Annotation of OpenXM/src/asir-contrib/packages/doc/Dmodule.texi, Revision 1.2
1.2 ! okutani 1: @c $OpenXM$
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
6: @c * dmod_make_dv::
7: * dmod_d_op_tosm1::
8: * dmod_d_op_toasir::
9: * dmod_d_op_fromasir::
10: * dmod_ch_ideal::
11: @c * dmod_ch_ideal_appell1::
12: @c * dmod_ch_ideal_appell2::
13: @c * dmod_ch_ideal_appell3::
14: @c * dmod_ch_ideal_appell4::
15: @c * dmod_ch_ideal_selberg2::
16: @c * dmod_ch_ideal_gkz::
17: * dmod_restriction::
18: @c * dmod_restriction_appell1::
19: @c * dmod_restriction_appell2::
20: @c * dmod_restriction_appell3::
21: @c * dmod_restriction_appell4::
22: @c * dmod_restriction_selberg2::
23: @c * dmod_restriction_gkz::
24: * dmod_elimination::
25: @c * dmod_elimination_appell1::
26: @c * dmod_elimination_appell2::
27: @c * dmod_elimination_appell3::
28: @c * dmod_elimination_appell4::
29: @c * dmod_elimination_selberg2::
30: @c * dmod_elimination_gkz::
31: @end menu
32:
33: @node dmod_d_op_tosm1,,, D-module
34: @subsection @code{dmod_d_op_tosm1}
35: @findex dmod_d_op_tosm1
36: @table @t
37: @item dmod_d_op_tosm1(@var{LL},@var{V})
38: :: $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$r(B sm1 $B7A<0$KJQ49$7$^$9(B.
39: @end table
40: @table @var
41: @item return
42: $B%j%9%H(B
43: @item LL
44: $B%j%9%H(B
45: @item V
46: $B%j%9%H(B
47: @end table
48: @itemize @bullet
49: @item $BHyJ,:nMQAG$N78?t$O@0?tB?9`<0$KJQ49$5$l$^$9(B.
50: @item @code{dmod_d_op_tosm1}$B$NNc(B
51: @end itemize
52: @example
53: [299] dmod_d_op_tosm1([[[x,[2,0]],[-1,[0,0]]],[[y,[0,2]],[-1,[0,0]]]],[x,y]);
54: [ + ( + (1) x) dx^2 + ( + (-1)), + ( + (1) y) dy^2 + ( + (-1))]
55:
56: [300] dmod_d_op_tosm1([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],[[1,[2,0]],[1,[0,2]]]],[x,y]);
57: [ + ( + (1) x) dx + ( + (1) y) dy + ( + (1)), + ( + (1)) dx^2 + ( + (1)) dy^2]
58:
59: [301] dmod_d_op_tosm1([[[1/2,[1,0]],[1,[0,0]]],[[1/3,[0,1]],[1/4,[0,0]]]],[x,y]);
60: [ + ( + (6)) dx + ( + (12)), + ( + (4)) dy + ( + (3))]
61:
62: [302] dmod_d_op_tosm1([[[1/2*x,[1,0]],[1,[0,0]]],[[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
63: [ + ( + (6) x) dx + ( + (12)), + ( + (4) y) dy + ( + (3))]
64: @end example
65:
66: @node dmod_d_op_toasir,,, D-module
67: @subsection @code{dmod_d_op_toasir}
68: @findex dmod_d_op_toasir
69: @table @t
70: @item dmod_d_op_toasir(@var{LL},@var{V})
1.2 ! okutani 71: :: $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H(B @var{LL} $B$r(B @code{asir} $B$NB?9`<0$KJQ49$7$^$9(B.
1.1 takayama 72: @end table
73: @table @var
74: @item return
75: $B%j%9%H(B
76: @item LL
77: $B%j%9%H(B
78: @item V
79: $B%j%9%H(B
80: @end table
81: @itemize @bullet
82: @item @code{dmod_d_op_toasir}$B$NNc(B
83: @end itemize
84: @example
85: [303] dmod_d_op_toasir([[[1/2*x,[1,0]],[1,[0,0]]],[[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
86: [1/2*x*dx+1,1/3*y*dy+1/4]
87:
88: [304] dmod_d_op_toasir([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],[[1,[2,0]],[1,[0,2]]]],[x,y]);
89: [x*dx+y*dy+1,dx^2+dy^2]
90: @end example
91:
92: @node dmod_d_op_fromasir,,, D-module
93: @subsection @code{dmod_d_op_fromasir}
94: @findex dmod_d_op_fromasir
95: @table @t
96: @item dmod_d_op_fromasir(@var{D_list},@var{V})
1.2 ! okutani 97: :: @code{asir} $B$NB?9`<0$+$i%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$KJQ49$7$^$9(B.
