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Submitted by : (unknown) at: 2007-11-17T22:13:48-08:00 (10 years ago)
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trigcat.spad

WS> ElementaryFunctionCategory(): Category == with
WS>     log : $ -> $       ++ log(x) returns the natural logarithm of x.
WS>     exp : $ -> $       ++ exp(x) returns %e to the power x.
WS>     "**": ($, $) -> $  ++ x**y returns x to the power y.
WS>  add
WS>    if $ has Monoid then
WS>      x ** y == exp(y * log x)

etc

The more such stuff I see, the better is my live experience,
the more efficient is bug identification progress.

Much thanks!

Vladimir


Sunday, January 16, 2005, 7:08:49 PM, you write:

WS> The error apparently comes from EXPR where the implementation is
WS>   x**y == exp(y * log(x))

WS> so exp^log(x) is computed as
 
WS>   exp(log(x) * log(exp))

WS> which should be ok, but then the system handles log exp and tries to 
simplify it
WS> to the identity map, and not finding the argument.

WS> William
WS> ---

>> 
>> Simpler:
>> 
>> (1) -> exp^3
>> 
>>            3
>>    (1)  exp
>>                                    Type: Polynomial Integer
>> (2) -> a^log(x)
>> 
>>          log(x)
>>    (2)  a
>>                                    Type: Expression Integer
>> (3) -> exp^log(x)
>> 
>>    >> System error:
>>    Cannot take first of an empty list
>> 
>> protected-symbol-warn called with (NIL)
>>






------------------------------------------------------------


prior post information --Mon, 17 Jan 2005 22:40:21 -0600

On the other hand, even though as Vladimir Bondareko reported:

> integrate(log^log(z), z)
> 
>    >> System error:
>    Cannot take first of an empty list

(14) -> log^(log(z))

 Function Selection for log
      Arguments: VARIABLE z
   -> no appropriate log found in Variable z
   -> no appropriate log found in Symbol
   -> no appropriate log found in Variable z
   -> no appropriate log found in Symbol

 Modemaps from Associated Packages
   no modemaps

 Remaining General Modemaps
   [1] FortranExpression(D1,D2,D3) -> FortranExpression(D1,D2,D3)
            from FortranExpression(D1,D2,D3)
            if D1: LIST SYMBOL and D2: LIST SYMBOL and D3 has FMTC
   [2] D -> D from D if D has ELEMFUN

 [1]  signature:   EXPR INT -> EXPR INT
      implemented: slot $$ from EXPR INT


 Function Selection for ^
      Arguments: (VARIABLE log,EXPR INT)

 [1]  signature:   (EXPR INT,EXPR INT) -> EXPR INT
      implemented: slot $$$ from EXPR INT


            log(z)
   (14)  log
                                        Type: Expression Integer

(17) -> log^exp(x)

 Function Selection for exp
      Arguments: VARIABLE x

 [1]  signature:   EXPR INT -> EXPR INT
      implemented: slot $$ from EXPR INT


 Function Selection for ^
      Arguments: (VARIABLE log,EXPR INT)

 [1]  signature:   (EXPR INT,EXPR INT) -> EXPR INT
      implemented: slot $$$ from EXPR INT


              x
            %e
   (17)  log
                                         Type: Expression Integer

-----------------------------------------------------------------------
Note that both works, and note that when looking for the function ^, the
interpreter recognized VARIABLE log.
-----------------------------------------------------------------------
(17) -> exp^log(x)

 Function Selection for log
      Arguments: VARIABLE x

 [1]  signature:   EXPR INT -> EXPR INT
      implemented: slot $$ from EXPR INT


 Function Selection for ^
      Arguments: (SYMBOL,EXPR INT)

 [1]  signature:   (EXPR INT,EXPR INT) -> EXPR INT
      implemented: slot $$$ from EXPR INT


   >> System error:
   Cannot take first of an empty list

protected-symbol-warn called with (NIL)

-----------------------------------------------------------------------
Note that  that when looking for the function ^, the interpreter recognized exp
as a SYMBOL, not a VARIABLE as in the case of log.
-----------------------------------------------------------------------

   (18)  log
                                         Type: Variable log
(19) -> exp

   (19)  exp
                                         Type: Symbol

-----------------------------------------------------------------------
On the other hand, "correcting" the difference does not help
-----------------------------------------------------------------------
(3) -> exp:=exp::Variable(exp)

   (3)  exp
                                           Type: Variable exp
(4) -> exp^log(x)

 Function Selection for log
      Arguments: VARIABLE x

 [1]  signature:   EXPR INT -> EXPR INT
      implemented: slot $$ from EXPR INT


 Function Selection for ^
      Arguments: (VARIABLE exp,EXPR INT)

 [1]  signature:   (EXPR INT,EXPR INT) -> EXPR INT
      implemented: slot $$$ from EXPR INT


   >> System error:
   Cannot take first of an empty list

protected-symbol-warn called with (NIL)
(4) -> exp

   (4)  exp
                                  Type: Variable exp

(5) )clear all

(1) -> exp(log(x)*log(exp))

          log(exp)log(x)
   (1)  %e
                                  Type: Expression Integer

The implementation x**y = exp(y*log(x)) seems not to be the problem.  Clearly
this points to an interpreter bug due to different treatment for log and exp
that runs deep. The error messages originates from lisp, so it may be an error
in LISP (such as a missing quote).

Whether the original 

   integrate(log^log(z),z)

is related to this is not clear.

Bug already existed in NAG version. So may be one of the known ones.






property change --Mon, 17 Jan 2005 22:40:32 -0600

Status: closed => open 




... --kratt6, Fri, 28 Dec 2007 14:31:14 -0800

Category: Axiom Mathematics => Axiom Library 




fixed in FriCAS revision 393 --kratt6, Sat, 27 Sep 2008 00:08:20 -0700

Status: open => fixed somewhere 




Fixed in OpenAxiom --gdr, Mon, 13 Oct 2008 19:43:26 -0700





From Fricas --alfredo, Thu, 16 Oct 2008 13:26:18 -0700

http://fricas.svn.sourceforge.net/viewvc/fricas?view=rev&revision=393



... --alfredo, Thu, 16 Oct 2008 13:26:57 -0700

Status: fixed somewhere => fix proposed 




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