Sage: Ticket #18956: incomplete gamma identities
https://trac.sagemath.org/ticket/18956
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This work depends on <a class="closed ticket" href="https://trac.sagemath.org/ticket/16697" title="defect: implement symbolic lower incomplete gamma function (closed: fixed)">#16697</a>, but I'd like to start it now.
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There is a quite simple identity for the incomplete gamma functions:
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<blockquote>
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gamma(x) == gamma_inc_lower(x, y) + gamma_inc(x, y)
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In the mathematica three-argument-gamma notation, this is a bit more clearly true:
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gamma(x, 0, oo) == gamma(x, 0, y) + gamma(x, y, oo)
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What bits of sage do I need to patch to teach the simplifier about this identity? Is this something I can do as a plain-old user? Also, what bits of the documentation cover this aspect of symbolic symplification, from both user and contributor perspectives?
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en-usSagehttps://trac.sagemath.org/chrome/site/logo_sagemath_trac.png
https://trac.sagemath.org/ticket/18956
Trac 1.1.6rwsTue, 28 Jul 2015 06:29:11 GMT
https://trac.sagemath.org/ticket/18956#comment:1
https://trac.sagemath.org/ticket/18956#comment:1
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The <code>simplify*/expand*</code> member functions are covered in <a class="ext-link" href="http://doc.sagemath.org/html/en/reference/calculus/sage/symbolic/expression.html"><span class="icon"></span>http://doc.sagemath.org/html/en/reference/calculus/sage/symbolic/expression.html</a>. Most of them use Maxima. If you have a function that does this rewrite it should be added in this module, and probably also to one of the <code>simplify*/expand*</code> functions. As to the details, best would be a function named <code>expand_xyz</code> because you expand <code>gamma(x)</code>, or <code>rewrite_xyz</code>. The same documentation contains specifics on pattern matching and overall expression manipulation, which is needed here.
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As to the second identity, we still haven't the gamma with three parameters.
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TicketbuckTue, 28 Jul 2015 15:45:01 GMT
https://trac.sagemath.org/ticket/18956#comment:2
https://trac.sagemath.org/ticket/18956#comment:2
<p>
Thanks!
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To be clear, there's just one identity here, with two notations.
I expect if/when we gain a three-argument gamma, the simplification logic won't need to be modified in order to Just Work.
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TicketpaulmassonSat, 02 Jul 2016 02:30:23 GMTcc set
https://trac.sagemath.org/ticket/18956#comment:3
https://trac.sagemath.org/ticket/18956#comment:3
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<li><strong>cc</strong>
<em>paulmasson</em> added
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