingular
}}}
The problem is that Sage doesn't pivot when doing Gaussian elimination:
{{{
sage: K = R.fraction_field()
sage: A.change_ring(K).augment(identity_matrix(K,3))._echelon_classical()
[ 1 + O(5^2) O(5^-1) O(5^-1) O(5^-1)
O(5^2) 5^-1 * 7 + O(5)]
[ O(5^2) 1 + O(5^2) 13 + O(5^2) 4 + O(5^2)
O(5^5) 5^2 * 19 + O(5^4)]
[ O(5^3) O(5^0) O(5^0) O(5^0)
1 + O(5^2) 5^-1 * 8 + O(5)]
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/17272>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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