Annotation of OpenXM/src/asir-contrib/packages/doc/Dmodule.texi, Revision 1.6
1.6 ! takayama 1: @c $OpenXM: OpenXM/src/asir-contrib/packages/doc/Dmodule.texi,v 1.5 2001/06/24 01:14:21 takayama Exp $
1.5 takayama 2: @node D-module (library by Okutani),,, Top
1.6 ! takayama 3: @chapter D-module (library by Okutani)
1.1 takayama 4: $B%U%!%$%k(B @file{gr}, @file{xm}, @file{Matrix}, @file{Diff} $B$,I,MW$G$9(B.
1.5 takayama 5:
6: Yukio Okutani $B;a$K$h$k(B D-$B2C727W;;MQ$N(B sm1 $B%5!<%P$H$N%$%s%?%U%'!<%9(B
7: $B%i%$%V%i%j$G$9(B. $B$9$Y$F$N4X?tL>$O(B odmodule_ $B$G;O$^$j$^$9(B.
8:
1.1 takayama 9: @menu
1.5 takayama 10: @c * odmodule_make_dv::
11: * odmodule_d_op_tosm1::
12: * odmodule_d_op_toasir::
13: * odmodule_d_op_fromasir::
14: * odmodule_ch_ideal::
15: * odmodule_singular_locus::
16: @c * odmodule_ch_ideal_appell1::
17: @c * odmodule_ch_ideal_appell2::
18: @c * odmodule_ch_ideal_appell3::
19: @c * odmodule_ch_ideal_appell4::
20: @c * odmodule_ch_ideal_selberg2::
21: @c * odmodule_ch_ideal_gkz::
22: * odmodule_restriction::
23: @c * odmodule_restriction_appell1::
24: @c * odmodule_restriction_appell2::
25: @c * odmodule_restriction_appell3::
26: @c * odmodule_restriction_appell4::
27: @c * odmodule_restriction_selberg2::
28: @c * odmodule_restriction_gkz::
29: * odmodule_elimination::
30: @c * odmodule_elimination_appell1::
31: @c * odmodule_elimination_appell2::
32: @c * odmodule_elimination_appell3::
33: @c * odmodule_elimination_appell4::
34: @c * odmodule_elimination_selberg2::
35: @c * odmodule_elimination_gkz::
1.1 takayama 36: @end menu
37:
1.5 takayama 38: @node odmodule_d_op_tosm1,,, D-module (library by Okutani)
39: @subsection @code{odmodule_d_op_tosm1}
40: @findex odmodule_d_op_tosm1
1.1 takayama 41: @table @t
1.5 takayama 42: @item odmodule_d_op_tosm1(@var{LL},@var{V})
1.1 takayama 43: :: $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$r(B sm1 $B7A<0$KJQ49$7$^$9(B.
44: @end table
45: @table @var
46: @item return
47: $B%j%9%H(B
48: @item LL
49: $B%j%9%H(B
50: @item V
51: $B%j%9%H(B
52: @end table
53: @itemize @bullet
54: @item $BHyJ,:nMQAG$N78?t$O@0?tB?9`<0$KJQ49$5$l$^$9(B.
1.4 okutani 55: @item $B$3$N4X?t$O(B@code{diff_op_tosm1}$B$HEy2A$G$9(B.
1.5 takayama 56: @item @code{odmodule_d_op_tosm1}$B$NNc(B
1.1 takayama 57: @end itemize
58: @example
1.5 takayama 59: [299] odmodule_d_op_tosm1([[[x,[2,0]],[-1,[0,0]]],
1.3 okutani 60: [[y,[0,2]],[-1,[0,0]]]],[x,y]);
1.1 takayama 61: [ + ( + (1) x) dx^2 + ( + (-1)), + ( + (1) y) dy^2 + ( + (-1))]
62:
1.5 takayama 63: [300] odmodule_d_op_tosm1([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],
1.3 okutani 64: [[1,[2,0]],[1,[0,2]]]],[x,y]);
1.1 takayama 65: [ + ( + (1) x) dx + ( + (1) y) dy + ( + (1)), + ( + (1)) dx^2 + ( + (1)) dy^2]
66:
1.5 takayama 67: [301] odmodule_d_op_tosm1([[[1/2,[1,0]],[1,[0,0]]],
1.3 okutani 68: [[1/3,[0,1]],[1/4,[0,0]]]],[x,y]);
1.1 takayama 69: [ + ( + (6)) dx + ( + (12)), + ( + (4)) dy + ( + (3))]
70:
1.5 takayama 71: [302] odmodule_d_op_tosm1([[[1/2*x,[1,0]],[1,[0,0]]],
1.3 okutani 72: [[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
1.1 takayama 73: [ + ( + (6) x) dx + ( + (12)), + ( + (4) y) dy + ( + (3))]
74: @end example
75:
1.5 takayama 76: @node odmodule_d_op_toasir,,, D-module (library by Okutani)
77: @subsection @code{odmodule_d_op_toasir}
78: @findex odmodule_d_op_toasir
1.1 takayama 79: @table @t
1.5 takayama 80: @item odmodule_d_op_toasir(@var{LL},@var{V})
1.2 okutani 81: :: $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H(B @var{LL} $B$r(B @code{asir} $B$NB?9`<0$KJQ49$7$^$9(B.
