id summary reporter owner description type status priority milestone component resolution keywords cc merged author reviewer upstream work_issues branch commit dependencies stopgaps
3166 Problems with echelon_form over ComplexField dunfield was "For certain well-conditioned floating-point matrices with entries in ComplexField, echelon_form can return matrices which are not in (approximate) echelon_form. This breaks methods like rank(), right_solve() and inverse(). I've attached a sample matrix which illustrates this
{{{
sage: A = load(""./prob-sol.sobj"")
sage: A.parent()
Full MatrixSpace of 5 by 5 dense matrices over Complex Field with 1010 bits of precision
sage: matrix(CDF, A.echelon_form())
[ 1.0 0 -3.5*I 0 -20.0 + 12.0*I]
[ 0 1.0 1.0 0 -4.0 + 1.0*I]
[ 0 0 1.0 + 4.55695126222e-305*I 0 -2.33592727654 + 0.497614402099*I]
[ 0 0 -4.0 1.0 -2.0]
[ 0 0 -2.0 0 0]
sage: CC(A.det())
76.1312551138321 - 5.28799080668534*I
sage: A.rank()
4
}}}
This bug is probably related to #2256 and #1132 but there the problem with echelon_form is more subtle (1 entries on the diagonal which aren't quite 1), which is why I opened this new ticket. " defect closed major sage-duplicate/invalid/wontfix linear algebra duplicate