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Diff for /OpenXM/src/asir-doc/parts/groebner.texi between version 1.2 and 1.3

version 1.2, 1999/12/21 02:47:31 version 1.3, 1999/12/24 04:38:04
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 @comment $OpenXM$  @comment $OpenXM: OpenXM/src/asir-doc/parts/groebner.texi,v 1.2 1999/12/21 02:47:31 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 1239  Refer to the sections for each functions.
Line 1239  Refer to the sections for each functions.
 * katsura hkatsura cyclic hcyclic::  * katsura hkatsura cyclic hcyclic::
 * dp_vtoe dp_etov::  * dp_vtoe dp_etov::
 * lex_hensel_gsl tolex_gsl tolex_gsl_d::  * lex_hensel_gsl tolex_gsl tolex_gsl_d::
   * primadec primedec::
 @end menu  @end menu
   
 \JP @node gr hgr gr_mod,,, $B%0%l%V%J4pDl$K4X$9$kH!?t(B  \JP @node gr hgr gr_mod,,, $B%0%l%V%J4pDl$K4X$9$kH!?t(B
Line 3547  u0^2-u0+2*u4^2+2*u3^2+2*u2^2+2*u1^2+2*u5^2]
Line 3548  u0^2-u0+2*u4^2+2*u3^2+2*u2^2+2*u1^2+2*u5^2]
 @fref{dp_dtop}.  @fref{dp_dtop}.
 @end table  @end table
   
   \JP @node primadec primedec,,, $B%0%l%V%J4pDl$K4X$9$kH!?t(B
   \EG @node primadec primedec,,, Functions for Groebner basis computation
   @subsection @code{primadec}, @code{primedec}
   @findex primadec
   @findex primedec
   
   @table @t
   @item primadec(@var{plist},@var{vlist})
   @item primedec(@var{plist},@var{vlist})
   \JP :: $B%$%G%"%k$NJ,2r(B
   \EG :: Computes decompositions of ideals.
   @end table
   
   @table @var
   @item return
   @itemx plist
   \JP $BB?9`<0%j%9%H(B
   \EG list of polynomials
   @item vlist
   \JP $BJQ?t%j%9%H(B
   \EG list of variables
   @end table
   
   @itemize @bullet
   \BJP
   @item
   @code{primadec()}, @code{primedec} $B$O(B @samp{primdec} $B$GDj5A$5$l$F$$$k(B.
   @item
   @code{primadec()}, @code{primedec()} $B$O$=$l$>$lM-M}?tBN>e$G$N%$%G%"%k$N(B
   $B=`AGJ,2r(B, $B:,4p$NAG%$%G%"%kJ,2r$r9T$&(B.
   @item
   $B0z?t$OB?9`<0%j%9%H$*$h$SJQ?t%j%9%H$G$"$k(B. $BB?9`<0$OM-M}?t78?t$N$_$,5v$5$l$k(B.
   @item
   @code{primadec} $B$O(B @code{[$B=`AG@.J,(B, $BIUB0AG%$%G%"%k(B]} $B$N%j%9%H$rJV$9(B.
   @item
   @code{primadec} $B$O(B $BAG0x;R$N%j%9%H$rJV$9(B.
   @item
   $B7k2L$K$*$$$F(B, $BB?9`<0%j%9%H$H$7$FI=<($5$l$F$$$k3F%$%G%"%k$OA4$F(B
   $B%0%l%V%J4pDl$G$"$k(B. $BBP1~$9$k9`=g=x$O(B, $B$=$l$>$l(B
   $BJQ?t(B @code{PRIMAORD}, @code{PRIMEORD} $B$K3JG<$5$l$F$$$k(B.
   @item
   @code{primadec} $B$O(B @code{[Shimoyama,Yokoyama]} $B$N=`AGJ,2r%"%k%4%j%:%`(B
   $B$r<BAu$7$F$$$k(B.
   @item
   $B$b$7AG0x;R$N$_$r5a$a$?$$$J$i(B, @code{primedec} $B$r;H$&J}$,$h$$(B.
   $B$3$l$O(B, $BF~NO%$%G%"%k$,:,4p%$%G%"%k$G$J$$>l9g$K(B, @code{primadec}
   $B$N7W;;$KM>J,$J%3%9%H$,I,MW$H$J$k>l9g$,$"$k$+$i$G$"$k(B.
   \E
   \BEG
   @item
   Function @code{primadec()} and @code{primedec} are defined in @samp{primdec}.
   @item
   @code{primadec()}, @code{primedec()} are the function for primary
   ideal decomposition and prime decomposition of the radical over the
   rationals respectively.
   @item
   The arguments are a list of polynomials and a list of variables.
   These functions accept ideals with rational function coefficients only.
   @item
   @code{primadec} returns the list of pair lists consisting a primary component
   and its associated prime.
   @item
   @code{primedec} returns the list of prime components.
   @item
   Each component is a Groebner basis and the corresponding term order
   is indicated by the global variables @code{PRIMAORD}, @code{PRIMEORD}
   respectively.
   @item
   @code{primadec} implements the primary decompostion algorithm
   in @code{[Shimoyama,Yokoyama]}.
   @item
   If one only wants to know the prime components of an ideal, then
   use @code{primedec} because @code{primadec} may need additional costs
   if an input ideal is not radical.
   \E
   @end itemize
   
   @example
   [84] load("primdec")$
   [102] primedec([p*q*x-q^2*y^2+q^2*y,-p^2*x^2+p^2*x+p*q*y,
   (q^3*y^4-2*q^3*y^3+q^3*y^2)*x-q^3*y^4+q^3*y^3,
   -q^3*y^4+2*q^3*y^3+(-q^3+p*q^2)*y^2],[p,q,x,y]);
   [[y,x],[y,p],[x,q],[q,p],[x-1,q],[y-1,p],[(y-1)*x-y,q*y^2-2*q*y-p+q]]
   [103] primadec([x,z*y,w*y^2,w^2*y-z^3,y^3],[x,y,z,w]);
   [[[x,z*y,y^2,w^2*y-z^3],[z,y,x]],[[w,x,z*y,z^3,y^3],[w,z,y,x]]]
   @end example
   
   @table @t
   \JP @item $B;2>H(B
   \EG @item References
   @fref{fctr sqfr},
   \JP @fref{$B9`=g=x$N@_Dj(B}.
   \EG @fref{Setting term orderings}.
   @end table
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