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Diff for /OpenXM/doc/Papers/rims2004-noro.tex between version 1.1 and 1.2

version 1.1, 2004/12/10 07:52:37 version 1.2, 2004/12/11 09:12:23
Line 60  $$m_i(x_1,\dots,x_i)=c_{d_i} x_i^{d_i}+c_{d_{i-1}}(x_1
Line 60  $$m_i(x_1,\dots,x_i)=c_{d_i} x_i^{d_i}+c_{d_{i-1}}(x_1
 $B$H$9$k(B. $B$3$N$H$-(B, $G=\{m_1,\ldots,m_n\}$ $B$O(B,  $B$H$9$k(B. $B$3$N$H$-(B, $G=\{m_1,\ldots,m_n\}$ $B$O(B,
 $x_n > x_{n-1} > \cdots > x_1$ $B$J$k<-=q<0=g=x$K4X$9$k(B $I$ $B$N%0%l%V%J!<4pDl$H$J$C$F$$$k(B.  $x_n > x_{n-1} > \cdots > x_1$ $B$J$k<-=q<0=g=x$K4X$9$k(B $I$ $B$N%0%l%V%J!<4pDl$H$J$C$F$$$k(B.
 $Q[X]/I$ $B$N85(B $h(x) \bmod I$ $B$KBP$7(B,  $Q[X]/I$ $B$N85(B $h(x) \bmod I$ $B$KBP$7(B,
 $h_0 \equiv h \bmod I$, $\deg_{x_i}(h_0) < d_i$ $B$J$k(B $h_i$ $B$O(B  $h_0 \equiv h \bmod I$, $\deg_{x_i}(h_0) < d_i$ $B$J$k(B $h_0$ $B$O(B
 $G$ $B$K4X$9$k@55,7A(B $\NF_G(h)$ $B$KEy$7$$(B.  $G$ $B$K4X$9$k@55,7A(B $\NF_G(h)$ $B$KEy$7$$(B.
   
 $h_0$ $B$O(B, $B%0%l%V%J!<4pDl$r;}$A=P$9$^$G$b$J$/(B, 1 $BJQ?tB?9`<0$N>jM>7W;;$K(B  $h_0$ $B$O(B, $B%0%l%V%J!<4pDl$r;}$A=P$9$^$G$b$J$/(B, 1 $BJQ?tB?9`<0$N>jM>7W;;$K(B
Line 162  $J =\langle B \rangle \subset R = F[x_1,\ldots,x_n]$
Line 162  $J =\langle B \rangle \subset R = F[x_1,\ldots,x_n]$
 $B$r(B $R$ $B$N??$N%$%G%"%k$H$9$k(B. $<$ $B$r(B $R$ $B$N9`=g=x$H$9$k(B. $R$ $B$N9`=g=x(B $<_F$ $B$r(B $<$ $B$*$h$S(B  $B$r(B $R$ $B$N??$N%$%G%"%k$H$9$k(B. $<$ $B$r(B $R$ $B$N9`=g=x$H$9$k(B. $R$ $B$N9`=g=x(B $<_F$ $B$r(B $<$ $B$*$h$S(B
 $F$ $B$N(B $t_1 < \cdots < t_l$ $B$J$k<-=q<0=g=x$+$i$J$k%V%m%C%/=g=x(B  $F$ $B$N(B $t_1 < \cdots < t_l$ $B$J$k<-=q<0=g=x$+$i$J$k%V%m%C%/=g=x(B
 ($t_1^{a_1}\cdots t_l^{a_l} <_F x_1^{b_1}\cdots x_n^{b_n}$)  ($t_1^{a_1}\cdots t_l^{a_l} <_F x_1^{b_1}\cdots x_n^{b_n}$)
 $B$H$9$k(B. $B$3$N$H$-(B, $B_F = B \cup \{m_1,\ldots,m_l\}$ $B$N(B $<_F$ $B$K4X$9$k(B  $B$H$9$k(B. $B$3$N$H$-(B, $B_F = B \cup \{m_1,\ldots,m_l\}$ $B$N@8@.$9$k%$%G%"%k(B
   $B$N(B $<_F$ $B$K4X$9$k(B
 $B%0%l%V%J!<4pDl(B $G_F$ $B$N85$N$&$AJQ?t(B $x_1,\ldots,x_n$ $B$r4^$`$b$N$N=89g(B  $B%0%l%V%J!<4pDl(B $G_F$ $B$N85$N$&$AJQ?t(B $x_1,\ldots,x_n$ $B$r4^$`$b$N$N=89g(B
 $G$ $B$O(B, $J$ $B$N(B $<$ $B$K4X$9$k%0%l%V%J!<4pDl$H$J$k(B. $G_F$ $B$,4JLs(B  $G$ $B$O(B, $J$ $B$N(B $<$ $B$K4X$9$k%0%l%V%J!<4pDl$H$J$k(B. $G_F$ $B$,4JLs(B
 $B%0%l%V%J!<4pDl$J$i$P(B, $G$ $B$N85$NF,9`$O(B $t_1,\ldots,t_l$ $B$r4^$^$J$$(B.  $B%0%l%V%J!<4pDl$J$i$P(B, $G$ $B$N85$NF,9`$O(B $t_1,\ldots,t_l$ $B$r4^$^$J$$(B.
Line 253  typedef struct oDAlg {
Line 254  typedef struct oDAlg {
   
