Annotation of OpenXM/src/asir-contrib/packages/doc/Dmodule-ja.texi, Revision 1.3
1.3 ! takayama 1: @c $OpenXM: OpenXM/src/asir-contrib/packages/doc/Dmodule-ja.texi,v 1.2 2002/08/04 07:37:46 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.
1.3 ! takayama 6:
! 7: OpenXM/Risa/Asir $B$G$NMxMQ$K$"$?$C$F$O(B,
! 8: @example
! 9: load("Diff")$ load("Dmodule")$
! 10: @end example
! 11: $B$,;O$a$KI,MW(B.
1.1 takayama 12:
13: Yukio Okutani $B;a$K$h$k(B D-$B2C727W;;MQ$N(B sm1 $B%5!<%P$H$N%$%s%?%U%'!<%9(B
14: $B%i%$%V%i%j$G$9(B. $B$9$Y$F$N4X?tL>$O(B odmodule_ $B$G;O$^$j$^$9(B.
15:
16: @menu
17: @c * odmodule_make_dv::
18: * odmodule_d_op_tosm1::
19: * odmodule_d_op_toasir::
20: * odmodule_d_op_fromasir::
21: * odmodule_ch_ideal::
22: * odmodule_singular_locus::
23: @c * odmodule_ch_ideal_appell1::
24: @c * odmodule_ch_ideal_appell2::
25: @c * odmodule_ch_ideal_appell3::
26: @c * odmodule_ch_ideal_appell4::
27: @c * odmodule_ch_ideal_selberg2::
28: @c * odmodule_ch_ideal_gkz::
29: * odmodule_restriction::
30: @c * odmodule_restriction_appell1::
31: @c * odmodule_restriction_appell2::
32: @c * odmodule_restriction_appell3::
33: @c * odmodule_restriction_appell4::
34: @c * odmodule_restriction_selberg2::
35: @c * odmodule_restriction_gkz::
36: * odmodule_elimination::
37: @c * odmodule_elimination_appell1::
38: @c * odmodule_elimination_appell2::
39: @c * odmodule_elimination_appell3::
40: @c * odmodule_elimination_appell4::
41: @c * odmodule_elimination_selberg2::
42: @c * odmodule_elimination_gkz::
43: @end menu
44:
45: @node odmodule_d_op_tosm1,,, D-module (library by Okutani)
46: @subsection @code{odmodule_d_op_tosm1}
47: @findex odmodule_d_op_tosm1
48: @table @t
49: @item odmodule_d_op_tosm1(@var{LL},@var{V})
50: :: $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$r(B sm1 $B7A<0$KJQ49$7$^$9(B.
51: @end table
52: @table @var
53: @item return
54: $B%j%9%H(B
55: @item LL
56: $B%j%9%H(B
57: @item V
58: $B%j%9%H(B
59: @end table
60: @itemize @bullet
61: @item $BHyJ,:nMQAG$N78?t$O@0?tB?9`<0$KJQ49$5$l$^$9(B.
62: @item $B$3$N4X?t$O(B@code{diff_op_tosm1}$B$HEy2A$G$9(B.
63: @item @code{odmodule_d_op_tosm1}$B$NNc(B
64: @end itemize
65: @example
66: [299] odmodule_d_op_tosm1([[[x,[2,0]],[-1,[0,0]]],
67: [[y,[0,2]],[-1,[0,0]]]],[x,y]);
68: [ + ( + (1) x) dx^2 + ( + (-1)), + ( + (1) y) dy^2 + ( + (-1))]
69:
70: [300] odmodule_d_op_tosm1([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],
71: [[1,[2,0]],[1,[0,2]]]],[x,y]);
72: [ + ( + (1) x) dx + ( + (1) y) dy + ( + (1)), + ( + (1)) dx^2 + ( + (1)) dy^2]
73:
74: [301] odmodule_d_op_tosm1([[[1/2,[1,0]],[1,[0,0]]],
75: [[1/3,[0,1]],[1/4,[0,0]]]],[x,y]);
76: [ + ( + (6)) dx + ( + (12)), + ( + (4)) dy + ( + (3))]
77:
78: [302] odmodule_d_op_tosm1([[[1/2*x,[1,0]],[1,[0,0]]],
79: [[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
80: [ + ( + (6) x) dx + ( + (12)), + ( + (4) y) dy + ( + (3))]
81: @end example
82:
83: @node odmodule_d_op_toasir,,, D-module (library by Okutani)
84: @subsection @code{odmodule_d_op_toasir}
85: @findex odmodule_d_op_toasir
86: @table @t
87: @item odmodule_d_op_toasir(@var{LL},@var{V})
88: :: $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H(B @var{LL} $B$r(B @code{asir} $B$NB?9`<0$KJQ49$7$^$9(B.
