=================================================================== 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$$$J$$$?$a9bB.$KH(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$*$1$kl9g$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$kB?9`<0$NeJ,2r$,IT2DG=$@$C(B +$B$?B?9`<0$r8zN($h$/J,2r$9$k$J$I(B, $BO(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$dFCl9g$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$K(B -\cite{WALK} $B$G0[$J$kJ}K!$,Ds0F$5$l$F$$$k(B. modular change of ordering -$B$*$h$S(B modular RUR $B$O(B Risa/Asir $B$Kl9g$K$OFC$K0U<1$9$kI,MW$O$J$$(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$$$F$O(B, $B:G(B +$B6aDs0F$5$l$?(B $F_4$ $B%"%k%4%j%:%`(B \cite{F} $B$,M-NO$G$"$k$,(B, $B$^$@HFMQ7W;;(B +$B5!Be?t%7%9%F%`$J$I$K$O$K(B Gr\"obner walk $B$H8F$P$l$kJ}K!$,(B +\cite{WALK} $B$GDs0F$5$l$F$$$k(B. modular change of ordering$B$*$h$S(B modular +RUR $B$O(B Risa/Asir $B$K