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Diff for /OpenXM/src/asir-doc/parts/groebner.texi between version 1.3 and 1.4

version 1.3, 1999/12/24 04:38:04 version 1.4, 2003/04/19 15:44:56
Line 1 
Line 1 
 @comment $OpenXM: OpenXM/src/asir-doc/parts/groebner.texi,v 1.2 1999/12/21 02:47:31 noro Exp $  @comment $OpenXM: OpenXM/src/asir-doc/parts/groebner.texi,v 1.3 1999/12/24 04:38:04 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 1263  Refer to the sections for each functions.
Line 1263  Refer to the sections for each functions.
 @item return  @item return
 \JP $B%j%9%H(B  \JP $B%j%9%H(B
 \EG list  \EG list
 @item plist, vlist, procs  @item plist  vlist  procs
 \JP $B%j%9%H(B  \JP $B%j%9%H(B
 \EG list  \EG list
 @item order  @item order
Line 1372  for communication.
Line 1372  for communication.
 @item return  @item return
 \JP $B%j%9%H(B  \JP $B%j%9%H(B
 \EG list  \EG list
 @item plist, vlist1, vlist2, procs  @item plist  vlist1  vlist2  procs
 \JP $B%j%9%H(B  \JP $B%j%9%H(B
 \EG list  \EG list
 @item order  @item order
Line 1586  processes.
Line 1586  processes.
 @item return  @item return
 \JP $B%j%9%H(B  \JP $B%j%9%H(B
 \EG list  \EG list
 @item plist, vlist1, vlist2, procs  @item plist  vlist1  vlist2  procs
 \JP $B%j%9%H(B  \JP $B%j%9%H(B
 \EG list  \EG list
 @item order  @item order
Line 1692  processes.
Line 1692  processes.
 @item return  @item return
 \JP $BB?9`<0(B  \JP $BB?9`<0(B
 \EG polynomial  \EG polynomial
 @item plist, vlist  @item plist  vlist
 \JP $B%j%9%H(B  \JP $B%j%9%H(B
 \EG list  \EG list
 @item order  @item order
Line 1789  for @code{gr_minipoly()}.
Line 1789  for @code{gr_minipoly()}.
 @item return  @item return
 \JP @code{tolexm()} : $B%j%9%H(B, @code{minipolym()} : $BB?9`<0(B  \JP @code{tolexm()} : $B%j%9%H(B, @code{minipolym()} : $BB?9`<0(B
 \EG @code{tolexm()} : list, @code{minipolym()} : polynomial  \EG @code{tolexm()} : list, @code{minipolym()} : polynomial
 @item plist, vlist1, vlist2  @item plist  vlist1  vlist2
 \JP $B%j%9%H(B  \JP $B%j%9%H(B
 \EG list  \EG list
 @item order  @item order
Line 1854  z^32+11405*z^31+20868*z^30+21602*z^29+...
Line 1854  z^32+11405*z^31+20868*z^30+21602*z^29+...
 @item return  @item return
 \JP $B%j%9%H(B  \JP $B%j%9%H(B
 \EG list  \EG list
 @item plist, vlist  @item plist  vlist
 \JP $B%j%9%H(B  \JP $B%j%9%H(B
 \EG list  \EG list
 @item order  @item order
Line 1966  Actual computation is controlled by various parameters
Line 1966  Actual computation is controlled by various parameters
 @item return  @item return
 \JP $B%j%9%H(B  \JP $B%j%9%H(B
 \EG list  \EG list
 @item plist, vlist  @item plist  vlist
 \JP $B%j%9%H(B  \JP $B%j%9%H(B
 \EG list  \EG list
 @item order  @item order
Line 2791  selection strategy of critical pairs in Groebner basis
Line 2791  selection strategy of critical pairs in Groebner basis
 @item return  @item return
 \JP $BJ,;6I=8=B?9`<0(B  \JP $BJ,;6I=8=B?9`<0(B
 \EG distributed polynomial  \EG distributed polynomial
 @item dpoly1, dpoly2  @item dpoly1  dpoly2
 \JP $BJ,;6I=8=B?9`<0(B  \JP $BJ,;6I=8=B?9`<0(B
 \EG distributed polynomial  \EG distributed polynomial
 @end table  @end table
Line 2834  two polynomials, where coefficient is always set to 1.
Line 2834  two polynomials, where coefficient is always set to 1.
