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version 1.2, 1999/11/29 05:01:42 version 1.3, 2000/01/03 09:15:53
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 @section D-module  @section D-module
 $B%U%!%$%k(B @file{gr}, @file{xm}, @file{Matrix}, @file{Diff} $B$,I,MW$G$9(B.  $B%U%!%$%k(B @file{gr}, @file{xm}, @file{Matrix}, @file{Diff} $B$,I,MW$G$9(B.
 @menu  @menu
 @c * dmod_make_dv::  @c * dmodule_make_dv::
 * dmod_d_op_tosm1::  * dmodule_d_op_tosm1::
 * dmod_d_op_toasir::  * dmodule_d_op_toasir::
 * dmod_d_op_fromasir::  * dmodule_d_op_fromasir::
 * dmod_ch_ideal::  * dmodule_ch_ideal::
 @c * dmod_ch_ideal_appell1::  @c * dmodule_ch_ideal_appell1::
 @c * dmod_ch_ideal_appell2::  @c * dmodule_ch_ideal_appell2::
 @c * dmod_ch_ideal_appell3::  @c * dmodule_ch_ideal_appell3::
 @c * dmod_ch_ideal_appell4::  @c * dmodule_ch_ideal_appell4::
 @c * dmod_ch_ideal_selberg2::  @c * dmodule_ch_ideal_selberg2::
 @c * dmod_ch_ideal_gkz::  @c * dmodule_ch_ideal_gkz::
 * dmod_restriction::  * dmodule_restriction::
 @c * dmod_restriction_appell1::  @c * dmodule_restriction_appell1::
 @c * dmod_restriction_appell2::  @c * dmodule_restriction_appell2::
 @c * dmod_restriction_appell3::  @c * dmodule_restriction_appell3::
 @c * dmod_restriction_appell4::  @c * dmodule_restriction_appell4::
 @c * dmod_restriction_selberg2::  @c * dmodule_restriction_selberg2::
 @c * dmod_restriction_gkz::  @c * dmodule_restriction_gkz::
 * dmod_elimination::  * dmodule_elimination::
 @c * dmod_elimination_appell1::  @c * dmodule_elimination_appell1::
 @c * dmod_elimination_appell2::  @c * dmodule_elimination_appell2::
 @c * dmod_elimination_appell3::  @c * dmodule_elimination_appell3::
 @c * dmod_elimination_appell4::  @c * dmodule_elimination_appell4::
 @c * dmod_elimination_selberg2::  @c * dmodule_elimination_selberg2::
 @c * dmod_elimination_gkz::  @c * dmodule_elimination_gkz::
 @end menu  @end menu
   
 @node dmod_d_op_tosm1,,, D-module  @node dmodule_d_op_tosm1,,, D-module
 @subsection @code{dmod_d_op_tosm1}  @subsection @code{dmodule_d_op_tosm1}
 @findex dmod_d_op_tosm1  @findex dmodule_d_op_tosm1
 @table @t  @table @t
 @item dmod_d_op_tosm1(@var{LL},@var{V})  @item dmodule_d_op_tosm1(@var{LL},@var{V})
 ::  $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$r(B sm1 $B7A<0$KJQ49$7$^$9(B.  ::  $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$r(B sm1 $B7A<0$KJQ49$7$^$9(B.
 @end table  @end table
 @table @var  @table @var
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 @end table  @end table
 @itemize @bullet  @itemize @bullet
 @item  $BHyJ,:nMQAG$N78?t$O@0?tB?9`<0$KJQ49$5$l$^$9(B.  @item  $BHyJ,:nMQAG$N78?t$O@0?tB?9`<0$KJQ49$5$l$^$9(B.
 @item  @code{dmod_d_op_tosm1}$B$NNc(B  @item  @code{dmodule_d_op_tosm1}$B$NNc(B
 @end itemize  @end itemize
 @example  @example
 [299] dmod_d_op_tosm1([[[x,[2,0]],[-1,[0,0]]],[[y,[0,2]],[-1,[0,0]]]],[x,y]);  [299] dmodule_d_op_tosm1([[[x,[2,0]],[-1,[0,0]]],
                             [[y,[0,2]],[-1,[0,0]]]],[x,y]);
 [ + ( + (1) x) dx^2 + ( + (-1)), + ( + (1) y) dy^2 + ( + (-1))]  [ + ( + (1) x) dx^2 + ( + (-1)), + ( + (1) y) dy^2 + ( + (-1))]
   
