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#345 fails to compute some simple limits ←	↑	→ #347 bug in map$Set

#346 Returns formal integration sign for (1 + tan(x))^(1/3), which is elementary

Edit detail for #346 Returns formal integration sign for (1 + tan(x))^(1/3), which is elementary revision 1 of 4

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Editor: Time: 2007/11/17 22:30:42 GMT-8
Note: typo in title

changed:
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This integral is elementary, but AXIOM returns the input as a formal integral. I thought this indicated a non-elementary result...



From kratt6 Thu Apr 5 15:04:01 -0500 2007
From: kratt6
Date: Thu, 05 Apr 2007 15:04:01 -0500
Subject: Is it really elementary?
Message-ID: <20070405150401-0500@wiki.axiom-developer.org>

I'm not so sure whether this integral really is elementary. Mathematica gives

\begin{verbatim}
In[1]:= Integrate[(1 + Tan[x])^(1/3),x]

                                                          1/3
                        3     6     Log[-#1 + (1 + Tan[x])   ] #1
        RootSum[2 - 2 #1  + #1  & , ----------------------------- & ]
                                                     3
                                              -1 + #1
Out[1]= -------------------------------------------------------------
                                      2

In[2]:= ?RootSum
RootSum[f, form] represents the sum of form[x] for all x that satisfy the
   polynomial equation f[x] == 0.
\end{verbatim}

Is the function "n-th root of some univariate polynomial" elementary?

Martin

From kratt6 Thu Apr 5 15:04:40 -0500 2007
From: kratt6
Date: Thu, 05 Apr 2007 15:04:40 -0500
Subject: typo in title
Message-ID: <20070405150440-0500@wiki.axiom-developer.org>

Name: '#346 Returns format integration sign for (1 + tan(x))^(1/3), which is elementary' => '#346 Returns formal integration sign for (1 + tan(x))^(1/3), which is elementary'

This integral is elementary, but AXIOM returns the input as a formal integral. I thought this indicated a non-elementary result...

Is it really elementary? --kratt6, Thu, 05 Apr 2007 15:04:01 -0500 reply

I'm not so sure whether this integral really is elementary. Mathematica gives

In[1]:= Integrate[(1 + Tan[x])^(1/3),x]<p> 1/3
3 6 Log[-#1 + (1 + Tan[x]<a class= ?) ] #1 RootSum?[2 - 2 #1 + #1 & , ----------------------------- & ]? 3 -1 + #1 Out[1]?= ------------------------------------------------------------- 2

In[2]:= ?RootSum? RootSum?[f, form]? represents the sum of form[x]? for all x that satisfy the polynomial equation f[x]? == 0. " title=" In[1]:= Integrate[(1 + Tan[x]?)^(1/3),x]

1/3 3 6 Log[-#1 + (1 + Tan[x]?) ] #1 RootSum?[2 - 2 #1 + #1 & , ----------------------------- & ]? 3 -1 + #1 Out[1]?= ------------------------------------------------------------- 2

In[2]:= ?RootSum? RootSum?[f, form]? represents the sum of form[x]? for all x that satisfy the polynomial equation f[x]? == 0. " class="equation" src="images/585158006443671166-16.0px.png" align="bottom" Style="vertical-align:text-bottom" width="526" height="248"/>

Is the function "n-th root of some univariate polynomial" elementary?

Martin

typo in title --kratt6, Thu, 05 Apr 2007 15:04:40 -0500 reply

Name: #346 Returns format integration sign for (1 + tan(x))^(1/3), which is elementary => #346 Returns formal integration sign for (1 + tan(x))^(1/3), which is elementary