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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 3 of 3

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Editor: test1 Time: 2015/10/13 11:47:58 GMT+0
Note:

changed:
-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 OldWishList, 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

Gruntz algorithm is now implemented and the first two examples work.  The
third example requires symbolic 'max' and 'min'.

For the following limit:

fricas

(1) -> 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 2 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

Gruntz algorithm is now implemented and the first two examples work. The third example requires symbolic max and min.