Return to Dmodule-ja.texi CVS log

Up to [local] / OpenXM / src / asir-contrib / packages / doc

Several fixed of typos in the manual (up to the section 23).
Imported new functions: glib_plot, pfp_omega, sm1_restriction.
Changed algorithm: omatrix_inverse uses invmat.

@c $OpenXM: OpenXM/src/asir-contrib/packages/doc/Dmodule-ja.texi,v 1.3 2002/08/08 08:56:32 takayama Exp $
@node D-module (library by Okutani),,, Top
@chapter D-module (library by Okutani)
$B%U%!%$%k(B @file{gr}, @file{xm}, @file{Matrix}, @file{Diff}, @file{Dmodule}
$B$,I,MW$G$9(B.

OpenXM/Risa/Asir $B$G$NMxMQ$K$"$?$C$F$O(B,
@example
load("Diff")$ load("Dmodule")$
@end example
$B$,;O$a$KI,MW(B.

Yukio Okutani $B;a$K$h$k(B D-$B2C727W;;MQ$N(B sm1 $B%5!<%P$H$N%$%s%?%U%'!<%9(B
$B%i%$%V%i%j$G$9(B. $B$9$Y$F$N4X?tL>$O(B odmodule_ $B$G;O$^$j$^$9(B. 

@menu
@c * odmodule_make_dv::
* odmodule_d_op_tosm1::
* odmodule_d_op_toasir::
* odmodule_d_op_fromasir::
* odmodule_ch_ideal::
* odmodule_singular_locus::
@c * odmodule_ch_ideal_appell1::
@c * odmodule_ch_ideal_appell2::
@c * odmodule_ch_ideal_appell3::
@c * odmodule_ch_ideal_appell4::
@c * odmodule_ch_ideal_selberg2::
@c * odmodule_ch_ideal_gkz::
* odmodule_restriction::
@c * odmodule_restriction_appell1::
@c * odmodule_restriction_appell2::
@c * odmodule_restriction_appell3::
@c * odmodule_restriction_appell4::
@c * odmodule_restriction_selberg2::
@c * odmodule_restriction_gkz::
* odmodule_elimination::
@c * odmodule_elimination_appell1::
@c * odmodule_elimination_appell2::
@c * odmodule_elimination_appell3::
@c * odmodule_elimination_appell4::
@c * odmodule_elimination_selberg2::
@c * odmodule_elimination_gkz::
@end menu

@node odmodule_d_op_tosm1,,, D-module (library by Okutani)
@subsection @code{odmodule_d_op_tosm1}
@findex odmodule_d_op_tosm1
@table @t
@item odmodule_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  $B$3$N4X?t$O(B@code{diff_op_tosm1}$B$HEy2A$G$9(B.
@item  @code{odmodule_d_op_tosm1}$B$NNc(B
@end itemize
@example
[299] odmodule_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] odmodule_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] odmodule_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] odmodule_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 odmodule_d_op_toasir,,, D-module (library by Okutani)
@subsection @code{odmodule_d_op_toasir}
@findex odmodule_d_op_toasir
@table @t
@item odmodule_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  $B$3$N4X?t$O(B@code{diff_op_toasir}$B$HEy2A$G$9(B.
@item  @code{odmodule_d_op_toasir}$B$NNc(B
@end itemize
@example
[303] odmodule_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] odmodule_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 odmodule_d_op_fromasir,,, D-module (library by Okutani)
@subsection @code{odmodule_d_op_fromasir}
@findex odmodule_d_op_fromasir
@table @t
@item odmodule_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  $B$3$N4X?t$O(B@code{diff_op_fromasir}$B$HEy2A$G$9(B.
@item  @code{odmodule_d_op_fromasir}$B$NNc(B
@end itemize
@example
[305] odmodule_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] odmodule_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 odmodule_ch_ideal,,, D-module (library by Okutani)
@subsection @code{odmodule_ch_ideal}
@findex odmodule_ch_ideal
@table @t
@item odmodule_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
$B%j%9%H(B
@end table
@itemize @bullet
@item  @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
@item  @code{odmodule_ch_ideal}$B$NNc(B
@end itemize
@example
[344] odmodule_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]

[348] odmodule_ch_ideal(diff_op_appell4(a,b,c1,c2,[x,y]),[x,y]);
[-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

@node odmodule_singular_locus,,, D-module (library by Okutani)
@subsection @code{odmodule_singular_locus}
@findex odmodule_singular_locus
@table @t
@item odmodule_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$-$^$9(B.
@item  @code{odmodule_singular_locus}$B$NNc(B
@end itemize
@example
[356] D = diff_op_appell4(a,b,c1,c2,[x,y])$
[357] odmodule_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] odmodule_singular_locus(D,[x]);
[x^2-x]
@end example

@node odmodule_restriction,,, D-module (library by Okutani)
@subsection @code{odmodule_restriction}
@findex odmodule_restriction
@table @t
@item odmodule_restriction(@var{D_ideal},@var{V},@var{Rest})
::  @var{D_ideal}$B$N(B 0 $B<!$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}
$B%j%9%H(B
@end table
@itemize @bullet
@item  @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
@item  @code{odmodule_restriction}$B$NNc(B.
@end itemize
@example
[345] odmodule_restriction([x*dx+y*dy+a,dx^2+dy^2],[x,y],[y]);
[[2,[-x*dx-a,-e0*x*dx-e0*a-e0]]]
@end example

@node odmodule_elimination,,, D-module (library by Okutani)
@subsection @code{odmodule_elimination}
@findex odmodule_elimination
@table @t
@item odmodule_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}
$B%j%9%H(B
@end table
@itemize @bullet
@item  @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
@item  @code{odmodule_elimination}$B$NNc(B.
@end itemize
@example
[346] odmodule_elimination([x*dx+y*dy+a,dx^2+dy^2],[x,y],[[y],[0]]);
[x^2*dx^2+(2*a+2)*x*dx+a^2+a]

[347] odmodule_elimination([x*dx+y*dy+a,dx^2+dy^2],[x,y],[[y],[b]]);
[(x^2+b^2)*dx^2+(2*a+2)*x*dx+a^2+a]
@end example