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Diff for /OpenXM/src/asir-contrib/packages/doc/Attic/Dmodule.texi between version 1.3 and 1.4

version 1.3, 2000/01/03 09:15:53 version 1.4, 2000/02/20 11:30:44
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 @c $OpenXM$  @c $OpenXM: OpenXM/src/asir-contrib/packages/doc/Dmodule.texi,v 1.3 2000/01/03 09:15:53 okutani Exp $
 @node D-module,,, $B$=$NB>$NH!?t(B  @node D-module,,, $B$=$NB>$NH!?t(B
 @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.
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 * dmodule_d_op_toasir::  * dmodule_d_op_toasir::
 * dmodule_d_op_fromasir::  * dmodule_d_op_fromasir::
 * dmodule_ch_ideal::  * dmodule_ch_ideal::
   * dmodule_singular_locus::
 @c * dmodule_ch_ideal_appell1::  @c * dmodule_ch_ideal_appell1::
 @c * dmodule_ch_ideal_appell2::  @c * dmodule_ch_ideal_appell2::
 @c * dmodule_ch_ideal_appell3::  @c * dmodule_ch_ideal_appell3::
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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  $B$3$N4X?t$O(B@code{diff_op_tosm1}$B$HEy2A$G$9(B.
 @item  @code{dmodule_d_op_tosm1}$B$NNc(B  @item  @code{dmodule_d_op_tosm1}$B$NNc(B
 @end itemize  @end itemize
 @example  @example
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 $B%j%9%H(B  $B%j%9%H(B
 @end table  @end table
 @itemize @bullet  @itemize @bullet
   @item  $B$3$N4X?t$O(B@code{diff_op_toasir}$B$HEy2A$G$9(B.
 @item  @code{dmodule_d_op_toasir}$B$NNc(B  @item  @code{dmodule_d_op_toasir}$B$NNc(B
 @end itemize  @end itemize
 @example  @example
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 $B%j%9%H(B  $B%j%9%H(B
 @end table  @end table
 @itemize @bullet  @itemize @bullet
   @item  $B$3$N4X?t$O(B@code{diff_op_fromasir}$B$HEy2A$G$9(B.
 @item  @code{dmodule_d_op_fromasir}$B$NNc(B  @item  @code{dmodule_d_op_fromasir}$B$NNc(B
 @end itemize  @end itemize
 @example  @example
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 $B%j%9%H(B  $B%j%9%H(B
 @end table  @end table
 @itemize @bullet  @itemize @bullet
   @item  @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
 @item  @code{dmodule_ch_ideal}$B$NNc(B  @item  @code{dmodule_ch_ideal}$B$NNc(B
 @end itemize  @end itemize
 @example  @example
 [301] dmodule_ch_ideal(["x dx + y dy + 1","dx^2 + dy^2"],[x,y]);  [344] dmodule_ch_ideal([x*dx+y*dy+a,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] dmodule_ch_ideal(["x dx + 1","dx dy"],[x,y]);  [348] dmodule_ch_ideal(diff_op_appell4(a,b,c1,c2,[x,y]),[x,y]);
 [x*dx,dy]  [-x*dx^2+y*dy^2,2*y*x*dy*dx+(y*x+y^2-y)*dy^2,
    (2*y^2-2*y)*dy^2*dx+(-y*x+3*y^2+y)*dy^3,
    2*y*x*dy^2*dx+(y*x^2+(-2*y^2-y)*x+y^3-y^2)*dy^3]
 @end example  @end example
   
   @node dmodule_singular_locus,,, D-module
   @subsection @code{dmodule_singular_locus}
   @findex dmodule_singular_locus
   @table @t
   @item dmodule_singular_locus(@var{D_ideal},@var{V})
   ::  @var{D_ideal}$B$N(Bsingular locus$B$r5a$a$^$9(B.
   @end table
   @table @var
   @item return
   $B%j%9%H(B
   @item D_ideal
   $B%j%9%H(B
   @item V
   $B%j%9%H(B
   @end table
   @itemize @bullet
   @item  @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
   @item  @code{dmodule_singular_locus}$B$NNc(B
   @end itemize
   @example
   [356] D = diff_op_appell4(a,b,c1,c2,[x,y])$
   [357] dmodule_singular_locus(D,[x,y]);
   [-y*x^3+(2*y^2+2*y)*x^2+(-y^3+2*y^2-y)*x]
   
   [358] D = diff_op_hg1(a,b,c,[x])$
   [359] dmodule_singular_locus(D,[x]);
   [x^2-x]
   @end example
   
 @node dmodule_restriction,,, D-module  @node dmodule_restriction,,, D-module
 @subsection @code{dmodule_restriction}  @subsection @code{dmodule_restriction}
 @findex dmodule_restriction  @findex dmodule_restriction
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 $B%j%9%H(B  $B%j%9%H(B
 @end table  @end table
 @itemize @bullet  @itemize @bullet
   @item  @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
 @item  @code{dmodule_restriction}$B$NNc(B.  @item  @code{dmodule_restriction}$B$NNc(B.
 @end itemize  @end itemize
 @example  @example
 [303] dmodule_restriction(["x dx + y dy + 1","dx^2 + dy^2"],[x,y],[y]);  [345] dmodule_restriction([x*dx+y*dy+a,dx^2+dy^2],[x,y],[y]);
 [[2,[-x*dx-1,-e0*x*dx-2*e0]]]  [[2,[-x*dx-a,-e0*x*dx-e0*a-e0]]]
 @end example  @end example
   
 @node dmodule_elimination,,, D-module  @node dmodule_elimination,,, D-module
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 $B%j%9%H(B  $B%j%9%H(B
 @end table  @end table
 @itemize @bullet  @itemize @bullet
   @item  @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
 @item  @code{dmodule_elimination}$B$NNc(B.  @item  @code{dmodule_elimination}$B$NNc(B.
 @end itemize  @end itemize
 @example  @example
 [305] dmodule_elimination(["x dx + y dy + 1","dx^2 + dy^2"],[x,y],[[y],[0]]);  [346] dmodule_elimination([x*dx+y*dy+a,dx^2+dy^2],[x,y],[[y],[0]]);
 [x^2*dx^2+4*x*dx+2]  [x^2*dx^2+(2*a+2)*x*dx+a^2+a]
   
 [306] dmodule_elimination(["x dx + y dy + 1","dx^2 + dy^2"],[x,y],[[y],[a]]);  [347] dmodule_elimination([x*dx+y*dy+a,dx^2+dy^2],[x,y],[[y],[b]]);
 [(x^2+a^2)*dx^2+4*x*dx+2]  [(x^2+b^2)*dx^2+(2*a+2)*x*dx+a^2+a]
 @end example  @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  
   
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