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#416 Wrong link to papers in home page ←	↑	→ #418 series expansion, but not differentiable

#417 slow integration

Edit detail for #417 slow integration revision 2 of 2

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Editor: test1 Time: 2014/05/06 19:03:37 GMT+0
Note:

added:

From test1 Tue May 6 19:03:37 +0000 2014
From: test1
Date: Tue, 06 May 2014 19:03:37 +0000
Subject: 
Message-ID: <20140506190337+0000@axiom-wiki.newsynthesis.org>

Name: '#417 integration failure' => '#417 slow integration'

Axiom seems to take forever on:

  integrate(sqrt(1-z)*(sqrt(1-sqrt(z))+sqrt(sqrt(z)+1))*(2*sqrt(1-_
          sqrt(z))*sqrt(sqrt(z)+1)*(2*z-1)-2*z-sqrt(z)+1)/z^(3/4), z=0..1, "noPole")

same for the indefinite version. (Vladimir 49)

Martin

This is quite heavy computation and in current implementation it is done in rather inefficient way. So very long compute time is expected. After doing setSimplifyDenomsFlag(true) FriCAS handles the last example below reasonably fast. The first below still needs too much time for MathAction. Also, FriCAS thinks that the first below is nonelementary, so it is left unevaluated). The case above is more complicated.

... --kratt6, Tue, 29 Jan 2008 11:29:48 -0800 reply

Another failure:

  integrate(sqrt(1 - z)*sqrt(sqrt(1 + z^2)), z)

It seems that friCAS finally hangs calling reduce from FiniteDivisor?, which in turn is called by torsionIfCan in PFO. Similar::

fricas

(1) -> setSimplifyDenomsFlag(true)

$\label{eq1} \mbox{\rm false}$

(1)

Type: Boolean

fricas

integrate(2*z*sqrt(sqrt(2*z*z+2*sqrt(2)*z+2)+z+sqrt(2)),z)

$\label{eq2}\frac{{\left({{\left({2 \ z \ {\sqrt{2}}}- 8 \right)}\ {\sqrt{{2 \ z \ {\sqrt{2}}}+{2 \ {{z}^{2}}}+ 2}}}+{8 \ {\sqrt{2}}}+{{1 2}\ {{z}^{3}}}+{4 \ z}\right)}\ {\sqrt{{\sqrt{{2 \ z \ {\sqrt{2}}}+{2 \ {{z}^{2}}}+ 2}}+{\sqrt{2}}+ z}}}{{15}\ z}$

(2)

Type: Union(Expression(Integer),...)

(Vladimir 48)

... --test1, Tue, 06 May 2014 19:03:37 +0000 reply

Name: #417 integration failure => #417 slow integration