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Diff for /OpenXM/src/asir-doc/parts/groebner.texi between version 1.19 and 1.22

version 1.19, 2016/08/29 04:56:58 version 1.22, 2019/03/29 04:54:25
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 @comment $OpenXM: OpenXM/src/asir-doc/parts/groebner.texi,v 1.18 2016/03/24 20:58:50 noro Exp $  @comment $OpenXM: OpenXM/src/asir-doc/parts/groebner.texi,v 1.21 2018/09/06 05:42:43 takayama Exp $
 \BJP  \BJP
 @node $B%0%l%V%J4pDl$N7W;;(B,,, Top  @node $B%0%l%V%J4pDl$N7W;;(B,,, Top
 @chapter $B%0%l%V%J4pDl$N7W;;(B  @chapter $B%0%l%V%J4pDl$N7W;;(B
Line 220  the head term and the head coefficient respectively.
Line 220  the head term and the head coefficient respectively.
 \E  \E
 @end table  @end table
   
   @noindent
   ChangeLog
   @itemize @bullet
 \BJP  \BJP
   @item $BJ,;6I=8=B?9`<0$OG$0U$N%*%V%8%'%/%H$r78?t$K$b$F$k$h$&$K$J$C$?(B.
   $B$^$?2C72$N(Bk$B@.J,$NMWAG$r<!$N7A<0(B <<d0,d1,...:k>> $B$GI=8=$9$k$h$&$K$J$C$?(B (2017-08-31).
   \E
   \BEG
   @item Distributed polynomials accept objects as coefficients.
   The k-th element of a free module is expressed as <<d0,d1,...:k>> (2017-08-31).
   \E
   @item
   1.15 algnum.c,
   1.53 ctrl.c,
   1.66 dp-supp.c,
   1.105 dp.c,
   1.73 gr.c,
   1.4 reduct.c,
   1.16 _distm.c,
   1.17 dalg.c,
   1.52 dist.c,
   1.20 distm.c,
   1.8  gmpq.c,
   1.238 engine/nd.c,
   1.102  ca.h,
   1.411  version.h,
   1.28 cpexpr.c,
   1.42 pexpr.c,
   1.20 pexpr_body.c,
   1.40 spexpr.c,
   1.27 arith.c,
   1.77 eval.c,
   1.56 parse.h,
   1.37 parse.y,
   1.8 stdio.c,
   1.31 plotf.c
   @end itemize
   
   \BJP
 @node $B%U%!%$%k$NFI$_9~$_(B,,, $B%0%l%V%J4pDl$N7W;;(B  @node $B%U%!%$%k$NFI$_9~$_(B,,, $B%0%l%V%J4pDl$N7W;;(B
 @section $B%U%!%$%k$NFI$_9~$_(B  @section $B%U%!%$%k$NFI$_9~$_(B
 \E  \E
Line 1465  Computation of the global b function is implemented as
Line 1503  Computation of the global b function is implemented as
 * 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::
 * dp_f4_main dp_f4_mod_main dp_weyl_f4_main dp_weyl_f4_mod_main::  * dp_f4_main dp_f4_mod_main dp_weyl_f4_main dp_weyl_f4_mod_main::
 * nd_gr nd_gr_trace nd_f4 nd_f4_trace nd_weyl_gr nd_weyl_gr_trace::  * nd_gr nd_gr_trace nd_f4 nd_f4_trace nd_weyl_gr nd_weyl_gr_trace::
   * nd_gr_postproc nd_weyl_gr_postproc::
 * dp_gr_flags dp_gr_print::  * dp_gr_flags dp_gr_print::
 * dp_ord::  * dp_ord::
 * dp_set_weight dp_set_top_weight dp_weyl_set_weight::  * dp_set_weight dp_set_top_weight dp_weyl_set_weight::
Line 1531  Computation of the global b function is implemented as
Line 1570  Computation of the global b function is implemented as
 @item  @item
 $BI8=`%i%$%V%i%j$N(B @samp{gr} $B$GDj5A$5$l$F$$$k(B.  $BI8=`%i%$%V%i%j$N(B @samp{gr} $B$GDj5A$5$l$F$$$k(B.
 @item  @item
   gr $B$rL>A0$K4^$`4X?t$O8=:_%a%s%F$5$l$F$$$J$$(B. @code{nd_gr}$B7O$N4X?t$rBe$o$j$KMxMQ$9$Y$-$G$"$k(B(@fref{nd_gr nd_gr_trace nd_f4 nd_f4_trace nd_weyl_gr nd_weyl_gr_trace}).
   @item
 $B$$$:$l$b(B, $BB?9`<0%j%9%H(B @var{plist} $B$N(B, $BJQ?t=g=x(B @var{vlist}, $B9`=g=x7?(B  $B$$$:$l$b(B, $BB?9`<0%j%9%H(B @var{plist} $B$N(B, $BJQ?t=g=x(B @var{vlist}, $B9`=g=x7?(B
 @var{order} $B$K4X$9$k%0%l%V%J4pDl$r5a$a$k(B. @code{gr()}, @code{hgr()}  @var{order} $B$K4X$9$k%0%l%V%J4pDl$r5a$a$k(B. @code{gr()}, @code{hgr()}
 $B$O(B $BM-M}?t78?t(B, @code{gr_mod()} $B$O(B GF(@var{p}) $B78?t$H$7$F7W;;$9$k(B.  $B$O(B $BM-M}?t78?t(B, @code{gr_mod()} $B$O(B GF(@var{p}) $B78?t$H$7$F7W;;$9$k(B.
Line 1562  CPU $B;~4V$G$"$j(B, $B$3$NH!?t$N>l9g$O$[$H$s$IDL?.$
Line 1603  CPU $B;~4V$G$"$j(B, $B$3$NH!?t$N>l9g$O$[$H$s$IDL?.$
 @item  @item
 These functions are defined in @samp{gr} in the standard library  These functions are defined in @samp{gr} in the standard library
 directory.  directory.
   @item
   Functions of which names contains gr are obsolted.
   Functions of @code{nd_gr} families should be used (@fref{nd_gr nd_gr_trace nd_f4 nd_f4_trace nd_weyl_gr nd_weyl_gr_trace}).
 @item  @item
 They compute a Groebner basis of a polynomial list @var{plist} with  They compute a Groebner basis of a polynomial list @var{plist} with
 respect to the variable order @var{vlist} and the order type @var{order}.  respect to the variable order @var{vlist} and the order type @var{order}.
Line 2450  ndv_alloc=1477188
Line 2494  ndv_alloc=1477188
 \JP @fref{$B7W;;$*$h$SI=<($N@)8f(B}.  \JP @fref{$B7W;;$*$h$SI=<($N@)8f(B}.
 \EG @fref{Controlling Groebner basis computations}  \EG @fref{Controlling Groebner basis computations}
 @end table  @end table
   
