===================================================================
RCS file: /home/cvs/OpenXM/doc/compalg/bib.tex,v
retrieving revision 1.1.1.1
retrieving revision 1.4
diff -u -p -r1.1.1.1 -r1.4
--- OpenXM/doc/compalg/bib.tex	2000/03/01 02:25:51	1.1.1.1
+++ OpenXM/doc/compalg/bib.tex	2001/02/27 08:07:24	1.4
@@ -1,3 +1,4 @@
+%$OpenXM: OpenXM/doc/compalg/bib.tex,v 1.3 2000/03/28 02:02:29 noro Exp $
 \begin{thebibliography}{99}
 \bibitem{ABBOTT}
 Abbott, J.A. et al, Factorisation of Polynomials: Old Ideas and Recent Results.
@@ -88,6 +89,11 @@ Giovini, A., Mora, T., Nielsi, G., Robbiano, L., Trave
 sugar cube, please'' OR Selection strategies in the Buchberger
 algorithm.  Proc. ISSAC '91, 49-54.
 
+\bibitem{HOEIJ}
+van Hoeij, M., Factoring polynomials and the knapsack problem.
+To appear in Journal of Number Theory. The preprint is available
+from {\tt http://euclid.math.fsu.edu/\verb+~+hoeij/papers.html}.
+
 \bibitem{KR}
 $B%+!<%K%O%s(B, B.W., $B%j%C%A!<(B, D.M., $B%W%m%0%i%_%s%08@8l(B C $BBh(B 2 $BHG(B. 
 $B6&N)=PHG(B (1989).
@@ -96,6 +102,10 @@ algorithm.  Proc. ISSAC '91, 49-54.
 Knuth, D.E., The Art of Computer Programming, Vol. 2. 
 Seminumerical Algorithms, 2nd ed. Addison-Wesley (1981).
 
+\bibitem{LENSTRA}
+Lenstra, A.K., Lenstra, H.W., Lob\'asz, Factoring polynomials with
+rational coefficients, Math, Ann. 261 (1982), 515-534.
+
 \bibitem{SUB}
 Loos, R., Generalized Polynomial Remainder Sequences.
 Computing, Suppl. 4 (1982), 115-137.
@@ -118,7 +128,7 @@ Computation of replicable functions on Risa/Asir.
 Proc. PASCO'97, ACM Press (1997), 130-138.
 
 \bibitem{NS}
-Noro, M. et al, Asir User's Manual, Edition4.2 for  Asir-20000124.
+Noro, M. et al, Asir.
 
 {\tt ftp://archives.cs.ehime-u.ac.jp/pub/asir2000}
 
@@ -223,8 +233,8 @@ gmp} \cite{GMP} $B$OBh(B 3 $B>O$G=R$Y$?%"%k%4%j%:%`
 $B>JN,$7$F$"$k$N$G(B, $BN}=,LdBj$H$7$F2r$$$F$_$l$P=|;;%"%k%4%j%:%`$N;EAH$_(B
 $B$,$h$/J,$+$k$H;W$&(B. $B$3$l$i$OA4$F(B \cite{KNUTH} $B$K>ZL@$,$"$k(B. 
 $B@0?t(B GCD $B$K$D$$$F$J$K$b=R$Y$J$+$C$?$,(B, Euclid $B8_=|K!$NB>$K(B binary
-GCD $B%"%k%4%j%:%`$H$h$P$l$k%?%$%W$N%"%k%4%j%:%`$,$"$j(B, $B%O!<%I%&%'%"$N(B
-$B=|;;$rMQ$$$J$$$?$a9bB.$K<B9T$G$-$k(B. $B$3$l$K4X$7$F$O$d$O$j(B \cite{KNUTH}
+GCD $B%"%k%4%j%:%`$H$h$P$l$k%?%$%W$N%"%k%4%j%:%`$,$"$j(B, $BG\@:EY@0?t=|;;(B
+$B$rMQ$$$J$$$?$a9bB.$K<B9T$G$-$k(B. $B$3$l$K4X$7$F$O$d$O$j(B \cite{KNUTH}
 $B$K2r@b$5$l$F$$$k(B. $B$^$?(B, $B:G6a$3$N%?%$%W$N%"%k%4%j%:%`$r$5$i$K?J2=(B
 $B$5$;$?$b$N$,Ds0F$5$l$F$$$k(B. $B$3$l$K$D$$$F$O(B \cite{BMOD} $B;2>H(B. 
 
