Annotation of OpenXM/src/asir-contrib/packages/doc/Dmodule.texi, Revision 1.4
1.4 ! okutani 1: @c $OpenXM: OpenXM/src/asir-contrib/packages/doc/Dmodule.texi,v 1.3 2000/01/03 09:15:53 okutani Exp $
1.1 takayama 2: @node D-module,,, $B$=$NB>$NH!?t(B
3: @section D-module
4: $B%U%!%$%k(B @file{gr}, @file{xm}, @file{Matrix}, @file{Diff} $B$,I,MW$G$9(B.
5: @menu
1.3 okutani 6: @c * dmodule_make_dv::
7: * dmodule_d_op_tosm1::
8: * dmodule_d_op_toasir::
9: * dmodule_d_op_fromasir::
10: * dmodule_ch_ideal::
1.4 ! okutani 11: * dmodule_singular_locus::
1.3 okutani 12: @c * dmodule_ch_ideal_appell1::
13: @c * dmodule_ch_ideal_appell2::
14: @c * dmodule_ch_ideal_appell3::
15: @c * dmodule_ch_ideal_appell4::
16: @c * dmodule_ch_ideal_selberg2::
17: @c * dmodule_ch_ideal_gkz::
18: * dmodule_restriction::
19: @c * dmodule_restriction_appell1::
20: @c * dmodule_restriction_appell2::
21: @c * dmodule_restriction_appell3::
22: @c * dmodule_restriction_appell4::
23: @c * dmodule_restriction_selberg2::
24: @c * dmodule_restriction_gkz::
25: * dmodule_elimination::
26: @c * dmodule_elimination_appell1::
27: @c * dmodule_elimination_appell2::
28: @c * dmodule_elimination_appell3::
29: @c * dmodule_elimination_appell4::
30: @c * dmodule_elimination_selberg2::
31: @c * dmodule_elimination_gkz::
1.1 takayama 32: @end menu
33:
1.3 okutani 34: @node dmodule_d_op_tosm1,,, D-module
35: @subsection @code{dmodule_d_op_tosm1}
36: @findex dmodule_d_op_tosm1
1.1 takayama 37: @table @t
1.3 okutani 38: @item dmodule_d_op_tosm1(@var{LL},@var{V})
1.1 takayama 39: :: $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$r(B sm1 $B7A<0$KJQ49$7$^$9(B.
40: @end table
41: @table @var
42: @item return
43: $B%j%9%H(B
44: @item LL
45: $B%j%9%H(B
46: @item V
47: $B%j%9%H(B
48: @end table
49: @itemize @bullet
50: @item $BHyJ,:nMQAG$N78?t$O@0?tB?9`<0$KJQ49$5$l$^$9(B.
1.4 ! okutani 51: @item $B$3$N4X?t$O(B@code{diff_op_tosm1}$B$HEy2A$G$9(B.
1.3 okutani 52: @item @code{dmodule_d_op_tosm1}$B$NNc(B
1.1 takayama 53: @end itemize
54: @example
1.3 okutani 55: [299] dmodule_d_op_tosm1([[[x,[2,0]],[-1,[0,0]]],
56: [[y,[0,2]],[-1,[0,0]]]],[x,y]);
1.1 takayama 57: [ + ( + (1) x) dx^2 + ( + (-1)), + ( + (1) y) dy^2 + ( + (-1))]
58:
1.3 okutani 59: [300] dmodule_d_op_tosm1([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],
60: [[1,[2,0]],[1,[0,2]]]],[x,y]);
1.1 takayama 61: [ + ( + (1) x) dx + ( + (1) y) dy + ( + (1)), + ( + (1)) dx^2 + ( + (1)) dy^2]
62:
1.3 okutani 63: [301] dmodule_d_op_tosm1([[[1/2,[1,0]],[1,[0,0]]],
64: [[1/3,[0,1]],[1/4,[0,0]]]],[x,y]);
1.1 takayama 65: [ + ( + (6)) dx + ( + (12)), + ( + (4)) dy + ( + (3))]
66:
1.3 okutani 67: [302] dmodule_d_op_tosm1([[[1/2*x,[1,0]],[1,[0,0]]],
68: [[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
1.1 takayama 69: [ + ( + (6) x) dx + ( + (12)), + ( + (4) y) dy + ( + (3))]
70: @end example
71:
1.3 okutani 72: @node dmodule_d_op_toasir,,, D-module
73: @subsection @code{dmodule_d_op_toasir}
74: @findex dmodule_d_op_toasir
1.1 takayama 75: @table @t
1.3 okutani 76: @item dmodule_d_op_toasir(@var{LL},@var{V})
1.2 okutani 77: :: $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H(B @var{LL} $B$r(B @code{asir} $B$NB?9`<0$KJQ49$7$^$9(B.
