Sage: Ticket #6231: Solving a system of equations ignores multiplicities
https://trac.sagemath.org/ticket/6231
<p>
A follow-up from <a class="ext-link" href="http://groups.google.com/group/sage-support/browse_thread/thread/d8e22deb18d97253"><span class="icon"></span>http://groups.google.com/group/sage-support/browse_thread/thread/d8e22deb18d97253</a> but different from <a class="closed ticket" href="https://trac.sagemath.org/ticket/6228" title="defect: [with patch, positive review] Wrong multiplicities when solving a ... (closed: fixed)">#6228</a>:
</p>
<pre class="wiki">sage: solve((x^2-1)^3==0, x, multiplicities=True)
([x == -1, x == 1], [3, 3])
sage: solve(((x^2-1)^3==0,(x^2-1)^3==0), x, multiplicities=True)
[[x == 1], [x == -1]]
</pre><p>
So, at least in this example, we get the correct multiplicities for a single equation, but we don't get any multiplicity when the same equation together with a copy of itself forms a <em>system</em> of equations.
</p>
<p>
Note that <code></code>maxima<code></code> does not seem to help here:
</p>
<pre class="wiki">sage: maxima.eval('solve([(x^2-1)^3,(x^2-1)^3],x)')
'[[x=1],[x=-1]]'
sage: maxima.get('multiplicities')
'[]'
</pre><p>
What format should the multiplicities be provided in?
</p>
<ul><li>When one solves a single equation with a single variable, the solutions are given by a simple list. Accordingly, the multiplicities are given as a simple list.
</li><li>When a system of equations in a single variable is given, the solutions are given by a list of lists. So, should the multiplicities be given by a list of lists?
</li></ul>en-usSagehttps://trac.sagemath.org/chrome/site/logo_sagemath_trac.png
https://trac.sagemath.org/ticket/6231
Trac 1.1.6SimonKingSat, 06 Jun 2009 16:33:24 GMTdescription, milestone changed
https://trac.sagemath.org/ticket/6231#comment:1
https://trac.sagemath.org/ticket/6231#comment:1
<ul>
<li><strong>description</strong>
modified (<a href="/ticket/6231?action=diff&version=1">diff</a>)
</li>
<li><strong>milestone</strong>
changed from <em>sage-4.0.2</em> to <em>sage-wishlist</em>
</li>
</ul>
Ticket