@@ -260,7 +270,15 @@ GCD $B%"%k%4%j%:%`$H$h$P$l$k%?%$%W$N%"%k%4%j%:%`$,$"$
 $B2r$b(B, $B?t3X$K$*$1$k<B83%D!<%k$H$7$F7W;;5!Be?t%7%9%F%`$rMQ$$$k>l9g$KBgJQ(B
 $BM-8z$J5!G=$G$"$k(B. $B$3$N>O$NFbMF$N$&$A(B, $BM-8BBN(B, $BM-M}?tBN>e$N0lJQ?tB?9`<0(B
 $B$N0x?tJ,2r$K4X$7$F$O(B \cite{KNUTH}, $BB?JQ?tB?9`<0$N0x?tJ,2r$K4X$7$F$O(B
-\cite{SASAKI} $B$"$k$$$O(B \cite{GEDDES} $B$r;2>H(B. 
+\cite{SASAKI} $B$"$k$$$O(B \cite{GEDDES} $B$r;2>H(B. $B$J$*(B, $B%"%k%4%j%:%`(B 
+\ref{zassenhaus} $B$O(B $BJ,2r$5$l$kB?9`<0$N<!?t(B $n$ $B$K4X$7$F:G0-7W;;NL$,(B 
+$O(2^n)$ $B$H$J$k$,(B, LLL $B%"%k%4%j%:%`(B $B$rMQ$$$kB?9`<0;~4V%"%k%4%j%:%`$,(B 
+\cite{LENSTRA} $B$K$h$jDs0F$5$l$F$$$k(B. $B$?$@$7$3$N%"%k%4%j%:%`$O<BMQE*$H(B
+$B$O$$$($:(B, $B0lHL$K$O%"%k%4%j%:%`(B \ref{zassenhaus}$B$,MQ$$$i$l$F$-$?(B. $B$4$/(B
+$B:G6a(B, $B0[$J$k4QE@$+$i(B LLL $B%"%k%4%j%:%`$rMQ$$$kJ}K!$,(B \cite{HOEIJ} 
+$B$K$h$jDs0F$5$l$?(B. $B$3$NJ}K!$O(B, $B$3$l$^$G$NJ}K!$G$O;v<B>eJ,2r$,IT2DG=$@$C(B
+$B$?B?9`<0$r8zN($h$/J,2r$9$k$J$I(B, $B<BMQE*$K$bM%$l$F$$$k$3$H$,Js9p$5$l$F$$(B
+$B$k(B.
 
 \noi
 $BBh(B 7 $B>O(B, $BBh(B 8 $B>O(B:
@@ -283,12 +301,12 @@ GCD $B%"%k%4%j%:%`$H$h$P$l$k%?%$%W$N%"%k%4%j%:%`$,$"$
 $BBh(B 10 $B>O(B, $BBh(B 11 $B>O(B:
 
 $B$3$l$i$N>O$O$d$dFC<l$JFbMF$r07$C$F$*$j(B, $B%0%l%V%J4pDl7W;;$r%D!<%k$H$7$F(B
-$BMQ$$$k>l9g$K$OFC$K0U<1$9$kI,MW$O$J$$(B. $B$7$+$7(B, $B$=$l$rC1$J$kJXMx$J%V%i%C%/(B
-$B%\%C%/%9$H9M$($k$H(B, $B$A$g$C$H$7$?LdBj$G$b$9$0$K7W;;$,GKC>$7$F$7$^$&$3$H(B
-$B$OCN$C$F$*$/I,MW$,$"$k(B. $BG$0UF~NO$+$i$N%0%l%V%J4pDl7W;;$K$D$$$F$O(B, 
-$B:G6aDs0F$5$l$?(B $F_4$ $B%"%k%4%j%:%`(B \cite{F} $B$,M-NO$G$"$k$,(B, $B$^$@(B
-$BHFMQ7W;;5!Be?t%7%9%F%`$J$I$K$O<BAu$5$l$F$$$J$$$h$&$G$"$k(B. 
-$B$^$?(B, change of ordering $B$K$D$$$F$O(B, $B$3$3$G=R$Y$?J}K!$NB>$K(B
-\cite{WALK} $B$G0[$J$kJ}K!$,Ds0F$5$l$F$$$k(B. modular change of ordering
-$B$*$h$S(B modular RUR $B$O(B Risa/Asir $B$K<BAu$5$l$F$$$k(B. 
+$BMQ$$$k>l9g$K$OFC$K0U<1$9$kI,MW$O$J$$(B. $B$7$+$7(B, $B$=$l$rC1$J$kJXMx$J%V%i%C(B
+$B%/%\%C%/%9$H9M$($k$H(B, $B$A$g$C$H$7$?LdBj$G$b$9$0$K7W;;$,GKC>$7$F$7$^$&$3(B
+$B$H$OCN$C$F$*$/I,MW$,$"$k(B. $BG$0UF~NO$+$i$N%0%l%V%J4pDl7W;;$K$D$$$F$O(B, $B:G(B
+$B6aDs0F$5$l$?(B $F_4$ $B%"%k%4%j%:%`(B \cite{F} $B$,M-NO$G$"$k$,(B, $B$^$@HFMQ7W;;(B
+$B5!Be?t%7%9%F%`$J$I$K$O<BAu$5$l$F$$$J$$$h$&$G$"$k(B. $B$^$?(B, change of
+ordering $B$K$D$$$F$O(B, $B$3$3$G=R$Y$?J}K!$NB>$K(B Gr\"obner walk $B$H8F$P$l$kJ}K!$,(B 
+\cite{WALK} $B$GDs0F$5$l$F$$$k(B. modular change of ordering$B$*$h$S(B modular
+RUR $B$O(B Risa/Asir $B$K<BAu$5$l$F$$$k(B.