1.1 takayama 78: @end table
79: @table @var
80: @item return
81: $B%j%9%H(B
82: @item LL
83: $B%j%9%H(B
84: @item V
85: $B%j%9%H(B
86: @end table
87: @itemize @bullet
1.4 ! okutani 88: @item $B$3$N4X?t$O(B@code{diff_op_toasir}$B$HEy2A$G$9(B.
1.3 okutani 89: @item @code{dmodule_d_op_toasir}$B$NNc(B
1.1 takayama 90: @end itemize
91: @example
1.3 okutani 92: [303] dmodule_d_op_toasir([[[1/2*x,[1,0]],[1,[0,0]]],
93: [[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
1.1 takayama 94: [1/2*x*dx+1,1/3*y*dy+1/4]
95:
1.3 okutani 96: [304] dmodule_d_op_toasir([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],
97: [[1,[2,0]],[1,[0,2]]]],[x,y]);
1.1 takayama 98: [x*dx+y*dy+1,dx^2+dy^2]
99: @end example
100:
1.3 okutani 101: @node dmodule_d_op_fromasir,,, D-module
102: @subsection @code{dmodule_d_op_fromasir}
103: @findex dmodule_d_op_fromasir
1.1 takayama 104: @table @t
1.3 okutani 105: @item dmodule_d_op_fromasir(@var{D_list},@var{V})
1.2 okutani 106: :: @code{asir} $B$NB?9`<0$+$i%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$KJQ49$7$^$9(B.
1.1 takayama 107: @end table
108: @table @var
109: @item return
110: $B%j%9%H(B
111: @item D_list
112: $B%j%9%H(B
113: @item V
114: $B%j%9%H(B
115: @end table
116: @itemize @bullet
1.4 ! okutani 117: @item $B$3$N4X?t$O(B@code{diff_op_fromasir}$B$HEy2A$G$9(B.
1.3 okutani 118: @item @code{dmodule_d_op_fromasir}$B$NNc(B
1.1 takayama 119: @end itemize
120: @example
1.3 okutani 121: [305] dmodule_d_op_fromasir([1/2*x*dx+1,1/3*y*dy+1/4],[x,y]);
1.1 takayama 122: [[[1/2*x,[1,0]],[1,[0,0]]],[[1/3*y,[0,1]],[1/4,[0,0]]]]
123:
1.3 okutani 124: [306] dmodule_d_op_fromasir([x*dx+y*dy+1,dx^2+dy^2],[x,y]);
1.1 takayama 125: [[[x,[1,0]],[y,[0,1]],[1,[0,0]]],[[1,[2,0]],[1,[0,2]]]]
126: @end example
127:
1.3 okutani 128: @node dmodule_ch_ideal,,, D-module
129: @subsection @code{dmodule_ch_ideal}
130: @findex dmodule_ch_ideal
1.1 takayama 131: @table @t
1.3 okutani 132: @item dmodule_ch_ideal(@var{D_ideal},@var{V})
1.1 takayama 133: :: @var{D_ideal}$B$N(Bcharacteristic ideal$B$r5a$a$^$9(B.
134: @end table
135: @table @var
136: @item return
137: $B%j%9%H(B
138: @item D_ideal
139: $B%j%9%H(B
140: @item V
141: $B%j%9%H(B
142: @end table
143: @itemize @bullet
1.4 ! okutani 144: @item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
1.3 okutani 145: @item @code{dmodule_ch_ideal}$B$NNc(B
1.1 takayama 146: @end itemize
147: @example
1.4 ! okutani 148: [344] dmodule_ch_ideal([x*dx+y*dy+a,dx^2+dy^2],[x,y]);
1.1 takayama 149: [x*dx+y*dy,dx^2+dy^2,y*dy*dx-x*dy^2,(x^2+y^2)*dy^2]
150:
1.4 ! okutani 151: [348] dmodule_ch_ideal(diff_op_appell4(a,b,c1,c2,[x,y]),[x,y]);
! 152: [-x*dx^2+y*dy^2,2*y*x*dy*dx+(y*x+y^2-y)*dy^2,
! 153: (2*y^2-2*y)*dy^2*dx+(-y*x+3*y^2+y)*dy^3,
! 154: 2*y*x*dy^2*dx+(y*x^2+(-2*y^2-y)*x+y^3-y^2)*dy^3]
! 155: @end example
! 156:
! 157: @node dmodule_singular_locus,,, D-module
! 158: @subsection @code{dmodule_singular_locus}
! 159: @findex dmodule_singular_locus
! 160: @table @t
! 161: @item dmodule_singular_locus(@var{D_ideal},@var{V})
! 162: :: @var{D_ideal}$B$N(Bsingular locus$B$r5a$a$^$9(B.
