version 1.1, 1999/11/27 11:25:18 |
version 1.4, 2000/02/20 11:30:44 |
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@c $OpenXM: OpenXM/src/asir99/lib/contrib/packages/doc/Dmodule.texi,v 1.3 1999/11/23 05:57:47 okutani Exp $ |
@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. |
@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:: |
* dmodule_singular_locus:: |
@c * dmod_ch_ideal_appell2:: |
@c * dmodule_ch_ideal_appell1:: |
@c * dmod_ch_ideal_appell3:: |
@c * dmodule_ch_ideal_appell2:: |
@c * dmod_ch_ideal_appell4:: |
@c * dmodule_ch_ideal_appell3:: |
@c * dmod_ch_ideal_selberg2:: |
@c * dmodule_ch_ideal_appell4:: |
@c * dmod_ch_ideal_gkz:: |
@c * dmodule_ch_ideal_selberg2:: |
* dmod_restriction:: |
@c * dmodule_ch_ideal_gkz:: |
@c * dmod_restriction_appell1:: |
* dmodule_restriction:: |
@c * dmod_restriction_appell2:: |
@c * dmodule_restriction_appell1:: |
@c * dmod_restriction_appell3:: |
@c * dmodule_restriction_appell2:: |
@c * dmod_restriction_appell4:: |
@c * dmodule_restriction_appell3:: |
@c * dmod_restriction_selberg2:: |
@c * dmodule_restriction_appell4:: |
@c * dmod_restriction_gkz:: |
@c * dmodule_restriction_selberg2:: |
* dmod_elimination:: |
@c * dmodule_restriction_gkz:: |
@c * dmod_elimination_appell1:: |
* dmodule_elimination:: |
@c * dmod_elimination_appell2:: |
@c * dmodule_elimination_appell1:: |
@c * dmod_elimination_appell3:: |
@c * dmodule_elimination_appell2:: |
@c * dmod_elimination_appell4:: |
@c * dmodule_elimination_appell3:: |
@c * dmod_elimination_selberg2:: |
@c * dmodule_elimination_appell4:: |
@c * dmod_elimination_gkz:: |
@c * dmodule_elimination_selberg2:: |
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@c * dmodule_elimination_gkz:: |
@end menu |
@end menu |
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@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 $B$3$N4X?t$O(B@code{diff_op_tosm1}$B$HEy2A$G$9(B. |
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@item @code{dmodule_d_op_tosm1}$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]]], |
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[[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))] |
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[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]]], |
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[[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] |
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[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]]], |
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[[1/3,[0,1]],[1/4,[0,0]]]],[x,y]); |
[ + ( + (6)) dx + ( + (12)), + ( + (4)) dy + ( + (3))] |
[ + ( + (6)) dx + ( + (12)), + ( + (4)) dy + ( + (3))] |
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[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]]], |
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[[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 |
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@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 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$7$^$9(B. |
@end table |
@end table |
@table @var |
@table @var |
@item return |
@item return |
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$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 $B$3$N4X?t$O(B@code{diff_op_toasir}$B$HEy2A$G$9(B. |
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@item @code{dmodule_d_op_toasir}$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]]], |
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[[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] |
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[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]]], |
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[[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 |
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@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}) |
:: 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$7$^$9(B. |
@end table |
@end table |
@table @var |
@table @var |
@item return |
@item return |
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$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 $B$3$N4X?t$O(B@code{diff_op_fromasir}$B$HEy2A$G$9(B. |
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@item @code{dmodule_d_op_fromasir}$B$NNc(B |
@end itemize |
@end itemize |
@example |
@example |
[305] dmod_d_op_fromasir([1/2*x*dx+1,1/3*y*dy+1/4],[x,y]); |
[305] dmodule_d_op_fromasir([1/2*x*dx+1,1/3*y*dy+1/4],[x,y]); |
[[[1/2*x,[1,0]],[1,[0,0]]],[[1/3*y,[0,1]],[1/4,[0,0]]]] |
[[[1/2*x,[1,0]],[1,[0,0]]],[[1/3*y,[0,1]],[1/4,[0,0]]]] |
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[306] dmod_d_op_fromasir([x*dx+y*dy+1,dx^2+dy^2],[x,y]); |
[306] dmodule_d_op_fromasir([x*dx+y*dy+1,dx^2+dy^2],[x,y]); |
[[[x,[1,0]],[y,[0,1]],[1,[0,0]]],[[1,[2,0]],[1,[0,2]]]] |
[[[x,[1,0]],[y,[0,1]],[1,[0,0]]],[[1,[2,0]],[1,[0,2]]]] |
@end example |
@end example |
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@node dmod_ch_ideal,,, D-module |
@node dmodule_ch_ideal,,, D-module |
@subsection @code{dmod_ch_ideal} |
@subsection @code{dmodule_ch_ideal} |
@findex dmod_ch_ideal |
@findex dmodule_ch_ideal |
@table @t |
