Sage: Ticket #9548: Sage does not support infinities with complex direction
https://trac.sagemath.org/ticket/9548
<p>
This should do something reasonable:
</p>
<pre class="wiki">sage: Infinity * I
---------------------------------------------------------------------------
ArithmeticError Traceback (most recent call last)
/home/fredrik/sage/<ipython console> in <module>()
/home/fredrik/sage/local/lib/python2.6/site-packages/sage/structure/element.so in sage.structure.element.RingElement.__mul__ (sage/structure/element.c:11428)()
/home/fredrik/sage/local/lib/python2.6/site-packages/sage/structure/coerce.so in sage.structure.coerce.CoercionModel_cache_maps.bin_op (sage/structure/coerce.c:6123)()
/home/fredrik/sage/local/lib/python2.6/site-packages/sage/structure/element.so in sage.structure.element.RingElement.__mul__ (sage/structure/element.c:11356)()
/home/fredrik/sage/local/lib/python2.6/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression._mul_ (sage/symbolic/expression.cpp:11042)()
ArithmeticError: x*Infinity with non real x encountered.
</pre>en-usSagehttps://trac.sagemath.org/chrome/site/logo_sagemath_trac.png
https://trac.sagemath.org/ticket/9548
Trac 1.1.6mmezzarobbaSun, 02 Feb 2014 11:40:02 GMTmilestone set
https://trac.sagemath.org/ticket/9548#comment:1
https://trac.sagemath.org/ticket/9548#comment:1
<ul>
<li><strong>milestone</strong>
set to <em>sage-wishlist</em>
</li>
</ul>
<p>
<code>I*Infinity</code> now returns an element of the symbolic ring. I'm leaving the ticket open (as a wishlist item), though, since it would probably make sense to make infinities with complex direction more similar to ±∞.
</p>
TicketrwsTue, 21 Apr 2015 14:42:19 GMT
https://trac.sagemath.org/ticket/9548#comment:2
https://trac.sagemath.org/ticket/9548#comment:2
<p>
This may be a stupid question but now that we have complex (unsigned) infinity, shouldn't that be the result of <code>I*Infinity</code>?
</p>
TicketmmezzarobbaWed, 22 Apr 2015 09:51:11 GMT
https://trac.sagemath.org/ticket/9548#comment:3
https://trac.sagemath.org/ticket/9548#comment:3
<p>
I don't know. It would definitely be useful to be able to write things like integrals from 0 to i∞, (1+i)∞, or exp(iθ)∞. Whether <code>I*infinity</code> should return on of these “directional” infinities or unsigned infinity is another question. Without thinking, I'd say <code>I*PlusInfinity()</code> should return the former and <code>I*UnsignedInfinity()</code> the latter.
</p>
Ticket