 [300] dmod_d_op_tosm1([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],[[1,[2,0]],[1,[0,2]]]],[x,y]);  [300] dmodule_d_op_tosm1([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],
                             [[1,[2,0]],[1,[0,2]]]],[x,y]);
 [ + ( + (1) x) dx + ( + (1) y) dy + ( + (1)), + ( + (1)) dx^2 + ( + (1)) dy^2]  [ + ( + (1) x) dx + ( + (1) y) dy + ( + (1)), + ( + (1)) dx^2 + ( + (1)) dy^2]
   
 [301] dmod_d_op_tosm1([[[1/2,[1,0]],[1,[0,0]]],[[1/3,[0,1]],[1/4,[0,0]]]],[x,y]);  [301] dmodule_d_op_tosm1([[[1/2,[1,0]],[1,[0,0]]],
                             [[1/3,[0,1]],[1/4,[0,0]]]],[x,y]);
 [ + ( + (6)) dx + ( + (12)), + ( + (4)) dy + ( + (3))]  [ + ( + (6)) dx + ( + (12)), + ( + (4)) dy + ( + (3))]
   
 [302] dmod_d_op_tosm1([[[1/2*x,[1,0]],[1,[0,0]]],[[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);  [302] dmodule_d_op_tosm1([[[1/2*x,[1,0]],[1,[0,0]]],
                             [[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
 [ + ( + (6) x) dx + ( + (12)), + ( + (4) y) dy + ( + (3))]  [ + ( + (6) x) dx + ( + (12)), + ( + (4) y) dy + ( + (3))]
 @end example  @end example
   
 @node dmod_d_op_toasir,,, D-module  @node dmodule_d_op_toasir,,, D-module
 @subsection @code{dmod_d_op_toasir}  @subsection @code{dmodule_d_op_toasir}
 @findex dmod_d_op_toasir  @findex dmodule_d_op_toasir
 @table @t  @table @t
 @item dmod_d_op_toasir(@var{LL},@var{V})  @item dmodule_d_op_toasir(@var{LL},@var{V})
 ::  $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H(B @var{LL} $B$r(B @code{asir} $B$NB?9`<0$KJQ49$7$^$9(B.  ::  $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H(B @var{LL} $B$r(B @code{asir} $B$NB?9`<0$KJQ49$7$^$9(B.
 @end table  @end table
 @table @var  @table @var
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 $B%j%9%H(B  $B%j%9%H(B
 @end table  @end table
 @itemize @bullet  @itemize @bullet
 @item  @code{dmod_d_op_toasir}$B$NNc(B  @item  @code{dmodule_d_op_toasir}$B$NNc(B
 @end itemize  @end itemize
 @example  @example
 [303] dmod_d_op_toasir([[[1/2*x,[1,0]],[1,[0,0]]],[[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);  [303] dmodule_d_op_toasir([[[1/2*x,[1,0]],[1,[0,0]]],
                              [[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
 [1/2*x*dx+1,1/3*y*dy+1/4]  [1/2*x*dx+1,1/3*y*dy+1/4]
   
 [304] dmod_d_op_toasir([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],[[1,[2,0]],[1,[0,2]]]],[x,y]);  [304] dmodule_d_op_toasir([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],
                              [[1,[2,0]],[1,[0,2]]]],[x,y]);
 [x*dx+y*dy+1,dx^2+dy^2]  [x*dx+y*dy+1,dx^2+dy^2]
 @end example  @end example
   
