Changes http://wiki.axiom-developer.org/329ErrorInIntegerFactor/diff
--
??changed:
-The title of this error report #329 was "Fuzzy error in factor". As first
reported by anonymous, factoring 12399! produces a composite number as a prime
factor. Subsequently, experimenting with different versions of Axiom exhibits
two "small" composite integers that the factor programs in several open source
versions tested are unable to factor and yet the programs prime? give correct
answers. These two numbers are:
+As first reported by anonymous, factoring 12399! produces a composite number
as a prime factor. Subsequently, experimenting with different versions of Axiom
exhibits some "small" composite integers that the factor programs in several
open source versions tested are unable to factor and yet the programs prime?
give correct answers. Two example numbers are:
++added:
+For the record, the factors are: 119643463 = (10111)(11833) and 129864959 =
(11027)(11777).
+
+The alogrithms in identifying a composite number and its factors are
probabilistic.
+The integer factorization algorithms used in Axiom (see PRIMES and INTFACT
packages in intfact.spad) acknowledged these possibilities (that is, when it
reports a number as prime, there is a certain probability that the answer is
wrong; when it reports it as composite, it is always correct) due to the nature
of the algorithm. The implementation for 'prime?' seems better than that for
'factor' and can be guaranteed correct for integers up to 341550071728321 with
probability of error less than 4^(-10) (about 1 in a million). For 'factor',
Lenstra's elliptic curve method is not implemented.
+
There are display problems for this page, apparently independent of the format
type chosen. It seems to be due to some extra LF/CR inserted by the system.
Even manually eliminating some does not help. Please use Edit to view until
display problems are fixed.
??changed:
-Details of original reports follow.
+(Edited) details of original reports follow.
??changed:
-The following is a transcript:
-
+<br>
+The following is a transcript (moved to end to avoid display problems):
+
+Somehow the above results were not all displayed (use edit to view please).
The display problems apparently are not affected by the choice of format type
of this page. I have tried a few of these.
+
+But in the Linux version (patch 50; September 2006), the last factor was
+$119970353 = 10253 \times 11701$ (and both primes were missing from the list,
which according to the Windows version has 1479 distinct prime factors).
+
+In the Linux version (Axiom 3.9, September 2005), the last factor was
$123643253 = 10243 \times 12071$.
+In the Linux version (Axiom 3.0 Beta, February 2005), there were TWO
incomplete factors: 119643463, 129864979 (both were not factorable using
'factor' in this version (that is at least consistent!) AND the Windows version
(this is inconsistent), whereas $119643463 = 10111 \times 11833$ and $129864979
= 11027 \times 11777$ (these primes were listed in the Windows version for
factor factorial 12399). More inconsistencies: prime? reports both of these as
'false' (correct answer). So it appears that the factorization program and the
primality check program are independent.
+
+\begin{axiom}
+factor 119643463
+prime? 119643463
+factor 129864979
+prime? 129864979
+\end{axiom}
+
+<br>
+In the Linux version (October 25, 2004), the last factor was $117661597 =
10651 \times 11047$. This version displays many more messages about loading
domains.
+
+
+Linux versions were run on the same machine under same OS (Fedora 2). Windows
version (November 30, 2004)was run on a different machine.
+
+<br>
\begin{verbatim}
??changed:
-Somehow the above results were not all displayed (use edit to view please).
The display problems apparently are not affected by the choice of format type
of this page. I have tried a few of these.
-
-But in the Linux version (patch 50; September 2006), the last factor was
-$119970353 = 10253 \times 11701$ (and both primes were missing from the list,
which according to the Windows version has 1479 distinct prime factors).
-
-In the Linux version (Axiom 3.9, September 2005), the last factor was
$123643253 = 10243 \times 12071$.
-In the Linux version (Axiom 3.0 Beta, February 2005), there were TWO
incomplete factors: 119643463, 129864979 (both were not factorable using
'factor' in this version (that is at least consistent!) AND the Windows version
(this is inconsistent), whereas $119643463 = 10111 \times 11833$ and $129864979
= 11027 \times 11777$ (these primes were listed in the Windows version for
factor factorial 12399). More inconsistencies: prime? reports both of these as
'false' (correct answer). So it appears that the factorization program and the
primality check program are independent.
-
-\begin{axiom}
-factor 119643463
-prime? 119643463
-factor 129864979
-prime? 129864979
-\end{axiom}
-
-
-In the Linux version (October 25, 2004), the last factor was $117661597 =
10651 \times 11047$. This version displays many more messages about loading
domains.
-
-
-Linux versions were run on the same machine under same OS (Fedora 2). Windows
version (November 30, 2004)was run on a different machine.
+On 17 Dec 2006 23:04:44 +0100
+ Francois Maltey <[EMAIL PROTECTED]> wrote:
+>I use my own compiled axiom without change for integer
+>and so.
+>I have a random reponse :
+>
+>petoncle:~/Axiom$ axiom -noht
+> AXIOM Computer Algebra System
+> Version: Axiom (September 2006)
+> Timestamp: Saturday October 28, 2006 at
+>12:18:07
+>-----------------------------------------------------------------------
+>
+>I test :
+>
+>[#factors (117661597+0*i) for i in 1..1000] -- there
+>are 1 and 2 factors
+>reduce (+, [#factors (117661597+0*i) for i in 1..1000])
+> -- around 1650
+>
+>The exact solution is 2000 of corse.
+
+
+
+
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