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

 From: Karl Hegbloom Subject: [Axiom-developer] [Bug?] "error in library; negative log" Date: Fri, 11 Nov 2005 21:15:12 -0800

```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
Source License: LGPL(gcl,gmp), GPL(unexec,bfd)
Binary License:  GPL due to GPL'ed components: (READLINE BFD UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter

Use (help) to get some basic information on how to use GCL.
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
Re-reading category.daase
Re-reading browse.daase
RationalInterpolationAlgorithms is now explicitly exposed in frame
initial
RationalInterpolationAlgorithms will be automatically loaded when
needed from
/home/karlheg/src/Mathematics/Axiom/Lib/RINTERPA.NRLIB/code
RationalInterpolation is now explicitly exposed in frame initial
RationalInterpolation will be automatically loaded when needed from
/home/karlheg/src/Mathematics/Axiom/Lib/RINTERP.NRLIB/code
PolynomialCommonDenominator is now explicitly exposed in frame
initial
PolynomialCommonDenominator will be automatically loaded when needed
from /home/karlheg/src/Mathematics/Axiom/Lib/PCDEN.NRLIB/code
GuessPolynomial is now explicitly exposed in frame initial
GuessPolynomial will be automatically loaded when needed from
/home/karlheg/src/Mathematics/Axiom/Lib/GUESSP.NRLIB/code
GuessInteger is now explicitly exposed in frame initial
GuessInteger will be automatically loaded when needed from
/home/karlheg/src/Mathematics/Axiom/Lib/GUESSINT.NRLIB/code
Guess is now explicitly exposed in frame initial
Guess will be automatically loaded when needed from
/home/karlheg/src/Mathematics/Axiom/Lib/GUESS.NRLIB/code
Loading /usr/lib/axiom-20050901/autoload/bc-matrix.
Loading /usr/lib/axiom-20050901/autoload/bc-misc.
Loading /usr/lib/axiom-20050901/autoload/bc-solve.
Loading /usr/lib/axiom-20050901/autoload/bc-util.
Loading /usr/lib/axiom-20050901/autoload/ht-util.
Loading /usr/lib/axiom-20050901/autoload/htsetvar.
Loading /usr/lib/axiom-20050901/autoload/ht-root.
Loading /usr/lib/axiom-20050901/autoload/br-con.
Loading /usr/lib/axiom-20050901/autoload/br-data.
Loading /usr/lib/axiom-20050901/autoload/showimp.
Loading /usr/lib/axiom-20050901/autoload/br-op1.
Loading /usr/lib/axiom-20050901/autoload/br-op2.
Loading /usr/lib/axiom-20050901/autoload/br-search.
Loading /usr/lib/axiom-20050901/autoload/br-util.
Loading /usr/lib/axiom-20050901/autoload/topics.
Loading /usr/lib/axiom-20050901/autoload/br-prof.
Loading /usr/lib/axiom-20050901/autoload/br-saturn.
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
Loading /usr/lib/axiom-20050901/algebra/IAN.o for domain
InnerAlgebraicNumber
Loading /usr/lib/axiom-20050901/algebra/ACFS-.o for domain
AlgebraicallyClosedFunctionSpace&
Loading /usr/lib/axiom-20050901/algebra/FS-.o for domain
FunctionSpace&
Loading /usr/lib/axiom-20050901/algebra/COMMONOP.o for package
CommonOperators
Loading /usr/lib/axiom-20050901/algebra/KDAGG-.o for domain
KeyedDictionary&
Loading /usr/lib/axiom-20050901/algebra/DIAGG-.o for domain
Dictionary&
Loading /usr/lib/axiom-20050901/algebra/BOP1.o for package
BasicOperatorFunctions1
Loading /usr/lib/axiom-20050901/algebra/ACF-.o for domain
AlgebraicallyClosedField&
Compiling body of rule f to compute value of type Expression Float
Loading /usr/lib/axiom-20050901/algebra/EQ.o for domain Equation
Loading /usr/lib/axiom-20050901/algebra/ES-.o for domain
ExpressionSpace&
Loading /usr/lib/axiom-20050901/algebra/FRETRCT-.o for domain
FullyRetractableTo&
Loading /usr/lib/axiom-20050901/algebra/EVALAB-.o for domain
Evalable&
Loading /usr/lib/axiom-20050901/algebra/FPS-.o for domain
FloatingPointSystem&
Loading /usr/lib/axiom-20050901/algebra/RNS-.o for domain
RealNumberSystem&
Loading /usr/lib/axiom-20050901/algebra/POLYCATQ.o for package
PolynomialCategoryQuotientFunctions
Loading /usr/lib/axiom-20050901/algebra/COMBF.o for package
CombinatorialFunction
Loading /usr/lib/axiom-20050901/algebra/EQ2.o for package
EquationFunctions2
Loading /usr/lib/axiom-20050901/algebra/POLY2.o for package
PolynomialFunctions2
Loading /usr/lib/axiom-20050901/algebra/POLYLIFT.o for package
PolynomialCategoryLifting
Loading /usr/lib/axiom-20050901/algebra/FSAGG-.o for domain
FiniteSetAggregate&
Loading /usr/lib/axiom-20050901/algebra/FLASORT.o for package
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) -> ```

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