 @node dmod_d_op_fromasir,,, D-module  @node dmodule_d_op_fromasir,,, D-module
 @subsection @code{dmod_d_op_fromasir}  @subsection @code{dmodule_d_op_fromasir}
 @findex dmod_d_op_fromasir  @findex dmodule_d_op_fromasir
 @table @t  @table @t
 @item dmod_d_op_fromasir(@var{D_list},@var{V})  @item dmodule_d_op_fromasir(@var{D_list},@var{V})
 ::  @code{asir} $B$NB?9`<0$+$i%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$KJQ49$7$^$9(B.  ::  @code{asir} $B$NB?9`<0$+$i%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$KJQ49$7$^$9(B.
 @end table  @end table
 @table @var  @table @var
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 $B%j%9%H(B  $B%j%9%H(B
 @end table  @end table
 @itemize @bullet  @itemize @bullet
 @item  @code{dmod_d_op_fromasir}$B$NNc(B  @item  @code{dmodule_d_op_fromasir}$B$NNc(B
 @end itemize  @end itemize
 @example  @example
 [305] dmod_d_op_fromasir([1/2*x*dx+1,1/3*y*dy+1/4],[x,y]);  [305] dmodule_d_op_fromasir([1/2*x*dx+1,1/3*y*dy+1/4],[x,y]);
 [[[1/2*x,[1,0]],[1,[0,0]]],[[1/3*y,[0,1]],[1/4,[0,0]]]]  [[[1/2*x,[1,0]],[1,[0,0]]],[[1/3*y,[0,1]],[1/4,[0,0]]]]
   
 [306] dmod_d_op_fromasir([x*dx+y*dy+1,dx^2+dy^2],[x,y]);  [306] dmodule_d_op_fromasir([x*dx+y*dy+1,dx^2+dy^2],[x,y]);
 [[[x,[1,0]],[y,[0,1]],[1,[0,0]]],[[1,[2,0]],[1,[0,2]]]]  [[[x,[1,0]],[y,[0,1]],[1,[0,0]]],[[1,[2,0]],[1,[0,2]]]]
 @end example  @end example
   
 @node dmod_ch_ideal,,, D-module  @node dmodule_ch_ideal,,, D-module
 @subsection @code{dmod_ch_ideal}  @subsection @code{dmodule_ch_ideal}
 @findex dmod_ch_ideal  @findex dmodule_ch_ideal
 @table @t  @table @t
 @item dmod_ch_ideal(@var{D_ideal},@var{V})  @item dmodule_ch_ideal(@var{D_ideal},@var{V})
 ::  @var{D_ideal}$B$N(Bcharacteristic ideal$B$r5a$a$^$9(B.  ::  @var{D_ideal}$B$N(Bcharacteristic ideal$B$r5a$a$^$9(B.
 @end table  @end table
 @table @var  @table @var
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 $B%j%9%H(B  $B%j%9%H(B
 @end table  @end table
 @itemize @bullet  @itemize @bullet
 @item  @code{dmod_ch_ideal}$B$NNc(B  @item  @code{dmodule_ch_ideal}$B$NNc(B
 @end itemize  @end itemize
 @example  @example
 [301] dmod_ch_ideal(["x dx + y dy + 1","dx^2 + dy^2"],[x,y]);  [301] dmodule_ch_ideal(["x dx + y dy + 1","dx^2 + dy^2"],[x,y]);
 [x*dx+y*dy,dx^2+dy^2,y*dy*dx-x*dy^2,(x^2+y^2)*dy^2]  [x*dx+y*dy,dx^2+dy^2,y*dy*dx-x*dy^2,(x^2+y^2)*dy^2]
   
 [302] dmod_ch_ideal(["x dx + 1","dx dy"],[x,y]);  [302] dmodule_ch_ideal(["x dx + 1","dx dy"],[x,y]);
 [x*dx,dy]  [x*dx,dy]
 @end example  @end example
   
