version 1.3, 2000/03/28 02:02:29 |
version 1.4, 2001/02/27 08:07:24 |
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%$OpenXM: OpenXM/doc/compalg/bib.tex,v 1.3 2000/03/28 02:02:29 noro Exp $ |
\begin{thebibliography}{99} |
\begin{thebibliography}{99} |
\bibitem{ABBOTT} |
\bibitem{ABBOTT} |
Abbott, J.A. et al, Factorisation of Polynomials: Old Ideas and Recent Results. |
Abbott, J.A. et al, Factorisation of Polynomials: Old Ideas and Recent Results. |
Line 89 Giovini, A., Mora, T., Nielsi, G., Robbiano, L., Trave |
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Line 89 Giovini, A., Mora, T., Nielsi, G., Robbiano, L., Trave |
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sugar cube, please'' OR Selection strategies in the Buchberger |
sugar cube, please'' OR Selection strategies in the Buchberger |
algorithm. Proc. ISSAC '91, 49-54. |
algorithm. Proc. ISSAC '91, 49-54. |
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\bibitem{HOEIJ} |
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van Hoeij, M., Factoring polynomials and the knapsack problem. |
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To appear in Journal of Number Theory. The preprint is available |
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from {\tt http://euclid.math.fsu.edu/\verb+~+hoeij/papers.html}. |
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\bibitem{KR} |
\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. |
$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). |
$B6&N)=PHG(B (1989). |
Line 97 algorithm. Proc. ISSAC '91, 49-54. |
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Line 102 algorithm. Proc. ISSAC '91, 49-54. |
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Knuth, D.E., The Art of Computer Programming, Vol. 2. |
Knuth, D.E., The Art of Computer Programming, Vol. 2. |
Seminumerical Algorithms, 2nd ed. Addison-Wesley (1981). |
Seminumerical Algorithms, 2nd ed. Addison-Wesley (1981). |
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\bibitem{LENSTRA} |
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Lenstra, A.K., Lenstra, H.W., Lob\'asz, Factoring polynomials with |
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rational coefficients, Math, Ann. 261 (1982), 515-534. |
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\bibitem{SUB} |
\bibitem{SUB} |
Loos, R., Generalized Polynomial Remainder Sequences. |
Loos, R., Generalized Polynomial Remainder Sequences. |
Computing, Suppl. 4 (1982), 115-137. |
Computing, Suppl. 4 (1982), 115-137. |
Line 261 GCD $B%"%k%4%j%:%`$H$h$P$l$k%?%$%W$N%"%k%4%j%:%`$,$"$ |
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Line 270 GCD $B%"%k%4%j%:%`$H$h$P$l$k%?%$%W$N%"%k%4%j%:%`$,$"$ |
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$B2r$b(B, $B?t3X$K$*$1$k<B83%D!<%k$H$7$F7W;;5!Be?t%7%9%F%`$rMQ$$$k>l9g$KBgJQ(B |
$B2r$b(B, $B?t3X$K$*$1$k<B83%D!<%k$H$7$F7W;;5!Be?t%7%9%F%`$rMQ$$$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 |
$BM-8z$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 |