@table @t |
@item dmod_ch_ideal(@var{D_ideal},@var{V}) |
@item dmodule_ch_ideal(@var{D_ideal},@var{V}) |
:: @var{D_ideal}$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$NNc(B |
@item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B. |
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@item @code{dmodule_ch_ideal}$B$NNc(B |
@end itemize |
@end itemize |
@example |
@example |
[301] dmod_ch_ideal(["x dx + y dy + 1","dx^2 + dy^2"],[x,y]); |
[344] dmodule_ch_ideal([x*dx+y*dy+a,dx^2+dy^2],[x,y]); |
[x*dx+y*dy,dx^2+dy^2,y*dy*dx-x*dy^2,(x^2+y^2)*dy^2] |
[x*dx+y*dy,dx^2+dy^2,y*dy*dx-x*dy^2,(x^2+y^2)*dy^2] |
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[302] dmod_ch_ideal(["x dx + 1","dx dy"],[x,y]); |
[348] dmodule_ch_ideal(diff_op_appell4(a,b,c1,c2,[x,y]),[x,y]); |
[x*dx,dy] |
[-x*dx^2+y*dy^2,2*y*x*dy*dx+(y*x+y^2-y)*dy^2, |
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(2*y^2-2*y)*dy^2*dx+(-y*x+3*y^2+y)*dy^3, |
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2*y*x*dy^2*dx+(y*x^2+(-2*y^2-y)*x+y^3-y^2)*dy^3] |
@end example |
@end example |
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@node dmod_restriction,,, D-module |
@node dmodule_singular_locus,,, D-module |
@subsection @code{dmod_restriction} |
@subsection @code{dmodule_singular_locus} |
@findex dmod_restriction |
@findex dmodule_singular_locus |
@table @t |
@table @t |
@item dmod_restriction(@var{D_ideal},@var{V},@var{Rest}) |
@item dmodule_singular_locus(@var{D_ideal},@var{V}) |
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:: @var{D_ideal}$B$N(Bsingular locus$B$r5a$a$^$9(B. |
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@end table |
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@table @var |
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@item return |
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$B%j%9%H(B |
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@item D_ideal |
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$B%j%9%H(B |
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@item V |
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$B%j%9%H(B |
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@end table |
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@itemize @bullet |
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@item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B. |
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@item @code{dmodule_singular_locus}$B$NNc(B |
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@end itemize |
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@example |
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[356] D = diff_op_appell4(a,b,c1,c2,[x,y])$ |
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[357] dmodule_singular_locus(D,[x,y]); |
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[-y*x^3+(2*y^2+2*y)*x^2+(-y^3+2*y^2-y)*x] |
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[358] D = diff_op_hg1(a,b,c,[x])$ |
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[359] dmodule_singular_locus(D,[x]); |
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[x^2-x] |
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@end example |
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@node dmodule_restriction,,, D-module |
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@subsection @code{dmodule_restriction} |
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@findex dmodule_restriction |
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@table @t |
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@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$NNc(B. |
@item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B. |
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@item @code{dmodule_restriction}$B$NNc(B. |
@end itemize |
@end itemize |
@example |
@example |
[303] dmod_restriction(["x dx + y dy + 1","dx^2 + dy^2"],[x,y],[y]); |
[345] dmodule_restriction([x*dx+y*dy+a,dx^2+dy^2],[x,y],[y]); |
[[2,[-x*dx-1,-e0*x*dx-2*e0]]] |
[[2,[-x*dx-a,-e0*x*dx-e0*a-e0]]] |
@end example |
@end example |
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@node dmod_elimination,,, D-module |
@node dmodule_elimination,,, D-module |
@subsection @code{dmod_elimination} |
@subsection @code{dmodule_elimination} |
@findex dmod_elimination |
@findex dmodule_elimination |
@table @t |
@table @t |
@item dmod_elimination(@var{D_ideal},@var{V},@var{Elim}) |
@item dmodule_elimination(@var{D_ideal},@var{V},@var{Elim}) |
:: @var{D_ideal}$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$NNc(B. |
@item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B. |
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@item @code{dmodule_elimination}$B$NNc(B. |
@end itemize |
@end itemize |
@example |
@example |
[304] dmod_elimination(["x dx + y dy + 1","dx^2 + dy^2"],[x,y],[y]); |
[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] |
@end example |
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[347] dmodule_elimination([x*dx+y*dy+a,dx^2+dy^2],[x,y],[[y],[b]]); |
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[(x^2+b^2)*dx^2+(2*a+2)*x*dx+a^2+a] |
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@end example |