89: @end table
90: @table @var
91: @item return
92: $B%j%9%H(B
93: @item LL
94: $B%j%9%H(B
95: @item V
96: $B%j%9%H(B
97: @end table
98: @itemize @bullet
99: @item $B$3$N4X?t$O(B@code{diff_op_toasir}$B$HEy2A$G$9(B.
100: @item @code{odmodule_d_op_toasir}$B$NNc(B
101: @end itemize
102: @example
103: [303] odmodule_d_op_toasir([[[1/2*x,[1,0]],[1,[0,0]]],
104: [[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
105: [1/2*x*dx+1,1/3*y*dy+1/4]
106:
107: [304] odmodule_d_op_toasir([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],
108: [[1,[2,0]],[1,[0,2]]]],[x,y]);
109: [x*dx+y*dy+1,dx^2+dy^2]
110: @end example
111:
112: @node odmodule_d_op_fromasir,,, D-module (library by Okutani)
113: @subsection @code{odmodule_d_op_fromasir}
114: @findex odmodule_d_op_fromasir
115: @table @t
116: @item odmodule_d_op_fromasir(@var{D_list},@var{V})
117: :: @code{asir} $B$NB?9`<0$+$i%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$KJQ49$7$^$9(B.
118: @end table
119: @table @var
120: @item return
121: $B%j%9%H(B
122: @item D_list
123: $B%j%9%H(B
124: @item V
125: $B%j%9%H(B
126: @end table
127: @itemize @bullet
128: @item $B$3$N4X?t$O(B@code{diff_op_fromasir}$B$HEy2A$G$9(B.
129: @item @code{odmodule_d_op_fromasir}$B$NNc(B
130: @end itemize
131: @example
132: [305] odmodule_d_op_fromasir([1/2*x*dx+1,1/3*y*dy+1/4],[x,y]);
133: [[[1/2*x,[1,0]],[1,[0,0]]],[[1/3*y,[0,1]],[1/4,[0,0]]]]
134:
135: [306] odmodule_d_op_fromasir([x*dx+y*dy+1,dx^2+dy^2],[x,y]);
136: [[[x,[1,0]],[y,[0,1]],[1,[0,0]]],[[1,[2,0]],[1,[0,2]]]]
137: @end example
138:
139: @node odmodule_ch_ideal,,, D-module (library by Okutani)
140: @subsection @code{odmodule_ch_ideal}
141: @findex odmodule_ch_ideal
142: @table @t
143: @item odmodule_ch_ideal(@var{D_ideal},@var{V})
144: :: @var{D_ideal}$B$N(Bcharacteristic ideal$B$r5a$a$^$9(B.
