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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 1 of 2

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Editor: test1 Time: 2014/05/06 19:02:58 GMT+0
Note:

changed:
-
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.


From kratt6 Tue Jan 29 11:29:48 -0800 2008
From: kratt6
Date: Tue, 29 Jan 2008 11:29:48 -0800
Subject: 
Message-ID: <20080129112948-0800@axiom-wiki.newsynthesis.org>

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::
\begin{axiom}
setSimplifyDenomsFlag(true)
integrate(2*z*sqrt(sqrt(2*z*z+2*sqrt(2)*z+2)+z+sqrt(2)),z)
\end{axiom}

(Vladimir 48)

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

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)

$\label{eq2}{\left({\left({ \begin{array}{@{}l} \displaystyle {{\left({ \begin{array}{@{}l} \displaystyle { \begin{array}{@{}l} \displaystyle 2 \ \cdot \ \ \displaystyle z \ \cdot \ \ \displaystyle {\sqrt{2}}$

(2)

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

(Vladimir 48)