Interesting. I'll look at it further. --Tim
On 9/24/2010 2:46 PM, Dr.-Ing. Ingo D. Rullhusen wrote:
Hello,
perhaps i have found a bug in the limit operation. I am using
AXIOM Computer Algebra System
Version: Axiom (July 2010)
Timestamp: Wednesday August 18, 2010 at 11:16:49
on a x86_64 with linux. There seems to be an error in the sign, if you
compare the limit result with the de L'Hospital one.
Example
-- problem with limit
)clear
Z:=sqrt(a^2+h^2)-a
N:=a*sqrt(a^2+h^2) - a^2 - h^2
limit( Z/N, h=0 )
-- this seems to be wrong!
-- because de L'Hospital says
dZ:=differentiate( Z, h, 2 )
dN:=differentiate( N, h, 2 )
eval(dZ/dN,h=0)
-- which seems to be right (see graph): opposite sign!
EndExample
which generates the output:
AXIOM Computer Algebra System
Version: Axiom (July 2010)
Timestamp: Wednesday August 18, 2010 at 11:16:49
-----------------------------------------------------------------------------
Issue )copyright to view copyright notices.
Issue )summary for a summary of useful system commands.
Issue )quit to leave AXIOM and return to shell.
Visit http://axiom-developer.org for more information
-----------------------------------------------------------------------------
Re-reading compress.daase Re-reading interp.daase
Re-reading operation.daase
Re-reading category.daase
Re-reading browse.daase
(1) ->
(1) -> )read hos.input
-- problem with limit
)clear
Use )clear all to clear everything in the workspace. Use )clear
completely to clear everything in the workspace and internal
tables. Other )clear keyword arguments are
modes
operations
properties
types
values
or abbreviations thereof. Issue )clear? for more information.
Z:=sqrt(a^2+h^2)-a
+-------+
| 2 2
(1) \|h + a - a
Type: Expression
Integer
N:=a*sqrt(a^2+h^2) - a^2 - h^2
+-------+
| 2 2 2 2
(2) a\|h + a - h - a
Type: Expression
Integer
limit( Z/N, h=0 )
1
(3) -
a
Type: Union(OrderedCompletion Expression
Integer,...)
-- this seems to be wrong!
-- because de L'Hospital says
dZ:=differentiate( Z, h, 2 )
2
a
(4) -------------------
+-------+
2 2 | 2 2
(h + a )\|h + a
Type: Expression
Integer
dN:=differentiate( N, h, 2 )
+-------+
2 2 | 2 2 3
(- 2h - 2a )\|h + a + a
(5) ----------------------------
+-------+
2 2 | 2 2
(h + a )\|h + a
Type: Expression
Integer
eval(dZ/dN,h=0)
1
(6) - ----------
+--+
| 2
2\|a - a
Type: Expression
Integer
(7) ->
(7) ->
(see sign)
Thanks
Ingo
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