 @node dmod_restriction,,, D-module  @node dmodule_restriction,,, D-module
 @subsection @code{dmod_restriction}  @subsection @code{dmodule_restriction}
 @findex dmod_restriction  @findex dmodule_restriction
 @table @t  @table @t
 @item dmod_restriction(@var{D_ideal},@var{V},@var{Rest})  @item dmodule_restriction(@var{D_ideal},@var{V},@var{Rest})
 ::  @var{D_ideal}$B$N(Brestriction$B$r5a$a$^$9(B.  ::  @var{D_ideal}$B$N(Brestriction$B$r5a$a$^$9(B.
 @end table  @end table
 @table @var  @table @var
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 $B%j%9%H(B  $B%j%9%H(B
 @end table  @end table
 @itemize @bullet  @itemize @bullet
 @item  @code{dmod_restriction}$B$NNc(B.  @item  @code{dmodule_restriction}$B$NNc(B.
 @end itemize  @end itemize
 @example  @example
 [303] dmod_restriction(["x dx + y dy + 1","dx^2 + dy^2"],[x,y],[y]);  [303] dmodule_restriction(["x dx + y dy + 1","dx^2 + dy^2"],[x,y],[y]);
 [[2,[-x*dx-1,-e0*x*dx-2*e0]]]  [[2,[-x*dx-1,-e0*x*dx-2*e0]]]
 @end example  @end example
   
 @node dmod_elimination,,, D-module  @node dmodule_elimination,,, D-module
 @subsection @code{dmod_elimination}  @subsection @code{dmodule_elimination}
 @findex dmod_elimination  @findex dmodule_elimination
 @table @t  @table @t
 @item dmod_elimination(@var{D_ideal},@var{V},@var{Elim})  @item dmodule_elimination(@var{D_ideal},@var{V},@var{Elim})
 ::  @var{D_ideal}$B$N(Belimination ideal$B$r5a$a$^$9(B.  ::  @var{D_ideal}$B$N(Belimination ideal$B$r5a$a$^$9(B.
 @end table  @end table
 @table @var  @table @var
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 $B%j%9%H(B  $B%j%9%H(B
 @end table  @end table
 @itemize @bullet  @itemize @bullet
 @item  @code{dmod_elimination}$B$NNc(B.  @item  @code{dmodule_elimination}$B$NNc(B.
 @end itemize  @end itemize
 @example  @example
 [304] dmod_elimination(["x dx + y dy + 1","dx^2 + dy^2"],[x,y],[y]);  [305] dmodule_elimination(["x dx + y dy + 1","dx^2 + dy^2"],[x,y],[[y],[0]]);
 [x^2*dx^2+4*x*dx+2]  [x^2*dx^2+4*x*dx+2]
   
   [306] dmodule_elimination(["x dx + y dy + 1","dx^2 + dy^2"],[x,y],[[y],[a]]);
   [(x^2+a^2)*dx^2+4*x*dx+2]
   @end example
   
   @node dmodule_elimination_generic,,, D-module
   @subsection @code{dmodule_elimination_generic}
   @findex dmodule_elimination_generic
   @table @t
   @item dmodule_elimination_generic(@var{D_ideal},@var{Param},@var{V},@var{Elim})
   ::  generic parameter$B$r4^$`(B@var{D_ideal}$B$N(Belimination ideal$B$r5a$a$^$9(B.
   @end table
   @table @var
   @item return
   $B%j%9%H(B
   @item @var{D_ideal}
   $B%j%9%H(B
   @item @var{Param}
   $B%j%9%H(B
   @item @var{V}
   $B%j%9%H(B
   @item @var{Elim}
   $B%j%9%H(B
   @end table
   @itemize @bullet
   @item  @code{dmodule_elimination_generic}$B$NNc(B.
   @end itemize
   @example
   [307] dmodule_elimination_generic(["x dx + y dy + 1","dx^2 + dy^2 + a"],
                                     [a],[x,y],[[y],[s]]);
   [(x^2+s^2)*dx^2+4*x*dx+a*s^2+2,2*a]
   
 @end example  @end example
   
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