 @item return  @item return
 \JP $B@0?t(B  \JP $B@0?t(B
 \EG integer  \EG integer
 @item dpoly1, dpoly2  @item dpoly1  dpoly2
 \JP $BJ,;6I=8=B?9`<0(B  \JP $BJ,;6I=8=B?9`<0(B
 \EG distributed polynomial  \EG distributed polynomial
 @end table  @end table
Line 2889  Used for finding candidate terms at reduction of polyn
Line 2889  Used for finding candidate terms at reduction of polyn
 @item return  @item return
 \JP $BJ,;6I=8=B?9`<0(B  \JP $BJ,;6I=8=B?9`<0(B
 \EG distributed polynomial  \EG distributed polynomial
 @item dpoly1, dpoly2  @item dpoly1  dpoly2
 \JP $BJ,;6I=8=B?9`<0(B  \JP $BJ,;6I=8=B?9`<0(B
 \EG distributed polynomial  \EG distributed polynomial
 @end table  @end table
Line 3113  values of @code{dp_mag()} for intermediate basis eleme
Line 3113  values of @code{dp_mag()} for intermediate basis eleme
 @item return  @item return
 \JP $B%j%9%H(B  \JP $B%j%9%H(B
 \EG list  \EG list
 @item dpoly1, dpoly2, dpoly3  @item dpoly1  dpoly2  dpoly3
 \JP $BJ,;6I=8=B?9`<0(B  \JP $BJ,;6I=8=B?9`<0(B
 \EG distributed polynomial  \EG distributed polynomial
 @item vlist  @item vlist
Line 3137  values of @code{dp_mag()} for intermediate basis eleme
Line 3137  values of @code{dp_mag()} for intermediate basis eleme
 $B$J$i$J$$(B.  $B$J$i$J$$(B.
 @item  @item
 $B0z?t$,@0?t78?t$N;~(B, $B4JLs$O(B, $BJ,?t$,8=$l$J$$$h$&(B, $B@0?t(B @var{a}, @var{b},  $B0z?t$,@0?t78?t$N;~(B, $B4JLs$O(B, $BJ,?t$,8=$l$J$$$h$&(B, $B@0?t(B @var{a}, @var{b},
 $B9`(B @var{t} $B$K$h$j(B @var{a(dpoly1 + dpoly2)-bt dpoly3} $B$H$7$F7W;;$5$l$k(B.  $B9`(B @var{t} $B$K$h$j(B @var{a}(@var{dpoly1} + @var{dpoly2})-@var{bt} @var{dpoly3} $B$H$7$F7W;;$5$l$k(B.
 @item  @item
 $B7k2L$O(B, @code{[@var{a dpoly1},@var{a dpoly2 - bt dpoly3}]} $B$J$k%j%9%H$G$"$k(B.  $B7k2L$O(B, @code{[@var{a dpoly1},@var{a dpoly2 - bt dpoly3}]} $B$J$k%j%9%H$G$"$k(B.
 \E  \E
Line 3156  the divisibility of the head term of @var{dpoly2} by t
Line 3156  the divisibility of the head term of @var{dpoly2} by t
 When integral coefficients, computation is so carefully performed that  When integral coefficients, computation is so carefully performed that
 no rational operations appear in the reduction procedure.  no rational operations appear in the reduction procedure.
 It is computed for integers @var{a} and @var{b}, and a term @var{t} as:  It is computed for integers @var{a} and @var{b}, and a term @var{t} as:
 @var{a(dpoly1 + dpoly2)-bt dpoly3}.  @var{a}(@var{dpoly1} + @var{dpoly2})-@var{bt} @var{dpoly3}.
 @item  @item
 The result is a list @code{[@var{a dpoly1},@var{a dpoly2 - bt dpoly3}]}.  The result is a list @code{[@var{a dpoly1},@var{a dpoly2 - bt dpoly3}]}.
 \E  \E
Line 3197  The result is a list @code{[@var{a dpoly1},@var{a dpol
Line 3197  The result is a list @code{[@var{a dpoly1},@var{a dpol
 @item return  @item return
 \JP $BJ,;6I=8=B?9`<0(B  \JP $BJ,;6I=8=B?9`<0(B
 \EG distributed polynomial  \EG distributed polynomial
 @item dpoly1, dpoly2  @item dpoly1  dpoly2
 \JP $BJ,;6I=8=B?9`<0(B  \JP $BJ,;6I=8=B?9`<0(B
 \EG distributed polynomial  \EG distributed polynomial
 @item mod  @item mod
Line 3273  as a form of @code{[numerator, denominator]})
Line 3273  as a form of @code{[numerator, denominator]})
 @item poly  @item poly
 \JP $BB?9`<0(B  \JP $BB?9`<0(B
 \EG polynomial  \EG polynomial
 @item plist,vlist  @item plist vlist
 \JP $B%j%9%H(B  \JP $B%j%9%H(B
 \EG list  \EG list
 @item order  @item order
Line 3428  u0^6,u0^5,u0^4,u0^3,u0^2,u0,1]
Line 3428  u0^6,u0^5,u0^4,u0^3,u0^2,u0,1]
 @table @var  @table @var
 \JP @item return 0 $B$^$?$O(B 1  \JP @item return 0 $B$^$?$O(B 1
 \EG @item return 0 or 1  \EG @item return 0 or 1
 @item plist1, plist2  @item plist1  plist2
 @end table  @end table
   
 @itemize @bullet  @itemize @bullet
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