8.10.8 `nd_gr', `nd_gr_trace', `nd_f4', `nd_f4_trace', `nd_weyl_gr', `nd_weyl_gr_trace'
---------------------------------------------------------------------------------------

nd_gr(PLIST,VLIST,P,ORDER)
nd_gr_trace(PLIST,VLIST,HOMO,P,ORDER)
nd_f4(PLIST,VLIST,MODULAR,ORDER)
nd_f4_trace(PLIST,VLIST,HOMO,P,ORDER)

nd_weyl_gr(PLIST,VLIST,P,ORDER)
nd_weyl_gr_trace(PLIST,VLIST,HOMO,P,ORDER)
     :: $B%0%l%V%J4pDl$N7W;;(B ($BAH$_9~$_H!?t(B)

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

PLIST  VLIST
     $B%j%9%H(B

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

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

MODULAR
     $B%U%i%0$^$?$OAG?t(B

   * $B$3$l$i$NH!?t$O(B, $B%0%l%V%J4pDl7W;;AH$_9~$_4X?t$N?7<BAu$G$"$k(B.

   * `nd_gr' $B$O(B, `p' $B$,(B 0 $B$N$H$-M-M}?tBN>e$N(B Buchberger
     $B%"%k%4%j%:%`$r<B9T$9$k(B. `p' $B$,(B 2 $B0J>e$N<+A3?t$N$H$-(B, GF(p) $B>e$N(B
     Buchberger $B%"%k%4%j%:%`$r<B9T$9$k(B.

   * `nd_gr_trace' $B$*$h$S(B `nd_f4_trace' $B$OM-M}?tBN>e$G(B trace
     $B%"%k%4%j%:%`$r<B9T$9$k(B.  `p' $B$,(B 0 $B$^$?$O(B 1 $B$N$H$-(B,
     $B<+F0E*$KA*$P$l$?AG?t$rMQ$$$F(B, $B@.8y$9$k(B $B$^$G(B trace
     $B%"%k%4%j%:%`$r<B9T$9$k(B.  `p' $B$,(B 2 $B0J>e$N$H$-(B, trace $B$O(BGF(p)
     $B>e$G7W;;$5$l$k(B. trace $B%"%k%4%j%:%`(B $B$,<:GT$7$?>l9g(B 0 $B$,JV$5$l$k(B.
     `p' $B$,Ii$N>l9g(B, $B%0%l%V%J4pDl%A%'%C%/$O(B $B9T$o$J$$(B. $B$3$N>l9g(B, `p' $B$,(B
     -1 $B$J$i$P<+F0E*$KA*$P$l$?AG?t$,(B,
     $B$=$l0J30$O;XDj$5$l$?AG?t$rMQ$$$F%0%l%V%J4pDl8uJd$N7W;;$,9T$o$l$k(B.
     `nd_f4_trace' $B$O(B, $B3FA4<!?t$K$D$$$F(B, $B$"$kM-8BBN>e$G(B F4 $B%"%k%4%j%:%`(B
     $B$G9T$C$?7k2L$r$b$H$K(B, $B$=$NM-8BBN>e$G(B 0 $B$G$J$$4pDl$rM?$($k(B
     S-$BB?9`<0$N$_$r(B $BMQ$$$F9TNs@8@.$r9T$$(B,
     $B$=$NA4<!?t$K$*$1$k4pDl$r@8@.$9$kJ}K!$G$"$k(B. $BF@$i$l$k(B
     $BB?9`<0=89g$O$d$O$j%0%l%V%J4pDl8uJd$G$"$j(B, `nd_gr_trace' $B$HF1MM$N(B
     $B%A%'%C%/$,9T$o$l$k(B.

   * `nd_f4' $B$O(B `modular' $B$,(B 0 $B$N$H$-M-M}?tBN>e$N(B, `modular' $B$,(B
     $B%^%7%s%5%$%:AG?t$N$H$-M-8BBN>e$N(B F4 $B%"%k%4%j%:%`$r<B9T$9$k(B.

   * `nd_weyl_gr', `nd_weyl_gr_trace' $B$O(B Weyl $BBe?tMQ$G$"$k(B.

   * $B$$$:$l$N4X?t$b(B, $BM-M}4X?tBN>e$N7W;;$OL$BP1~$G$"$k(B.

   * $B0lHL$K(B `dp_gr_main', `dp_gr_mod_main' $B$h$j9bB.$G$"$k$,(B,
     $BFC$KM-8BBN>e$N>l9g82Cx$G$"$k(B.

     [38] load("cyclic")$
     [49] C=cyclic(7)$
     [50] V=vars(C)$
     [51] cputime(1)$
     [52] dp_gr_mod_main(C,V,0,31991,0)$
     26.06sec + gc : 0.313sec(26.4sec)
     [53] nd_gr(C,V,31991,0)$
     ndv_alloc=1477188
     5.737sec + gc : 0.1837sec(5.921sec)
     [54] dp_f4_mod_main(C,V,31991,0)$
     3.51sec + gc : 0.7109sec(4.221sec)
     [55] nd_f4(C,V,31991,0)$
     1.906sec + gc : 0.126sec(2.032sec)

$B;2>H(B
     *Note `dp_ord': dp_ord, *Note `dp_gr_flags dp_gr_print':
     dp_gr_flags dp_gr_print, *Note `$B7W;;$*$h$SI=<($N@)8f(B':
     $B7W;;$*$h$SI=<($N@)8f(B.

