Annotation of OpenXM/src/asir-contrib/packages/doc/Dmodule-ja.texi, Revision 1.2
1.2 ! takayama 1: @c $OpenXM: OpenXM/src/asir-contrib/packages/doc/Dmodule-ja.texi,v 1.1 2002/07/29 02:56:26 takayama Exp $
1.1 takayama 2: @node D-module (library by Okutani),,, Top
3: @chapter D-module (library by Okutani)
1.2 ! takayama 4: $B%U%!%$%k(B @file{gr}, @file{xm}, @file{Matrix}, @file{Diff}, @file{Dmodule}
! 5: $B$,I,MW$G$9(B.
1.1 takayama 6:
7: Yukio Okutani $B;a$K$h$k(B D-$B2C727W;;MQ$N(B sm1 $B%5!<%P$H$N%$%s%?%U%'!<%9(B
8: $B%i%$%V%i%j$G$9(B. $B$9$Y$F$N4X?tL>$O(B odmodule_ $B$G;O$^$j$^$9(B.
9:
10: @menu
11: @c * odmodule_make_dv::
12: * odmodule_d_op_tosm1::
13: * odmodule_d_op_toasir::
14: * odmodule_d_op_fromasir::
15: * odmodule_ch_ideal::
16: * odmodule_singular_locus::
17: @c * odmodule_ch_ideal_appell1::
18: @c * odmodule_ch_ideal_appell2::
19: @c * odmodule_ch_ideal_appell3::
20: @c * odmodule_ch_ideal_appell4::
21: @c * odmodule_ch_ideal_selberg2::
22: @c * odmodule_ch_ideal_gkz::
23: * odmodule_restriction::
24: @c * odmodule_restriction_appell1::
25: @c * odmodule_restriction_appell2::
26: @c * odmodule_restriction_appell3::
27: @c * odmodule_restriction_appell4::
28: @c * odmodule_restriction_selberg2::
29: @c * odmodule_restriction_gkz::
30: * odmodule_elimination::
31: @c * odmodule_elimination_appell1::
32: @c * odmodule_elimination_appell2::
33: @c * odmodule_elimination_appell3::
34: @c * odmodule_elimination_appell4::
35: @c * odmodule_elimination_selberg2::
36: @c * odmodule_elimination_gkz::
37: @end menu
38:
39: @node odmodule_d_op_tosm1,,, D-module (library by Okutani)
40: @subsection @code{odmodule_d_op_tosm1}
41: @findex odmodule_d_op_tosm1
42: @table @t
43: @item odmodule_d_op_tosm1(@var{LL},@var{V})
44: :: $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$r(B sm1 $B7A<0$KJQ49$7$^$9(B.
45: @end table
46: @table @var
47: @item return
48: $B%j%9%H(B
49: @item LL
50: $B%j%9%H(B
51: @item V
52: $B%j%9%H(B
53: @end table
54: @itemize @bullet
55: @item $BHyJ,:nMQAG$N78?t$O@0?tB?9`<0$KJQ49$5$l$^$9(B.
56: @item $B$3$N4X?t$O(B@code{diff_op_tosm1}$B$HEy2A$G$9(B.
57: @item @code{odmodule_d_op_tosm1}$B$NNc(B
58: @end itemize
59: @example
60: [299] odmodule_d_op_tosm1([[[x,[2,0]],[-1,[0,0]]],
61: [[y,[0,2]],[-1,[0,0]]]],[x,y]);
62: [ + ( + (1) x) dx^2 + ( + (-1)), + ( + (1) y) dy^2 + ( + (-1))]
63:
64: [300] odmodule_d_op_tosm1([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],
65: [[1,[2,0]],[1,[0,2]]]],[x,y]);
66: [ + ( + (1) x) dx + ( + (1) y) dy + ( + (1)), + ( + (1)) dx^2 + ( + (1)) dy^2]
67:
68: [301] odmodule_d_op_tosm1([[[1/2,[1,0]],[1,[0,0]]],
69: [[1/3,[0,1]],[1/4,[0,0]]]],[x,y]);
70: [ + ( + (6)) dx + ( + (12)), + ( + (4)) dy + ( + (3))]
71:
72: [302] odmodule_d_op_tosm1([[[1/2*x,[1,0]],[1,[0,0]]],
73: [[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
74: [ + ( + (6) x) dx + ( + (12)), + ( + (4) y) dy + ( + (3))]
75: @end example
76:
77: @node odmodule_d_op_toasir,,, D-module (library by Okutani)
78: @subsection @code{odmodule_d_op_toasir}
79: @findex odmodule_d_op_toasir
80: @table @t
81: @item odmodule_d_op_toasir(@var{LL},@var{V})
82: :: $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H(B @var{LL} $B$r(B @code{asir} $B$NB?9`<0$KJQ49$7$^$9(B.
