8.10.2 `lex_hensel', `lex_tl', `tolex', `tolex_d', `tolex_tl'
-------------------------------------------------------------

lex_hensel(PLIST,VLIST1,ORDER,VLIST2,HOMO)
lex_tl(PLIST,VLIST1,ORDER,VLIST2,HOMO)
     :: $B4pDlJQ49$K$h$k<-=q<0=g=x%0%l%V%J4pDl$N7W;;(B

tolex(PLIST,VLIST1,ORDER,VLIST2)
tolex_d(PLIST,VLIST1,ORDER,VLIST2,PROCS)
tolex_tl(PLIST,VLIST1,ORDER,VLIST2,HOMO)
     :: $B%0%l%V%J4pDl$rF~NO$H$9$k(B,
     $B4pDlJQ49$K$h$k<-=q<0=g=x%0%l%V%J4pDl$N7W;;(B

RETURN
     $B%j%9%H(B

PLIST  VLIST1  VLIST2  PROCS
     $B%j%9%H(B

ORDER
     $B?t(B, $B%j%9%H$^$?$O9TNs(B

HOMO
     $B%U%i%0(B

   * $BI8=`%i%$%V%i%j$N(B `gr' $B$GDj5A$5$l$F$$$k(B.

   * `lex_hensel()', `lex_tl()' $B$O(B, $BB?9`<0%j%9%H(B PLIST $B$N(B, $BJQ?t=g=x(B
     VLIST1, $B9`=g=x7?(B ORDER $B$K4X$9$k%0%l%V%J4pDl$r5a$a(B, $B$=$l$r(B,
     $BJQ?t=g=x(B VLIST2 $B$N<-=q<0=g=x%0%l%V%J4pDl$KJQ49$9$k(B.

   * `tolex()', `tolex_tl()' $B$O(B, $BJQ?t=g=x(B VLIST1, $B9`=g=x7?(B ORDER
     $B$K4X$9$k%0%l%V%J4pDl$G$"$k(B $BB?9`<0%j%9%H(B PLIST $B$rJQ?t=g=x(B VLIST2
     $B$N<-=q<0=g=x%0%l%V%J(B $B4pDl$KJQ49$9$k(B.  `tolex_d()' $B$O(B, `tolex()'
     $B$K$*$1$k(B, $B3F4pDl$N7W;;$r(B, $B;R%W%m%;%9(B $B%j%9%H(B PROCS
     $B$N3F%W%m%;%9$KJ,;67W;;$5$;$k(B.

   * `lex_hensel()', `lex_tl()' $B$K$*$$$F$O(B, $B<-=q<0=g=x%0%l%V%J4pDl$N(B
     $B7W;;$O<!$N$h$&$K9T$o$l$k(B. (`[Noro,Yokoyama]' $B;2>H(B.)
       1. VLIST1, ORDER $B$K4X$9$k%0%l%V%J4pDl(B G0 $B$r7W;;$9$k(B.
          (`lex_hensel()' $B$N$_(B. )

       2. G0 $B$N3F85$N(B VLIST2 $B$K4X$9$k<-=q<0=g=x$K$*$1$kF,78?t$r3d$i$J$$(B
          $B$h$&$JAG?t(B P $B$rA*$S(B, GF(P) $B>e$G$N<-=q<0=g=x%0%l%V%J4pDl(B GP
          $B$r7W;;$9$k(B.

       3. GP $B$K8=$l$k$9$Y$F$N9`$N(B, G0 $B$K4X$9$k@55,7A(B NF $B$r7W;;$9$k(B.

       4. GP $B$N3F85(B F $B$K$D$-(B, F $B$N78?t$rL$Dj78?t$G(B, F $B$N3F9`$rBP1~$9$k(B
          NF $B$N85$GCV$-49$((B, $B3F9`$N78?t$r(B 0 $B$HCV$$$?(B,
          $BL$Dj78?t$K4X$9$k@~7AJ}Dx<07O(B LF $B$r:n$k(B.

       5. LF $B$,(B, $BK!(B P $B$G0l0U2r$r;}$D$3$H$rMQ$$$F(B LF $B$N2r$r(B $BK!(B P$B$N2r$+$i(B
          Hensel $B9=@.$K$h$j5a$a$k(B.

