Sage: Ticket #22699: simplify arccos+arcsin
https://trac.sagemath.org/ticket/22699
<pre class="wiki">assume(x>-1)
assume(x<1)
arcsin(x)+arccos(x)
</pre><p>
should, in principle, over the reals, simplify to pi/2 on the interval -1 to 1. I'm sure numerous problems would result with branches and step functions and whatnot if one actually attempted to implement this ... but in a wishlist world, one can dream!
</p>
<p>
Upstream at <a class="ext-link" href="https://sourceforge.net/p/maxima/bugs/3298/"><span class="icon"></span>https://sourceforge.net/p/maxima/bugs/3298/</a>
</p>
en-usSagehttps://trac.sagemath.org/chrome/site/logo_sagemath_trac.png
https://trac.sagemath.org/ticket/22699
Trac 1.1.6mforetsWed, 29 Mar 2017 20:46:17 GMT
https://trac.sagemath.org/ticket/22699#comment:1
https://trac.sagemath.org/ticket/22699#comment:1
<p>
not sure if this makes dreams come true, but just in case:
</p>
<pre class="wiki">sage: giac('assume(x>-1 and x<1)')
x
sage: giac('simplify(acos(x)+asin(x))')
1/2*pi
</pre>
TicketkcrismanThu, 30 Mar 2017 01:37:42 GMT
https://trac.sagemath.org/ticket/22699#comment:2
https://trac.sagemath.org/ticket/22699#comment:2
<p>
Ha, nice! This can definitely be part of the solution given that giac is apparently now going to be standard?
</p>
TicketmforetsThu, 30 Mar 2017 05:57:08 GMT
https://trac.sagemath.org/ticket/22699#comment:3
https://trac.sagemath.org/ticket/22699#comment:3
<p>
.. if it makes sense to add interfaces to the simplify function, then i'd be willing to collaborate
</p>
TicketkcrismanThu, 30 Mar 2017 14:08:33 GMTcc set
https://trac.sagemath.org/ticket/22699#comment:4
https://trac.sagemath.org/ticket/22699#comment:4
<ul>
<li><strong>cc</strong>
<em>rws</em> added
</li>
</ul>
<p>
It may, but that would definitely be a different ticket! We have had <code>.simplify()</code> be just sending to Maxima and back for so long it would make quite the changes in our documentation. <code>.simplify_full()</code> all the more so. But maybe it is time for that discussion. rws is currently taking the lead on a lot of this, as you know, so copying him (however, not to suggest this tiny ticket is worth adding giac in that way all by itself).
</p>
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