83: @end table
84: @table @var
85: @item return
86: $B%j%9%H(B
87: @item LL
88: $B%j%9%H(B
89: @item V
90: $B%j%9%H(B
91: @end table
92: @itemize @bullet
93: @item $B$3$N4X?t$O(B@code{diff_op_toasir}$B$HEy2A$G$9(B.
94: @item @code{odmodule_d_op_toasir}$B$NNc(B
95: @end itemize
96: @example
97: [303] odmodule_d_op_toasir([[[1/2*x,[1,0]],[1,[0,0]]],
98: [[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
99: [1/2*x*dx+1,1/3*y*dy+1/4]
100:
101: [304] odmodule_d_op_toasir([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],
102: [[1,[2,0]],[1,[0,2]]]],[x,y]);
103: [x*dx+y*dy+1,dx^2+dy^2]
104: @end example
105:
106: @node odmodule_d_op_fromasir,,, D-module (library by Okutani)
107: @subsection @code{odmodule_d_op_fromasir}
108: @findex odmodule_d_op_fromasir
109: @table @t
110: @item odmodule_d_op_fromasir(@var{D_list},@var{V})
111: :: @code{asir} $B$NB?9`<0$+$i%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$KJQ49$7$^$9(B.
112: @end table
113: @table @var
114: @item return
115: $B%j%9%H(B
116: @item D_list
117: $B%j%9%H(B
118: @item V
119: $B%j%9%H(B
120: @end table
121: @itemize @bullet
122: @item $B$3$N4X?t$O(B@code{diff_op_fromasir}$B$HEy2A$G$9(B.
123: @item @code{odmodule_d_op_fromasir}$B$NNc(B
124: @end itemize
125: @example
126: [305] odmodule_d_op_fromasir([1/2*x*dx+1,1/3*y*dy+1/4],[x,y]);
127: [[[1/2*x,[1,0]],[1,[0,0]]],[[1/3*y,[0,1]],[1/4,[0,0]]]]
128:
129: [306] odmodule_d_op_fromasir([x*dx+y*dy+1,dx^2+dy^2],[x,y]);
130: [[[x,[1,0]],[y,[0,1]],[1,[0,0]]],[[1,[2,0]],[1,[0,2]]]]
131: @end example
132:
133: @node odmodule_ch_ideal,,, D-module (library by Okutani)
134: @subsection @code{odmodule_ch_ideal}
135: @findex odmodule_ch_ideal
136: @table @t
137: @item odmodule_ch_ideal(@var{D_ideal},@var{V})
138: :: @var{D_ideal}$B$N(Bcharacteristic ideal$B$r5a$a$^$9(B.