   \JP @node nd_gr_postproc nd_weyl_gr_postproc,,, $B%0%l%V%J4pDl$K4X$9$kH!?t(B
   \EG @node nd_gr_postproc nd_weyl_gr_postproc,,, Functions for Groebner basis computation
   @subsection @code{nd_gr_postproc}, @code{nd_weyl_gr_postproc}
   @findex nd_gr_postproc
   @findex nd_weyl_gr_postproc
   
   @table @t
   @item nd_gr_postproc(@var{plist},@var{vlist},@var{p},@var{order},@var{check})
   @itemx nd_weyl_gr_postproc(@var{plist},@var{vlist},@var{p},@var{order},@var{check})
   \JP :: $B%0%l%V%J4pDl8uJd$N%A%'%C%/$*$h$SAj8_4JLs(B
   \EG :: Check of Groebner basis candidate and inter-reduction
   @end table
   
   @table @var
   @item return
   \JP $B%j%9%H(B $B$^$?$O(B 0
   \EG list or 0
   @item plist  vlist
   \JP $B%j%9%H(B
   \EG list
   @item p
   \JP $BAG?t$^$?$O(B 0
   \EG prime or 0
   @item order
   \JP $B?t(B, $B%j%9%H$^$?$O9TNs(B
   \EG number, list or matrix
   @item check
   \JP 0 $B$^$?$O(B 1
   \EG 0 or 1
   @end table
   
   @itemize @bullet
   \BJP
   @item
   $B%0%l%V%J4pDl(B($B8uJd(B)$B$NAj8_4JLs$r9T$&(B.
   @item
   @code{nd_weyl_gr_postproc} $B$O(B Weyl $BBe?tMQ$G$"$k(B.
   @item
   @var{check=1} $B$N>l9g(B, @var{plist} $B$,(B, @var{vlist}, @var{p}, @var{order} $B$G;XDj$5$l$kB?9`<04D(B, $B9`=g=x$G%0%l%V%J!<4pDl$K$J$C$F$$$k$+(B
   $B$N%A%'%C%/$b9T$&(B.
   @item
   $B@F<!2=$7$F7W;;$7$?%0%l%V%J!<4pDl$rHs@F<!2=$7$?$b$N$rAj8_4JLs$r9T$&(B, CRT $B$G7W;;$7$?%0%l%V%J!<4pDl8uJd$N%A%'%C%/$r9T$&$J$I$N>l9g$KMQ$$$k(B.
   \E
   \BEG
   @item
   Perform the inter-reduction for a Groebner basis (candidate).
   @item
   @code{nd_weyl_gr_postproc} is for Weyl algebra.
   @item
   If @var{check=1} then the check whether @var{plist} is a Groebner basis with respect to a term order in a polynomial ring
   or Weyl algebra specified by @var{vlist}, @var{p} and @var{order}.
   @item
   This function is used for inter-reduction of a non-reduced Groebner basis that is obtained by dehomogenizing a Groebner basis
   computed via homogenization, or Groebner basis check of a Groebner basis candidate computed by CRT.
   \E
   @end itemize
   
   @example
   afo
   @end example
   
 \JP @node dp_gr_flags dp_gr_print,,, $B%0%l%V%J4pDl$K4X$9$kH!?t(B  \JP @node dp_gr_flags dp_gr_print,,, $B%0%l%V%J4pDl$K4X$9$kH!?t(B
 \EG @node dp_gr_flags dp_gr_print,,, Functions for Groebner basis computation  \EG @node dp_gr_flags dp_gr_print,,, Functions for Groebner basis computation
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