1.1 takayama 82: @end table
83: @table @var
84: @item return
85: $B%j%9%H(B
86: @item LL
87: $B%j%9%H(B
88: @item V
89: $B%j%9%H(B
90: @end table
91: @itemize @bullet
1.4 okutani 92: @item $B$3$N4X?t$O(B@code{diff_op_toasir}$B$HEy2A$G$9(B.
1.5 takayama 93: @item @code{odmodule_d_op_toasir}$B$NNc(B
1.1 takayama 94: @end itemize
95: @example
1.5 takayama 96: [303] odmodule_d_op_toasir([[[1/2*x,[1,0]],[1,[0,0]]],
1.3 okutani 97: [[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
1.1 takayama 98: [1/2*x*dx+1,1/3*y*dy+1/4]
99:
1.5 takayama 100: [304] odmodule_d_op_toasir([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],
1.3 okutani 101: [[1,[2,0]],[1,[0,2]]]],[x,y]);
1.1 takayama 102: [x*dx+y*dy+1,dx^2+dy^2]
103: @end example
104:
1.5 takayama 105: @node odmodule_d_op_fromasir,,, D-module (library by Okutani)
106: @subsection @code{odmodule_d_op_fromasir}
107: @findex odmodule_d_op_fromasir
1.1 takayama 108: @table @t
1.5 takayama 109: @item odmodule_d_op_fromasir(@var{D_list},@var{V})
1.2 okutani 110: :: @code{asir} $B$NB?9`<0$+$i%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$KJQ49$7$^$9(B.
1.1 takayama 111: @end table
112: @table @var
113: @item return
114: $B%j%9%H(B
115: @item D_list
116: $B%j%9%H(B
117: @item V
118: $B%j%9%H(B
119: @end table
120: @itemize @bullet
1.4 okutani 121: @item $B$3$N4X?t$O(B@code{diff_op_fromasir}$B$HEy2A$G$9(B.
1.5 takayama 122: @item @code{odmodule_d_op_fromasir}$B$NNc(B
1.1 takayama 123: @end itemize
124: @example
1.5 takayama 125: [305] odmodule_d_op_fromasir([1/2*x*dx+1,1/3*y*dy+1/4],[x,y]);
1.1 takayama 126: [[[1/2*x,[1,0]],[1,[0,0]]],[[1/3*y,[0,1]],[1/4,[0,0]]]]
127:
1.5 takayama 128: [306] odmodule_d_op_fromasir([x*dx+y*dy+1,dx^2+dy^2],[x,y]);
1.1 takayama 129: [[[x,[1,0]],[y,[0,1]],[1,[0,0]]],[[1,[2,0]],[1,[0,2]]]]
130: @end example
131:
1.5 takayama 132: @node odmodule_ch_ideal,,, D-module (library by Okutani)
133: @subsection @code{odmodule_ch_ideal}
134: @findex odmodule_ch_ideal
1.1 takayama 135: @table @t
1.5 takayama 136: @item odmodule_ch_ideal(@var{D_ideal},@var{V})
1.1 takayama 137: :: @var{D_ideal}$B$N(Bcharacteristic ideal$B$r5a$a$^$9(B.