139: @end table
140: @table @var
141: @item return
142: $B%j%9%H(B
143: @item D_ideal
144: $B%j%9%H(B
145: @item V
146: $B%j%9%H(B
147: @end table
148: @itemize @bullet
149: @item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
150: @item @code{odmodule_ch_ideal}$B$NNc(B
151: @end itemize
152: @example
153: [344] odmodule_ch_ideal([x*dx+y*dy+a,dx^2+dy^2],[x,y]);
154: [x*dx+y*dy,dx^2+dy^2,y*dy*dx-x*dy^2,(x^2+y^2)*dy^2]
155:
156: [348] odmodule_ch_ideal(diff_op_appell4(a,b,c1,c2,[x,y]),[x,y]);
157: [-x*dx^2+y*dy^2,2*y*x*dy*dx+(y*x+y^2-y)*dy^2,
158: (2*y^2-2*y)*dy^2*dx+(-y*x+3*y^2+y)*dy^3,
159: 2*y*x*dy^2*dx+(y*x^2+(-2*y^2-y)*x+y^3-y^2)*dy^3]
160: @end example
161:
162: @node odmodule_singular_locus,,, D-module (library by Okutani)
163: @subsection @code{odmodule_singular_locus}
164: @findex odmodule_singular_locus
165: @table @t
166: @item odmodule_singular_locus(@var{D_ideal},@var{V})
167: :: @var{D_ideal}$B$N(Bsingular locus$B$r5a$a$^$9(B.
168: @end table
169: @table @var
170: @item return
171: $B%j%9%H(B
172: @item D_ideal
173: $B%j%9%H(B
174: @item V
175: $B%j%9%H(B
176: @end table
177: @itemize @bullet
178: @item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
179: @item @code{odmodule_singular_locus}$B$NNc(B
180: @end itemize
181: @example
182: [356] D = diff_op_appell4(a,b,c1,c2,[x,y])$
183: [357] odmodule_singular_locus(D,[x,y]);
184: [-y*x^3+(2*y^2+2*y)*x^2+(-y^3+2*y^2-y)*x]
185:
186: [358] D = diff_op_hg1(a,b,c,[x])$
187: [359] odmodule_singular_locus(D,[x]);
188: [x^2-x]
189: @end example
190:
191: @node odmodule_restriction,,, D-module (library by Okutani)
192: @subsection @code{odmodule_restriction}
193: @findex odmodule_restriction
194: @table @t
195: @item odmodule_restriction(@var{D_ideal},@var{V},@var{Rest})
1.2 ! takayama 196: :: @var{D_ideal}$B$N(B 0 $B<!$N(Brestriction$B$r5a$a$^$9(B.
1.1 takayama 197: @end table
198: @table @var
199: @item return
200: $B%j%9%H(B
201: @item @var{D_ideal}
202: $B%j%9%H(B
203: @item @var{V}
204: $B%j%9%H(B
205: @item @var{Rest}
206: $B%j%9%H(B
207: @end table
208: @itemize @bullet
209: @item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
210: @item @code{odmodule_restriction}$B$NNc(B.
211: @end itemize
212: @example
213: [345] odmodule_restriction([x*dx+y*dy+a,dx^2+dy^2],[x,y],[y]);
214: [[2,[-x*dx-a,-e0*x*dx-e0*a-e0]]]
215: @end example
216:
217: @node odmodule_elimination,,, D-module (library by Okutani)
218: @subsection @code{odmodule_elimination}
219: @findex odmodule_elimination
220: @table @t
221: @item odmodule_elimination(@var{D_ideal},@var{V},@var{Elim})
222: :: @var{D_ideal}$B$N(Belimination ideal$B$r5a$a$^$9(B.
223: @end table
224: @table @var
225: @item return
226: $B%j%9%H(B
227: @item @var{D_ideal}
228: $B%j%9%H(B
229: @item @var{V}
230: $B%j%9%H(B
231: @item @var{Elim}
232: $B%j%9%H(B
233: @end table
234: @itemize @bullet
235: @item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
236: @item @code{odmodule_elimination}$B$NNc(B.
237: @end itemize
238: @example
239: [346] odmodule_elimination([x*dx+y*dy+a,dx^2+dy^2],[x,y],[[y],[0]]);
240: [x^2*dx^2+(2*a+2)*x*dx+a^2+a]
241:
242: [347] odmodule_elimination([x*dx+y*dy+a,dx^2+dy^2],[x,y],[[y],[b]]);
243: [(x^2+b^2)*dx^2+(2*a+2)*x*dx+a^2+a]
244: @end example
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