145: @end table
146: @table @var
147: @item return
148: $B%j%9%H(B
149: @item D_ideal
150: $B%j%9%H(B
151: @item V
152: $B%j%9%H(B
153: @end table
154: @itemize @bullet
155: @item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
156: @item @code{odmodule_ch_ideal}$B$NNc(B
157: @end itemize
158: @example
159: [344] odmodule_ch_ideal([x*dx+y*dy+a,dx^2+dy^2],[x,y]);
160: [x*dx+y*dy,dx^2+dy^2,y*dy*dx-x*dy^2,(x^2+y^2)*dy^2]
161:
162: [348] odmodule_ch_ideal(diff_op_appell4(a,b,c1,c2,[x,y]),[x,y]);
163: [-x*dx^2+y*dy^2,2*y*x*dy*dx+(y*x+y^2-y)*dy^2,
164: (2*y^2-2*y)*dy^2*dx+(-y*x+3*y^2+y)*dy^3,
165: 2*y*x*dy^2*dx+(y*x^2+(-2*y^2-y)*x+y^3-y^2)*dy^3]
166: @end example
167:
168: @node odmodule_singular_locus,,, D-module (library by Okutani)
169: @subsection @code{odmodule_singular_locus}
170: @findex odmodule_singular_locus
171: @table @t
172: @item odmodule_singular_locus(@var{D_ideal},@var{V})
173: :: @var{D_ideal}$B$N(Bsingular locus$B$r5a$a$^$9(B.
174: @end table
175: @table @var
176: @item return
177: $B%j%9%H(B
178: @item D_ideal
179: $B%j%9%H(B
180: @item V
181: $B%j%9%H(B
182: @end table
183: @itemize @bullet
184: @item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
185: @item @code{odmodule_singular_locus}$B$NNc(B
186: @end itemize
187: @example
188: [356] D = diff_op_appell4(a,b,c1,c2,[x,y])$
189: [357] odmodule_singular_locus(D,[x,y]);
190: [-y*x^3+(2*y^2+2*y)*x^2+(-y^3+2*y^2-y)*x]
191:
192: [358] D = diff_op_hg1(a,b,c,[x])$
193: [359] odmodule_singular_locus(D,[x]);
194: [x^2-x]
195: @end example
196:
197: @node odmodule_restriction,,, D-module (library by Okutani)
198: @subsection @code{odmodule_restriction}
199: @findex odmodule_restriction
200: @table @t
201: @item odmodule_restriction(@var{D_ideal},@var{V},@var{Rest})
1.2 takayama 202: :: @var{D_ideal}$B$N(B 0 $B<!$N(Brestriction$B$r5a$a$^$9(B.
1.1 takayama 203: @end table
204: @table @var
205: @item return
206: $B%j%9%H(B
207: @item @var{D_ideal}
208: $B%j%9%H(B
209: @item @var{V}
210: $B%j%9%H(B
211: @item @var{Rest}
212: $B%j%9%H(B
213: @end table
214: @itemize @bullet
215: @item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
216: @item @code{odmodule_restriction}$B$NNc(B.
217: @end itemize
218: @example
219: [345] odmodule_restriction([x*dx+y*dy+a,dx^2+dy^2],[x,y],[y]);
220: [[2,[-x*dx-a,-e0*x*dx-e0*a-e0]]]
221: @end example
222:
223: @node odmodule_elimination,,, D-module (library by Okutani)
224: @subsection @code{odmodule_elimination}
225: @findex odmodule_elimination
226: @table @t
227: @item odmodule_elimination(@var{D_ideal},@var{V},@var{Elim})
228: :: @var{D_ideal}$B$N(Belimination ideal$B$r5a$a$^$9(B.
229: @end table
230: @table @var
231: @item return
232: $B%j%9%H(B
233: @item @var{D_ideal}
234: $B%j%9%H(B
235: @item @var{V}
236: $B%j%9%H(B
237: @item @var{Elim}
238: $B%j%9%H(B
239: @end table
240: @itemize @bullet
241: @item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
242: @item @code{odmodule_elimination}$B$NNc(B.
243: @end itemize
244: @example
245: [346] odmodule_elimination([x*dx+y*dy+a,dx^2+dy^2],[x,y],[[y],[0]]);
246: [x^2*dx^2+(2*a+2)*x*dx+a^2+a]
247:
248: [347] odmodule_elimination([x*dx+y*dy+a,dx^2+dy^2],[x,y],[[y],[b]]);
249: [(x^2+b^2)*dx^2+(2*a+2)*x*dx+a^2+a]
250: @end example
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