       6. $B$9$Y$F$N(B GP $B$N85$K$D$-@~7AJ}Dx<0$,2r$1$?$i$=$N2rA4BN$,5a$a$k(B
          $B<-=q<0=g=x$G$N%0%l%V%J4pDl(B.
          $B$b$7$I$l$+$N@~7AJ}Dx<0$N5a2r$K<:GT$7$?$i(B, P
          $B$r$H$jD>$7$F$d$jD>$9(B.

   * `lex_tl()', `tolex_tl()' $B$K$*$$$F$O(B, $B<-=q<0=g=x%0%l%V%J4pDl$N(B
     $B7W;;$O<!$N$h$&$K9T$o$l$k(B.

       1. VLIST1, ORDER $B$K4X$9$k%0%l%V%J4pDl(B G0 $B$r7W;;$9$k(B.
          (`lex_hensel()' $B$N$_(B. )

       2. G0 $B$,(B 0 $B<!85%7%9%F%`$G$J$$$H$-(B, G0 $B$rF~NO$H$7$F(B, G0 $B$N3F85$N(B
          VLIST2 $B$K4X$9$k<-=q<0=g=x$K$*$1$kF,78?t$r3d$i$J$$(B $B$h$&$JAG?t(B
          P $B$rA*$S(B, P $B$rMQ$$$?(B trace-lifting $B$K$h$j<-=q<0(B
          $B=g=x$N%0%l%V%J4pDl8uJd$r5a$a(B,
          $B$b$75a$^$C$?$J$i%A%'%C%/$J$7$K$=$l$,5a$a$k(B
          $B%0%l%V%J4pDl$H$J$k(B. $B$b$7<:GT$7$?$i(B, P $B$r$H$jD>$7$F$d$jD>$9(B.

       3. G0 $B$,(B 0 $B<!85%7%9%F%`$N$H$-(B, G0 $B$rF~NO$H$7$F(B, $B$^$:(B, VLIST2
          $B$N:G8e$NJQ?t0J30$r>C5n$9$k>C5n=g=x$K$h$j(B $B%0%l%V%J4pDl(B G1
          $B$r7W;;$7(B, $B$=$l$+$i<-=q<0=g=x$N%0%l%V%J4pDl$r(B $B7W;;$9$k(B.
          $B$=$N:](B, $B3F%9%F%C%W$G$O(B, $BF~NO$N3F85$N(B, $B5a$a$k=g=x$K$*$1$k(B
          $BF,78?t$r3d$i$J$$AG?t$rMQ$$$?(B trace-lifting
          $B$G%0%l%V%J4pDl8uJd$r5a$a(B,
          $B$b$75a$^$C$?$i%A%'%C%/$J$7$K$=$l$,$=$N=g=x$G$N%0%l%V%J4pDl$H$J$k(B.

   * $BM-M}<078?t$N7W;;$O(B, `lex_tl()', `tolex_tl()' $B$N$_<u$1IU$1$k(B.

   * `homo' $B$,(B 0 $B$G$J$$>l9g(B, $BFbIt$G5/F0$5$l$k(B Buchberger $B%"%k%4%j%:%`$K(B
     $B$*$$$F(B, $B@F<!2=$,9T$o$l$k(B.

   * `tolex_d()' $B$GI=<($5$l$k;~4V$O(B, $B$3$NH!?t$,<B9T$5$l$F$$$k%W%m%;%9$K(B
     $B$*$$$F9T$o$l$?7W;;$KBP1~$7$F$$$F(B,
     $B;R%W%m%;%9$K$*$1$k;~4V$O4^$^$l$J$$(B.

     [78] K=katsura(5)$
     30msec + gc : 20msec
     [79] V=[u5,u4,u3,u2,u1,u0]$
     0msec
     [80] G0=hgr(K,V,2)$
     91.558sec + gc : 15.583sec
     [81] G1=lex_hensel(K,V,0,V,0)$
     49.049sec + gc : 9.961sec
     [82] G2=lex_tl(K,V,0,V,1)$
     31.186sec + gc : 3.500sec
     [83] gb_comp(G0,G1);
     1
     10msec
     [84] gb_comp(G0,G2);
     1

$B;2>H(B
     *Note `dp_gr_main dp_gr_mod_main dp_gr_f_main dp_weyl_gr_main
     dp_weyl_gr_mod_main dp_weyl_gr_f_main': dp_gr_main dp_gr_mod_main
     dp_gr_f_main dp_weyl_gr_main dp_weyl_gr_mod_main dp_weyl_gr_f_main,
     *Note `dp_ord': dp_ord, *Note `$BJ,;67W;;(B': $BJ,;67W;;(B.

