| version 1.18, 2016/03/24 20:58:50 |
version 1.21, 2018/09/06 05:42:43 |
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| @comment $OpenXM: OpenXM/src/asir-doc/parts/groebner.texi,v 1.17 2006/09/06 23:53:31 noro Exp $ |
@comment $OpenXM: OpenXM/src/asir-doc/parts/groebner.texi,v 1.20 2017/08/31 04:54:36 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 201 In an @b{Asir} session, it is displayed in the form li |
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| Line 201 In an @b{Asir} session, it is displayed in the form li |
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| \EG and also can be input in such a form. |
\EG and also can be input in such a form. |
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| \BJP |
\BJP |
| @itemx $BF,C19`<0(B (head monomial) |
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| @item $BF,9`(B (head term) |
@item $BF,9`(B (head term) |
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@itemx $BF,C19`<0(B (head monomial) |
| @itemx $BF,78?t(B (head coefficient) |
@itemx $BF,78?t(B (head coefficient) |
| $BJ,;6I=8=B?9`<0$K$*$1$k3FC19`<0$O(B, $B9`=g=x$K$h$j@0Ns$5$l$k(B. $B$3$N;~=g(B |
$BJ,;6I=8=B?9`<0$K$*$1$k3FC19`<0$O(B, $B9`=g=x$K$h$j@0Ns$5$l$k(B. $B$3$N;~=g(B |
| $B=x:GBg$NC19`<0$rF,C19`<0(B, $B$=$l$K8=$l$k9`(B, $B78?t$r$=$l$>$lF,9`(B, $BF,78?t(B |
$B=x:GBg$NC19`<0$rF,C19`<0(B, $B$=$l$K8=$l$k9`(B, $B78?t$r$=$l$>$lF,9`(B, $BF,78?t(B |
| $B$H8F$V(B. |
$B$H8F$V(B. |
| \E |
\E |
| \BEG |
\BEG |
| @itemx head monomial |
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| @item head term |
@item head term |
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@itemx head monomial |
| @itemx head coefficient |
@itemx head coefficient |
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| Monomials in a distributed polynomial is sorted by a total order. |
Monomials in a distributed polynomial is sorted by a total order. |
| Line 220 the head term and the head coefficient respectively. |
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| Line 220 the head term and the head coefficient respectively. |
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| \E |
\E |
| @end table |
@end table |
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@noindent |
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ChangeLog |
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@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$?(B. |
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$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). |
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\E |
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\BEG |
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@item Distributed polynomials accept objects as coefficients. |
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The k-th element of a free module is expressed as <<d0,d1,...:k>> (2017-08-31). |
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\E |
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@item |
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1.15 algnum.c, |
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1.53 ctrl.c, |
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1.66 dp-supp.c, |
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1.105 dp.c, |
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1.73 gr.c, |
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1.4 reduct.c, |
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1.16 _distm.c, |
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1.17 dalg.c, |
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1.52 dist.c, |
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1.20 distm.c, |
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1.8 gmpq.c, |
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1.238 engine/nd.c, |
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1.102 ca.h, |
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1.411 version.h, |
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1.28 cpexpr.c, |
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1.42 pexpr.c, |
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1.20 pexpr_body.c, |
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1.40 spexpr.c, |
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1.27 arith.c, |
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1.77 eval.c, |
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1.56 parse.h, |
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1.37 parse.y, |
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1.8 stdio.c, |
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1.31 plotf.c |
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@end itemize |
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\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 1531 Computation of the global b function is implemented as |
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| Line 1569 Computation of the global b function is implemented as |
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| @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}). |
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@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?.$ |
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| Line 1602 CPU $B;~4V$G$"$j(B, $B$3$NH!?t$N>l9g$O$[$H$s$IDL?.$ |
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| @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. |
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@item |
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Functions of which names contains gr are obsolted. |
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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 2320 except for lack of the argument for controlling homoge |
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| Line 2363 except for lack of the argument for controlling homoge |
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| @itemx nd_gr_trace(@var{plist},@var{vlist},@var{homo},@var{p},@var{order}) |
@itemx nd_gr_trace(@var{plist},@var{vlist},@var{homo},@var{p},@var{order}) |
| @itemx nd_f4(@var{plist},@var{vlist},@var{modular},@var{order}) |
@itemx nd_f4(@var{plist},@var{vlist},@var{modular},@var{order}) |
| @itemx nd_f4_trace(@var{plist},@var{vlist},@var{homo},@var{p},@var{order}) |
@itemx nd_f4_trace(@var{plist},@var{vlist},@var{homo},@var{p},@var{order}) |
| @item nd_weyl_gr(@var{plist},@var{vlist},@var{p},@var{order}) |
@itemx nd_weyl_gr(@var{plist},@var{vlist},@var{p},@var{order}) |
| @itemx nd_weyl_gr_trace(@var{plist},@var{vlist},@var{homo},@var{p},@var{order}) |
@itemx nd_weyl_gr_trace(@var{plist},@var{vlist},@var{homo},@var{p},@var{order}) |
| \JP :: $B%0%l%V%J4pDl$N7W;;(B ($BAH$_9~$_H!?t(B) |
\JP :: $B%0%l%V%J4pDl$N7W;;(B ($BAH$_9~$_H!?t(B) |
| \EG :: Groebner basis computation (built-in functions) |
\EG :: Groebner basis computation (built-in functions) |
| Line 2973 These are used internally in @code{hgr()} etc. |
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| Line 3016 These are used internally in @code{hgr()} etc. |
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| into an integral distributed polynomial such that GCD of all its coefficients |
into an integral distributed polynomial such that GCD of all its coefficients |
| is 1. |
is 1. |
| \E |
\E |
| @itemx dp_prim(@var{dpoly}) |
@item dp_prim(@var{dpoly}) |
| \JP :: $BM-M}<0G\$7$F78?t$r@0?t78?tB?9`<078?t$+$D78?t$NB?9`<0(B GCD $B$r(B 1 $B$K$9$k(B. |
\JP :: $BM-M}<0G\$7$F78?t$r@0?t78?tB?9`<078?t$+$D78?t$NB?9`<0(B GCD $B$r(B 1 $B$K$9$k(B. |
| \BEG |
\BEG |
| :: Converts a distributed polynomial @var{poly} with rational function |
:: Converts a distributed polynomial @var{poly} with rational function |
| Line 3900 refer to @code{dp_true_nf()} and @code{dp_true_nf_mod( |
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| Line 3943 refer to @code{dp_true_nf()} and @code{dp_true_nf_mod( |
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| @fref{dp_ptod}, |
@fref{dp_ptod}, |
| @fref{dp_dtop}, |
@fref{dp_dtop}, |
| @fref{dp_ord}, |
@fref{dp_ord}, |
| @fref{dp_nf dp_nf_mod dp_true_nf dp_true_nf_mod}. |
@fref{dp_nf dp_nf_mod dp_true_nf dp_true_nf_mod dp_weyl_nf dp_weyl_nf_mod}. |
| @end table |
@end table |
| |
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| \JP @node p_terms,,, $B%0%l%V%J4pDl$K4X$9$kH!?t(B |
\JP @node p_terms,,, $B%0%l%V%J4pDl$K4X$9$kH!?t(B |
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