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version 1.3, 1999/12/21 02:47:30 version 1.4, 1999/12/24 04:38:04
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 @comment $OpenXM$  @comment $OpenXM: OpenXM/src/asir-doc/parts/appendix.texi,v 1.3 1999/12/21 02:47:30 noro Exp $
 \BJP  \BJP
 @node $BIUO?(B,,, Top  @node $BIUO?(B,,, Top
 @appendix $BIUO?(B  @appendix $BIUO?(B
Line 512  result and then summing them up all.
Line 512  result and then summing them up all.
 @item primdec  @item primdec
 \BJP  \BJP
 $BB?9`<0%$%G%"%k$N=`AG%$%G%"%kJ,2r$H$=$N:,4p$NAG%$%G%"%kJ,2r(B  $BB?9`<0%$%G%"%k$N=`AG%$%G%"%kJ,2r$H$=$N:,4p$NAG%$%G%"%kJ,2r(B
 (@code{[Shimoyama,Yokoyama]} $B;2>H(B).  (@pxref{primadec primedec}).
 $B=`AG%$%G%"%kJ,2r$O(B @code{primadec()}, $BAG%$%G%"%kJ,2r$O(B, @code{primedec()}  
 $B$H$$$&4X?t$G(B, $BMQ0U$5$l$F$$$k(B. $B0z?t$O(B, $BB?9`<0%j%9%H$HJQ?t$G$"$k(B.  
 $BM-M}<078?t$NB?9`<0%$%G%"%k$d(B, 0$B<!85$G$J$$%$%G%"%k$b07$($k(B.  
 @code{primadec} $B$O(B, $B=`AG@.J,$H$=$NAG@.J,$N%Z%"%j%9%H$N%j%9%H$rJV$9(B.  
 @code{primedec} $B$O(B, $BAG@.J,$N%j%9%H$rJV$9(B.  
 $B$=$N7k2L$O$$$:$l$b%0%l%V%J4pDl$K$J$C$F$$$k$,(B, $B$=$N(B  
 $BJQ?t=g=x$O(B, $B$=$l$>$lBg0hJQ?t(B @code{PRIMAORD}, @code{PRIMEORD}  
  $B$NCM(B 0,1 $B$"$k$$$O(B 2 $B$K$h$C$F7h$^$k(B.  
 \E  \E
 \BEG  \BEG
 Primary ideal decomposition of polynomial ideals and prime compotision  Primary ideal decomposition of polynomial ideals and prime compotision
 of radicals  of radicals (@pxref{primadec primedec}).
 (Refer to @code{[Shimoyama,Yokoyama]}).  
 @code{primadec()}, @code{primedec()} are the function for primary  
 ideal decomposition and prime decomposition of the radical respectively.  
 The arguments are a list of polynomials and a list of variables.  
 These functions accept ideals with rational function coefficients  
 and non zero-dimenstional ideals.  
 @code{primadec} returns the list of pair lists consisting a primary component  
 and its associated prime.  
 @code{primedec} returns the list of prime components.  
 Each component is a Groebner basis and the corresponding term order  
 is indicated by the global variables @code{PRIMAORD}, @code{PRIMEORD}  
 respectively.  
 \E  \E
 @example  
 [84] load("primdec")$  
 [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  
 @end table  @end table
   
 \BJP  \BJP
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