1.1 takayama 98: @end table
99: @table @var
100: @item return
101: $B%j%9%H(B
102: @item D_list
103: $B%j%9%H(B
104: @item V
105: $B%j%9%H(B
106: @end table
107: @itemize @bullet
108: @item @code{dmod_d_op_fromasir}$B$NNc(B
109: @end itemize
110: @example
111: [305] dmod_d_op_fromasir([1/2*x*dx+1,1/3*y*dy+1/4],[x,y]);
112: [[[1/2*x,[1,0]],[1,[0,0]]],[[1/3*y,[0,1]],[1/4,[0,0]]]]
113:
114: [306] dmod_d_op_fromasir([x*dx+y*dy+1,dx^2+dy^2],[x,y]);
115: [[[x,[1,0]],[y,[0,1]],[1,[0,0]]],[[1,[2,0]],[1,[0,2]]]]
116: @end example
117:
118: @node dmod_ch_ideal,,, D-module
119: @subsection @code{dmod_ch_ideal}
120: @findex dmod_ch_ideal
121: @table @t
122: @item dmod_ch_ideal(@var{D_ideal},@var{V})
123: :: @var{D_ideal}$B$N(Bcharacteristic ideal$B$r5a$a$^$9(B.
124: @end table
125: @table @var
126: @item return
127: $B%j%9%H(B
128: @item D_ideal
129: $B%j%9%H(B
130: @item V
131: $B%j%9%H(B
132: @end table
133: @itemize @bullet
134: @item @code{dmod_ch_ideal}$B$NNc(B
135: @end itemize
136: @example
137: [301] dmod_ch_ideal(["x dx + y dy + 1","dx^2 + dy^2"],[x,y]);
138: [x*dx+y*dy,dx^2+dy^2,y*dy*dx-x*dy^2,(x^2+y^2)*dy^2]
139:
140: [302] dmod_ch_ideal(["x dx + 1","dx dy"],[x,y]);
141: [x*dx,dy]
142: @end example
143:
144: @node dmod_restriction,,, D-module
145: @subsection @code{dmod_restriction}
146: @findex dmod_restriction
147: @table @t
148: @item dmod_restriction(@var{D_ideal},@var{V},@var{Rest})
149: :: @var{D_ideal}$B$N(Brestriction$B$r5a$a$^$9(B.
150: @end table
151: @table @var
152: @item return
153: $B%j%9%H(B
154: @item @var{D_ideal}
155: $B%j%9%H(B
156: @item @var{V}
157: $B%j%9%H(B
158: @item @var{Rest}
159: $B%j%9%H(B
160: @end table
161: @itemize @bullet
162: @item @code{dmod_restriction}$B$NNc(B.
163: @end itemize
164: @example
165: [303] dmod_restriction(["x dx + y dy + 1","dx^2 + dy^2"],[x,y],[y]);
166: [[2,[-x*dx-1,-e0*x*dx-2*e0]]]
167: @end example
168:
169: @node dmod_elimination,,, D-module
170: @subsection @code{dmod_elimination}
171: @findex dmod_elimination
172: @table @t
173: @item dmod_elimination(@var{D_ideal},@var{V},@var{Elim})
174: :: @var{D_ideal}$B$N(Belimination ideal$B$r5a$a$^$9(B.
175: @end table
176: @table @var
177: @item return
178: $B%j%9%H(B
179: @item @var{D_ideal}
180: $B%j%9%H(B
181: @item @var{V}
182: $B%j%9%H(B
183: @item @var{Elim}
184: $B%j%9%H(B
185: @end table
186: @itemize @bullet
187: @item @code{dmod_elimination}$B$NNc(B.
188: @end itemize
189: @example
190: [304] dmod_elimination(["x dx + y dy + 1","dx^2 + dy^2"],[x,y],[y]);
191: [x^2*dx^2+4*x*dx+2]
192: @end example
193:
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