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> "**": (,ドル $) -> $ ++ 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 --2005年1月17日 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 --2005年1月17日 22:40:32 -0600 Status: closed => open ... --kratt6, 2007年12月28日 14:31:14 -0800 Category: Axiom Mathematics => Axiom Library fixed in FriCAS revision 393 --kratt6, 2008年9月27日 00:08:20 -0700 Status: open => fixed somewhere Fixed in OpenAxiom --gdr, 2008年10月13日 19:43:26 -0700 From Fricas --alfredo, 2008年10月16日 13:26:18 -0700 http://fricas.svn.sourceforge.net/viewvc/fricas?view=rev&revision=393 ... --alfredo, 2008年10月16日 13:26:57 -0700 Status: fixed somewhere => fix proposed