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Diff for /OpenXM/src/asir-doc/parts/groebner.texi between version 1.18 and 1.19

version 1.18, 2016/03/24 20:58:50 version 1.19, 2016/08/29 04:56:58
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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 1.18 2016/03/24 20:58:50 noro 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
Line 201  In an @b{Asir} session, it is displayed in the form li
 \EG and also can be input in such a form.  \EG and also can be input in such a form.
   
 \BJP  \BJP
 @itemx $BF,C19`<0(B (head monomial)  
 @item $BF,9`(B (head term)  @item $BF,9`(B (head term)
   @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  
 @item head term  @item head term
   @itemx head monomial
 @itemx head coefficient  @itemx head coefficient
   
 Monomials in a distributed polynomial is sorted by a total order.  Monomials in a distributed polynomial is sorted by a total order.
Line 2320  except for lack of the argument for controlling homoge
Line 2320  except for lack of the argument for controlling homoge
 @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  is 1.
Line 2973  is 1.
 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(
Line 3900  refer to @code{dp_true_nf()} and @code{dp_true_nf_mod(
 @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
   
 \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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