138: @end table
139: @table @var
140: @item return
141: $B%j%9%H(B
142: @item D_ideal
143: $B%j%9%H(B
144: @item V
145: $B%j%9%H(B
146: @end table
147: @itemize @bullet
1.4 okutani 148: @item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
1.5 takayama 149: @item @code{odmodule_ch_ideal}$B$NNc(B
1.1 takayama 150: @end itemize
151: @example
1.5 takayama 152: [344] odmodule_ch_ideal([x*dx+y*dy+a,dx^2+dy^2],[x,y]);
1.1 takayama 153: [x*dx+y*dy,dx^2+dy^2,y*dy*dx-x*dy^2,(x^2+y^2)*dy^2]
154:
1.5 takayama 155: [348] odmodule_ch_ideal(diff_op_appell4(a,b,c1,c2,[x,y]),[x,y]);
1.4 okutani 156: [-x*dx^2+y*dy^2,2*y*x*dy*dx+(y*x+y^2-y)*dy^2,
157: (2*y^2-2*y)*dy^2*dx+(-y*x+3*y^2+y)*dy^3,
158: 2*y*x*dy^2*dx+(y*x^2+(-2*y^2-y)*x+y^3-y^2)*dy^3]
159: @end example
160:
1.5 takayama 161: @node odmodule_singular_locus,,, D-module (library by Okutani)
162: @subsection @code{odmodule_singular_locus}
163: @findex odmodule_singular_locus
1.4 okutani 164: @table @t
1.5 takayama 165: @item odmodule_singular_locus(@var{D_ideal},@var{V})
1.4 okutani 166: :: @var{D_ideal}$B$N(Bsingular locus$B$r5a$a$^$9(B.
167: @end table
168: @table @var
169: @item return
170: $B%j%9%H(B
171: @item D_ideal
172: $B%j%9%H(B
173: @item V
174: $B%j%9%H(B
175: @end table
176: @itemize @bullet
177: @item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
1.5 takayama 178: @item @code{odmodule_singular_locus}$B$NNc(B
1.4 okutani 179: @end itemize
180: @example
181: [356] D = diff_op_appell4(a,b,c1,c2,[x,y])$
1.5 takayama 182: [357] odmodule_singular_locus(D,[x,y]);
1.4 okutani 183: [-y*x^3+(2*y^2+2*y)*x^2+(-y^3+2*y^2-y)*x]
184:
185: [358] D = diff_op_hg1(a,b,c,[x])$
1.5 takayama 186: [359] odmodule_singular_locus(D,[x]);
1.4 okutani 187: [x^2-x]
1.1 takayama 188: @end example
189:
1.5 takayama 190: @node odmodule_restriction,,, D-module (library by Okutani)
191: @subsection @code{odmodule_restriction}
192: @findex odmodule_restriction
1.1 takayama 193: @table @t
1.5 takayama 194: @item odmodule_restriction(@var{D_ideal},@var{V},@var{Rest})
1.1 takayama 195: :: @var{D_ideal}$B$N(Brestriction$B$r5a$a$^$9(B.
196: @end table
197: @table @var
198: @item return
199: $B%j%9%H(B
200: @item @var{D_ideal}
201: $B%j%9%H(B
202: @item @var{V}
203: $B%j%9%H(B
204: @item @var{Rest}
205: $B%j%9%H(B
206: @end table
207: @itemize @bullet
1.4 okutani 208: @item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
1.5 takayama 209: @item @code{odmodule_restriction}$B$NNc(B.
1.1 takayama 210: @end itemize
211: @example
1.5 takayama 212: [345] odmodule_restriction([x*dx+y*dy+a,dx^2+dy^2],[x,y],[y]);
1.4 okutani 213: [[2,[-x*dx-a,-e0*x*dx-e0*a-e0]]]
1.1 takayama 214: @end example
215:
1.5 takayama 216: @node odmodule_elimination,,, D-module (library by Okutani)
217: @subsection @code{odmodule_elimination}
218: @findex odmodule_elimination
1.1 takayama 219: @table @t
1.5 takayama 220: @item odmodule_elimination(@var{D_ideal},@var{V},@var{Elim})
1.1 takayama 221: :: @var{D_ideal}$B$N(Belimination ideal$B$r5a$a$^$9(B.
222: @end table
223: @table @var
224: @item return
225: $B%j%9%H(B
226: @item @var{D_ideal}
227: $B%j%9%H(B
228: @item @var{V}
229: $B%j%9%H(B
230: @item @var{Elim}
231: $B%j%9%H(B
232: @end table
233: @itemize @bullet
1.4 okutani 234: @item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
1.5 takayama 235: @item @code{odmodule_elimination}$B$NNc(B.
1.1 takayama 236: @end itemize
237: @example
1.5 takayama 238: [346] odmodule_elimination([x*dx+y*dy+a,dx^2+dy^2],[x,y],[[y],[0]]);
1.4 okutani 239: [x^2*dx^2+(2*a+2)*x*dx+a^2+a]
1.3 okutani 240:
1.5 takayama 241: [347] odmodule_elimination([x*dx+y*dy+a,dx^2+dy^2],[x,y],[[y],[b]]);
1.4 okutani 242: [(x^2+b^2)*dx^2+(2*a+2)*x*dx+a^2+a]
1.1 takayama 243: @end example
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