[Axiom-developer] [#23 using exp as a symbol in ** ] prior post information

[anonymous]

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.



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