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#296 PERMGRP should compute cycle indicator polynomial ←	↑	→ #298 undesirable horizontal scroll bar

#297 Wrong values of limit

Edit detail for #297 Wrong values of limit revision 1 of 3

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Editor: Time: 2007/11/17 22:22:56 GMT-8
Note:

changed:
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For the following limit:
\begin{axiom}
limit(exp(exp(2*log(x^5+x)*log(log(x))))/exp(exp(10*log(x)*log(log(x)))), x = %plusInfinity)
\end{axiom}
the correct answer is +infinity.
Simpler version is:
\begin{axiom}
limit(exp(2*log(x^5+x)*log(log(x)))-exp(10*log(x)*log(log(x))), x = %plusInfinity)
\end{axiom}
(again the correct answer is +infinity).

Another problematic limit is:
\begin{axiom}
limit(max(x, exp(x))/log(min(exp(-x), exp(-exp(x)))), x = %plusInfinity)
\end{axiom}
where the correct answer is -1.

BTW both examples are taken from Dominik Gruntz thesis form 1996

Waldek Hebisch

From kratt6 Mon Jun 5 02:10:40 -0500 2006
From: kratt6
Date: Mon, 05 Jun 2006 02:10:40 -0500
Subject: 
Message-ID: <20060605021040-0500@wiki.axiom-developer.org>

Yes, somebody should reorganize the limit package and implement Gruntz algorithm. This is on the WishList, by the way. I believe this is also related to asymptotic expansions as provided by Gdev from Maple, but I'm not sure.

Could you do this?

Martin

For the following limit:

fricas

limit(exp(exp(2*log(x^5+x)*log(log(x))))/exp(exp(10*log(x)*log(log(x)))), x = %plusInfinity)

$\label{eq1}+ \infty$

(1)

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

the correct answer is +infinity. Simpler version is:

fricas

limit(exp(2*log(x^5+x)*log(log(x)))-exp(10*log(x)*log(log(x))), x = %plusInfinity)

$\label{eq2}+ \infty$

(2)

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

(again the correct answer is +infinity).

Another problematic limit is:

fricas

limit(max(x, exp(x))/log(min(exp(-x), exp(-exp(x)))), x = %plusInfinity)

   There are 1 exposed and 2 unexposed library operations named max 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                               )display op max
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named max 
      with argument type(s) 
                                 Variable(x)
                             Expression(Integer)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

where the correct answer is -1.

BTW both examples are taken from Dominik Gruntz thesis form 1996

Waldek Hebisch

... --kratt6, Mon, 05 Jun 2006 02:10:40 -0500 reply

Yes, somebody should reorganize the limit package and implement Gruntz algorithm. This is on the WishList?, by the way. I believe this is also related to asymptotic expansions as provided by Gdev from Maple, but I'm not sure.

Could you do this?

Martin