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@c $OpenXM: OpenXM/src/asir-contrib/packages/doc/Dmodule.texi,v 1.2 1999/11/29 05:01:42 okutani Exp $
@node D-module,,, $B$=$NB>$NH!?t(B
@section D-module
$B%U%!%$%k(B @file{gr}, @file{xm}, @file{Matrix}, @file{Diff} $B$,I,MW$G$9(B.
@menu
@c * dmod_make_dv::
* dmod_d_op_tosm1::
* dmod_d_op_toasir::
* dmod_d_op_fromasir::
* dmod_ch_ideal::
@c * dmod_ch_ideal_appell1::
@c * dmod_ch_ideal_appell2::
@c * dmod_ch_ideal_appell3::
@c * dmod_ch_ideal_appell4::
@c * dmod_ch_ideal_selberg2::
@c * dmod_ch_ideal_gkz::
* dmod_restriction::
@c * dmod_restriction_appell1::
@c * dmod_restriction_appell2::
@c * dmod_restriction_appell3::
@c * dmod_restriction_appell4::
@c * dmod_restriction_selberg2::
@c * dmod_restriction_gkz::
* dmod_elimination::
@c * dmod_elimination_appell1::
@c * dmod_elimination_appell2::
@c * dmod_elimination_appell3::
@c * dmod_elimination_appell4::
@c * dmod_elimination_selberg2::
@c * dmod_elimination_gkz::
@end menu

@node dmod_d_op_tosm1,,, D-module
@subsection @code{dmod_d_op_tosm1}
@findex dmod_d_op_tosm1
@table @t
@item dmod_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.
@end table
@table @var
@item return
$B%j%9%H(B
@item LL
$B%j%9%H(B
@item V
$B%j%9%H(B
@end table
@itemize @bullet
@item  $BHyJ,:nMQAG$N78?t$O@0?tB?9`<0$KJQ49$5$l$^$9(B.
@item  @code{dmod_d_op_tosm1}$B$NNc(B
@end itemize
@example
[299] dmod_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))]

[300] dmod_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]

[301] dmod_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))]

[302] dmod_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))]
@end example

@node dmod_d_op_toasir,,, D-module
@subsection @code{dmod_d_op_toasir}
@findex dmod_d_op_toasir
@table @t
@item dmod_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.
@end table
@table @var
@item return
$B%j%9%H(B
@item LL
$B%j%9%H(B
@item V
$B%j%9%H(B
@end table
@itemize @bullet
@item  @code{dmod_d_op_toasir}$B$NNc(B
@end itemize
@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]);
[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]);
[x*dx+y*dy+1,dx^2+dy^2]
@end example

@node dmod_d_op_fromasir,,, D-module
@subsection @code{dmod_d_op_fromasir}
@findex dmod_d_op_fromasir
@table @t
@item dmod_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.
@end table
@table @var
@item return
$B%j%9%H(B
@item D_list
$B%j%9%H(B
@item V
$B%j%9%H(B
@end table
@itemize @bullet
@item  @code{dmod_d_op_fromasir}$B$NNc(B
@end itemize
@example
[305] dmod_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]]]]

[306] dmod_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]]]]
@end example

@node dmod_ch_ideal,,, D-module
@subsection @code{dmod_ch_ideal}
@findex dmod_ch_ideal
@table @t
@item dmod_ch_ideal(@var{D_ideal},@var{V})
::  @var{D_ideal}$B$N(Bcharacteristic ideal$B$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
$B%j%9%H(B
@end table
@itemize @bullet
@item  @code{dmod_ch_ideal}$B$NNc(B
@end itemize
@example
[301] dmod_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]

[302] dmod_ch_ideal(["x dx + 1","dx dy"],[x,y]);
[x*dx,dy]
@end example

@node dmod_restriction,,, D-module
@subsection @code{dmod_restriction}
@findex dmod_restriction
@table @t
@item dmod_restriction(@var{D_ideal},@var{V},@var{Rest})
::  @var{D_ideal}$B$N(Brestriction$B$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{V}
$B%j%9%H(B
@item @var{Rest}
$B%j%9%H(B
@end table
@itemize @bullet
@item  @code{dmod_restriction}$B$NNc(B.
@end itemize
@example
[303] dmod_restriction(["x dx + y dy + 1","dx^2 + dy^2"],[x,y],[y]);
[[2,[-x*dx-1,-e0*x*dx-2*e0]]]
@end example

@node dmod_elimination,,, D-module
@subsection @code{dmod_elimination}
@findex dmod_elimination
@table @t
@item dmod_elimination(@var{D_ideal},@var{V},@var{Elim})
::  @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{V}
$B%j%9%H(B
@item @var{Elim}
$B%j%9%H(B
@end table
@itemize @bullet
@item  @code{dmod_elimination}$B$NNc(B.
@end itemize
@example
[304] dmod_elimination(["x dx + y dy + 1","dx^2 + dy^2"],[x,y],[y]);
[x^2*dx^2+4*x*dx+2]
@end example