Sage: Ticket #3166: Problems with echelon_form over ComplexField
https://trac.sagemath.org/ticket/3166
<p>
For certain well-conditioned floating-point matrices with entries in <a class="missing wiki">ComplexField?</a>, 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
</p>
<pre class="wiki">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
</pre><p>
This bug is probably related to <a class="closed ticket" href="https://trac.sagemath.org/ticket/2256" title="defect: [with patch, positive review] matrix inverse over CC raises ... (closed: fixed)">#2256</a> and <a class="closed ticket" href="https://trac.sagemath.org/ticket/1132" title="defect: error inverting matrix over RQDF (closed: wontfix)">#1132</a> 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.
</p>
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https://trac.sagemath.org/ticket/3166
Trac 1.1.6dunfieldMon, 12 May 2008 00:54:01 GMTstatus changed; resolution set
https://trac.sagemath.org/ticket/3166#comment:1
https://trac.sagemath.org/ticket/3166#comment:1
<ul>
<li><strong>status</strong>
changed from <em>new</em> to <em>closed</em>
</li>
<li><strong>resolution</strong>
set to <em>duplicate</em>
</li>
</ul>
TicketmabshoffMon, 12 May 2008 02:03:07 GMTmilestone changed
https://trac.sagemath.org/ticket/3166#comment:2
https://trac.sagemath.org/ticket/3166#comment:2
<ul>
<li><strong>milestone</strong>
changed from <em>sage-3.0.2</em> to <em>sage-duplicate/invalid</em>
</li>
</ul>
Ticket