 $B8=:_$N;n83E*<BAu$O(B, {\tt nd\_gr} $B$*$h$S(B {\tt nd\_gr\_trace} $B$r(B, $BF~NOB?(B  $B8=:_$N;n83E*<BAu$O(B, {\tt nd\_gr} $B$*$h$S(B {\tt nd\_gr\_trace} $B$r(B, $BF~NOB?(B
 $B9`<0=89g$K:G>.B?9`<0$rDI2C$7$F<B9T$7(B, $BA0@a$G=R$Y$?$h$&$JJQ99(B (monic $B2=(B)  $B9`<0=89g$K:G>.B?9`<0$rDI2C$7$F<B9T$7(B, $BA0@a$G=R$Y$?$h$&$JJQ99(B (monic $B2=(B)
 $B$r2C$($k(B, $B$H$$$&7A$G9T$C$F$$$k(B. $B$3$l$KBP$7(B, $BBe?tE*?t$r40A4$K78?t$K<h$j(B  $B$r2C$($k(B, $B$H$$$&7A$G9T$C$F$$$k(B. $BF~NO$O(B, {\tt Alg} $B7?$r78?t$K4^$`(B
   $BB?9`<0=89g$G$h$$(B. $BNc$($P(B $\langle \sqrt{2}x^2+(\sqrt{2}+\sqrt{3})xy+\sqrt{3}y^2-\sqrt{3},(\sqrt{2}-2\sqrt{3})x^2+2\sqrt{3}xy+2\sqrt{2}x^2+\sqrt{2}+\sqrt{3}\rangle$ $B$N<-=q<0=g=x%0%l%V%J!<4pDl$N7W;;$O<!$N$h$&$K$9$l$P$h$$(B.
   \begin{verbatim}
   [0] S2=newalg(x^2-2);
   (#0)
   [1] S3=newalg(x^2-3);
   (#1)
   [2] F1=S2*x^2+(S2+S3)*x*y+S3*y^2-S3$
   F2=(S2-2*S3)*x^2+2*S3*x*y+2*S2*x^2+S2+S3]$
   [3] nd_gr_trace([F1,F2],[x,y],1,1,2);
   [90*y^4+(-21*#0*#1-246)*y^2+(16*#0*#1+144),
   20*x+(15*#0*#1-60)*y^3+(-7*#0*#1+83)*y]
   \end{verbatim}
   $BFbItE*$K$O(B, $BBe?tE*?t$O(B, $B85$NB?9`<0JQ?t$HF1Ey$K07$o$l(B, $B@55,2=7W;;$OM-M}?tBN(B
   $B>e$G9T$o$l$k(B. monic $B2=$N:]$K$N$_(B, $BK\Mh$N78?t$,Be?tE*?t(B ({\tt DAlg $B7?(B}) $B$H(B
   $B$7$F<h$j=P$5$l(B, $B5U857W;;$J$I$,9T$o$l$k(B.
   $B$3$l$KBP$7(B, $BBe?tE*?t$r40A4$K78?t$K<h$j(B
 $B9~$s$G(B, $B78?t$K4X$7$F4{$K=R$Y$?$h$&$J4JLs2=$*$h$S5U857W;;$r9T$&$H$$$&J}(B  $B9~$s$G(B, $B78?t$K4X$7$F4{$K=R$Y$?$h$&$J4JLs2=$*$h$S5U857W;;$r9T$&$H$$$&J}(B
 $BK!$b9M$($i$l$k(B. $BA0<T$N>l9g(B, $B4JLs2=$,(B $\Q$ $B>e$G9T$o$l$k$N$G(B, $B4{$K<BAu$7(B  $BK!$b9M$($i$l$k(B. $BA0<T$N>l9g(B, $B4JLs2=$,(B $\Q$ $B>e$G9T$o$l$k$N$G(B, $B4{$K<BAu$7(B
 $B$F$"$k(B, $B78?t$N(B content $B=|5n$,<+F0E*$KE,MQ$5$l$k(B.  sugar $BCM$K(B, $BBe?tE*?t(B  $B$F$"$k(B, $B78?t$N(B content $B=|5n$,<+F0E*$KE,MQ$5$l$k(B.  sugar $BCM$K(B, $BBe?tE*?t(B
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