$B$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 |
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\ref{zassenhaus} $B$O(B $BJ,2r$5$l$kB?9`<0$N<!?t(B $n$ $B$K4X$7$F:G0-7W;;NL$,(B |
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$O(2^n)$ $B$H$J$k$,(B, LLL $B%"%k%4%j%:%`(B $B$rMQ$$$kB?9`<0;~4V%"%k%4%j%:%`$,(B |
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\cite{LENSTRA} $B$K$h$jDs0F$5$l$F$$$k(B. $B$?$@$7$3$N%"%k%4%j%:%`$O<BMQE*$H(B |
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$B$O$$$($:(B, $B0lHL$K$O%"%k%4%j%:%`(B \ref{zassenhaus}$B$,MQ$$$i$l$F$-$?(B. $B$4$/(B |
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$B:G6a(B, $B0[$J$k4QE@$+$i(B LLL $B%"%k%4%j%:%`$rMQ$$$kJ}K!$,(B \cite{HOEIJ} |
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$B$K$h$jDs0F$5$l$?(B. $B$3$NJ}K!$O(B, $B$3$l$^$G$NJ}K!$G$O;v<B>eJ,2r$,IT2DG=$@$C(B |
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$B$?B?9`<0$r8zN($h$/J,2r$9$k$J$I(B, $B<BMQE*$K$bM%$l$F$$$k$3$H$,Js9p$5$l$F$$(B |
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$B$k(B. |
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\noi |
\noi |
$BBh(B 7 $B>O(B, $BBh(B 8 $B>O(B: |
$BBh(B 7 $B>O(B, $BBh(B 8 $B>O(B: |
Line 284 GCD $B%"%k%4%j%:%`$H$h$P$l$k%?%$%W$N%"%k%4%j%:%`$,$"$ |
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Line 301 GCD $B%"%k%4%j%:%`$H$h$P$l$k%?%$%W$N%"%k%4%j%:%`$,$"$ |
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$BBh(B 10 $B>O(B, $BBh(B 11 $B>O(B: |
$BBh(B 10 $B>O(B, $BBh(B 11 $B>O(B: |
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$B$3$l$i$N>O$O$d$dFC<l$JFbMF$r07$C$F$*$j(B, $B%0%l%V%J4pDl7W;;$r%D!<%k$H$7$F(B |
$B$3$l$i$N>O$O$d$dFC<l$JFbMF$r07$C$F$*$j(B, $B%0%l%V%J4pDl7W;;$r%D!<%k$H$7$F(B |
$BMQ$$$k>l9g$K$OFC$K0U<1$9$kI,MW$O$J$$(B. $B$7$+$7(B, $B$=$l$rC1$J$kJXMx$J%V%i%C%/(B |
$BMQ$$$k>l9g$K$OFC$K0U<1$9$kI,MW$O$J$$(B. $B$7$+$7(B, $B$=$l$rC1$J$kJXMx$J%V%i%C(B |
$B%\%C%/%9$H9M$($k$H(B, $B$A$g$C$H$7$?LdBj$G$b$9$0$K7W;;$,GKC>$7$F$7$^$&$3$H(B |
$B%/%\%C%/%9$H9M$($k$H(B, $B$A$g$C$H$7$?LdBj$G$b$9$0$K7W;;$,GKC>$7$F$7$^$&$3(B |
$B$OCN$C$F$*$/I,MW$,$"$k(B. $BG$0UF~NO$+$i$N%0%l%V%J4pDl7W;;$K$D$$$F$O(B, |
$B$H$OCN$C$F$*$/I,MW$,$"$k(B. $BG$0UF~NO$+$i$N%0%l%V%J4pDl7W;;$K$D$$$F$O(B, $B:G(B |
$B:G6aDs0F$5$l$?(B $F_4$ $B%"%k%4%j%:%`(B \cite{F} $B$,M-NO$G$"$k$,(B, $B$^$@(B |
$B6aDs0F$5$l$?(B $F_4$ $B%"%k%4%j%:%`(B \cite{F} $B$,M-NO$G$"$k$,(B, $B$^$@HFMQ7W;;(B |
$BHFMQ7W;;5!Be?t%7%9%F%`$J$I$K$O<BAu$5$l$F$$$J$$$h$&$G$"$k(B. |
$B5!Be?t%7%9%F%`$J$I$K$O<BAu$5$l$F$$$J$$$h$&$G$"$k(B. $B$^$?(B, change of |
$B$^$?(B, change of ordering $B$K$D$$$F$O(B, $B$3$3$G=R$Y$?J}K!$NB>$K(B |
ordering $B$K$D$$$F$O(B, $B$3$3$G=R$Y$?J}K!$NB>$K(B Gr\"obner walk $B$H8F$P$l$kJ}K!$,(B |
\cite{WALK} $B$G0[$J$kJ}K!$,Ds0F$5$l$F$$$k(B. modular change of ordering |
\cite{WALK} $B$GDs0F$5$l$F$$$k(B. modular change of ordering$B$*$h$S(B modular |
$B$*$h$S(B modular RUR $B$O(B Risa/Asir $B$K<BAu$5$l$F$$$k(B. |
RUR $B$O(B Risa/Asir $B$K<BAu$5$l$F$$$k(B. |
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