! 163: @end table
! 164: @table @var
! 165: @item return
! 166: $B%j%9%H(B
! 167: @item D_ideal
! 168: $B%j%9%H(B
! 169: @item V
! 170: $B%j%9%H(B
! 171: @end table
! 172: @itemize @bullet
! 173: @item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
! 174: @item @code{dmodule_singular_locus}$B$NNc(B
! 175: @end itemize
! 176: @example
! 177: [356] D = diff_op_appell4(a,b,c1,c2,[x,y])$
! 178: [357] dmodule_singular_locus(D,[x,y]);
! 179: [-y*x^3+(2*y^2+2*y)*x^2+(-y^3+2*y^2-y)*x]
! 180:
! 181: [358] D = diff_op_hg1(a,b,c,[x])$
! 182: [359] dmodule_singular_locus(D,[x]);
! 183: [x^2-x]
1.1 takayama 184: @end example
185:
1.3 okutani 186: @node dmodule_restriction,,, D-module
187: @subsection @code{dmodule_restriction}
188: @findex dmodule_restriction
1.1 takayama 189: @table @t
1.3 okutani 190: @item dmodule_restriction(@var{D_ideal},@var{V},@var{Rest})
1.1 takayama 191: :: @var{D_ideal}$B$N(Brestriction$B$r5a$a$^$9(B.
192: @end table
193: @table @var
194: @item return
195: $B%j%9%H(B
196: @item @var{D_ideal}
197: $B%j%9%H(B
198: @item @var{V}
199: $B%j%9%H(B
200: @item @var{Rest}
201: $B%j%9%H(B
202: @end table
203: @itemize @bullet
1.4 ! okutani 204: @item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
1.3 okutani 205: @item @code{dmodule_restriction}$B$NNc(B.
1.1 takayama 206: @end itemize
207: @example
1.4 ! okutani 208: [345] dmodule_restriction([x*dx+y*dy+a,dx^2+dy^2],[x,y],[y]);
! 209: [[2,[-x*dx-a,-e0*x*dx-e0*a-e0]]]
1.1 takayama 210: @end example
211:
1.3 okutani 212: @node dmodule_elimination,,, D-module
213: @subsection @code{dmodule_elimination}
214: @findex dmodule_elimination
1.1 takayama 215: @table @t
1.3 okutani 216: @item dmodule_elimination(@var{D_ideal},@var{V},@var{Elim})
1.1 takayama 217: :: @var{D_ideal}$B$N(Belimination ideal$B$r5a$a$^$9(B.
218: @end table
219: @table @var
220: @item return
221: $B%j%9%H(B
222: @item @var{D_ideal}
223: $B%j%9%H(B
224: @item @var{V}
225: $B%j%9%H(B
226: @item @var{Elim}
227: $B%j%9%H(B
228: @end table
229: @itemize @bullet
1.4 ! okutani 230: @item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
1.3 okutani 231: @item @code{dmodule_elimination}$B$NNc(B.
1.1 takayama 232: @end itemize
233: @example
1.4 ! okutani 234: [346] dmodule_elimination([x*dx+y*dy+a,dx^2+dy^2],[x,y],[[y],[0]]);
! 235: [x^2*dx^2+(2*a+2)*x*dx+a^2+a]
1.3 okutani 236:
1.4 ! okutani 237: [347] dmodule_elimination([x*dx+y*dy+a,dx^2+dy^2],[x,y],[[y],[b]]);
! 238: [(x^2+b^2)*dx^2+(2*a+2)*x*dx+a^2+a]
1.1 takayama 239: @end example
FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>
![[BACK]](/icons/cvsweb/back.gif){kind=icon}
Return to Dmodule.texi CVS log ![[TXT]](/icons/cvsweb/text.gif){kind=icon}
![[DIR]](/icons/cvsweb/dir.gif){kind=icon}
Up to [local] / OpenXM / src / asir-contrib / packages / doc