[Axiom-developer] [Bug?] "error in library; negative log"

[Karl Hegbloom]

Attached is a session log showing an error that I receive while
attempting to produce a sequence from an expression in Axiom.  Maxima
seems to have no trouble with the similar expression, and computing the
value of the expression by hand, as you can see, seems to work fine
also.

Another problem I have is that taking the limit of an expression
containing (-1)^n always returns "failed", where my TI-89 Titanium
calculator will give a finite limit.  For example:

 limit( 2 + (-2/%pi)^n, n=%plusInfinity )  ===> "failed"

... but the TI-89t returns 2.

The TI-89t says that the limit of (-1)^n as n approaches infinity is -1,
implying that it believes that infinity is an odd number.  That kind of
makes sense to me, since if you divide infinity in half, you still have
infinity, and you keep adding 1 to get to infinity, making it odd.  If
infinity is even then the answer should be 1, and if we can't know if
infinity is even or odd, then the answer is uncertain or undefined.

On the other hand, the TI-89t says that lim ( (-1)^n * (n + 1)/n ) is
undefined.  But it already told me that lim (-1)^n = -1, and that lim (n
+ 1)/n = 1.  If the limit of a product is the product of the limits of
the factors, then lim ( (-1)^n * (n + 1)/n ) should be -1, right?

So, who's right?

-- 
Karl Hegbloom <address@hidden>

Q:      What do monsters eat?
A:      Things.

Q:      What do monsters drink?
A:      Coke.  (Because Things go better with Coke.)
% axiom
GCL (GNU Common Lisp)  2.6.7 CLtL1    Sep 26 2005 15:30:02
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                        AXIOM Computer Algebra System 
                     Version: Axiom 3.9 (September 2005)
              Timestamp: Monday September 26, 2005 at 17:32:58 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
 
   Re-reading compress.daase   Re-reading interp.daase
   Re-reading operation.daase
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   Re-reading browse.daase
   RationalInterpolationAlgorithms is now explicitly exposed in frame 
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      needed from 
      /home/karlheg/src/Mathematics/Axiom/Lib/RINTERPA.NRLIB/code
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      /home/karlheg/src/Mathematics/Axiom/Lib/RINTERP.NRLIB/code
   PolynomialCommonDenominator is now explicitly exposed in frame 
      initial 
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      from /home/karlheg/src/Mathematics/Axiom/Lib/PCDEN.NRLIB/code
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   Loading /usr/lib/axiom-20050901/autoload/bc-matrix.
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initial (1) -> 
frame0 (1) -> f == 2.0 + (-2.0/(%pi::Float))**n;
                                                                   Type: Void
frame0 (2) -> [[i,(eval(f,n=i))] for i in 1..20]
   Loading /usr/lib/axiom-20050901/algebra/FLOAT.o for domain Float 
   Loading /usr/lib/axiom-20050901/algebra/HACKPI.o for domain Pi 
   Loading /usr/lib/axiom-20050901/algebra/UPMP.o for package 
      UnivariatePolynomialMultiplicationPackage 
   Loading /usr/lib/axiom-20050901/algebra/EXPR.o for domain Expression
      
   Loading /usr/lib/axiom-20050901/algebra/KERNEL.o for domain Kernel 
   Loading /usr/lib/axiom-20050901/algebra/BOP.o for domain 
      BasicOperator 
   Loading /usr/lib/axiom-20050901/algebra/SCACHE.o for package 
      SortedCache 
   Loading /usr/lib/axiom-20050901/algebra/VOID.o for domain Void 
   Loading /usr/lib/axiom-20050901/algebra/AN.o for domain 
      AlgebraicNumber 
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      InnerAlgebraicNumber 
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      AlgebraicallyClosedFunctionSpace& 
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      FunctionSpace& 
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      CommonOperators 
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      KeyedDictionary& 
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      Dictionary& 
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      BasicOperatorFunctions1 
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      AlgebraicallyClosedField& 
   Compiling body of rule f to compute value of type Expression Float 
   Loading /usr/lib/axiom-20050901/algebra/EQ.o for domain Equation 
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      ExpressionSpace& 
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      FullyRetractableTo& 
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      Evalable& 
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      FloatingPointSystem& 
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      RealNumberSystem& 
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      CombinatorialFunction 
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      EquationFunctions2 
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      FiniteLinearAggregateSort 
   Loading /usr/lib/axiom-20050901/algebra/LIST2MAP.o for package 
      ListToMap 
 
   >> Error detected within library code:
   negative log

frame0 (2) -> f == 2.0 + (-2.0/(%pi::Float))**n;
   Compiled code for f has been cleared.
   1 old definition(s) deleted for function or rule f 
                                                                   Type: Void
frame0 (3) -> [[i,(eval(f,n=i))] for i in 1..20]
   Compiling body of rule f to compute value of type Expression Float 
   Loading /usr/lib/axiom-20050901/algebra/IDPOAMS.o for domain 
      IndexedDirectProductOrderedAbelianMonoidSup 
   Loading /usr/lib/axiom-20050901/algebra/IDPOAM.o for domain 
      IndexedDirectProductOrderedAbelianMonoid 
 
   >> Error detected within library code:
   negative log

frame0 (3) -> f == 2.0 + (-2.0/(%pi::Float))**n;
   Compiled code for f has been cleared.
   1 old definition(s) deleted for function or rule f 
                                                                   Type: Void
frame0 (4) -> [[i,(eval(f,n=i))] for i in 1..20]
   Compiling body of rule f to compute value of type Expression Float 
 
   >> Error detected within library code:
   negative log

frame0 (4) -> f

   Loading /usr/lib/axiom-20050901/algebra/UNISEG.o for domain 
      UniversalSegment 
                                         n
   (4)  (- 0.6366197723 6758134307 55351)  + 2.0
                                                       Type: Expression Float
frame0 (5) -> -2.0/%pi::Float

   (5)  - 0.6366197723 6758134307 55351
                                                                  Type: Float
frame0 (6) -> % ** 2

   (6)  0.4052847345 6935108577 55179
                                                                  Type: Float
frame0 (7) -> 2 + %

   (7)  2.4052847345 6935108577 5518
                                                                  Type: Float
frame0 (8) -> %%(5)**3

   (8)  - 0.2580122754 6559591347 53764
                                                                  Type: Float
frame0 (9) -> 2 + %

   (9)  1.7419877245 3440408652 4624
                                                                  Type: Float
frame0 (10) ->