Annotation of OpenXM/src/asir-contrib/packages/doc/Dmodule.texi, Revision 1.3
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
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::
! 11: @c * dmodule_ch_ideal_appell1::
! 12: @c * dmodule_ch_ideal_appell2::
! 13: @c * dmodule_ch_ideal_appell3::
! 14: @c * dmodule_ch_ideal_appell4::
! 15: @c * dmodule_ch_ideal_selberg2::
! 16: @c * dmodule_ch_ideal_gkz::
! 17: * dmodule_restriction::
! 18: @c * dmodule_restriction_appell1::
! 19: @c * dmodule_restriction_appell2::
! 20: @c * dmodule_restriction_appell3::
! 21: @c * dmodule_restriction_appell4::
! 22: @c * dmodule_restriction_selberg2::
! 23: @c * dmodule_restriction_gkz::
! 24: * dmodule_elimination::
! 25: @c * dmodule_elimination_appell1::
! 26: @c * dmodule_elimination_appell2::
! 27: @c * dmodule_elimination_appell3::
! 28: @c * dmodule_elimination_appell4::
! 29: @c * dmodule_elimination_selberg2::
! 30: @c * dmodule_elimination_gkz::
1.1 takayama 31: @end menu
32:
1.3 ! okutani 33: @node dmodule_d_op_tosm1,,, D-module
! 34: @subsection @code{dmodule_d_op_tosm1}
! 35: @findex dmodule_d_op_tosm1
1.1 takayama 36: @table @t
1.3 ! okutani 37: @item dmodule_d_op_tosm1(@var{LL},@var{V})
1.1 takayama 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$^$9(B.
1.3 ! okutani 50: @item @code{dmodule_d_op_tosm1}$B$NNc(B
1.1 takayama 51: @end itemize
52: @example
1.3 ! okutani 53: [299] dmodule_d_op_tosm1([[[x,[2,0]],[-1,[0,0]]],
! 54: [[y,[0,2]],[-1,[0,0]]]],[x,y]);
1.1 takayama 55: [ + ( + (1) x) dx^2 + ( + (-1)), + ( + (1) y) dy^2 + ( + (-1))]
56:
1.3 ! okutani 57: [300] dmodule_d_op_tosm1([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],
! 58: [[1,[2,0]],[1,[0,2]]]],[x,y]);
1.1 takayama 59: [ + ( + (1) x) dx + ( + (1) y) dy + ( + (1)), + ( + (1)) dx^2 + ( + (1)) dy^2]
60:
1.3 ! okutani 61: [301] dmodule_d_op_tosm1([[[1/2,[1,0]],[1,[0,0]]],
! 62: [[1/3,[0,1]],[1/4,[0,0]]]],[x,y]);
1.1 takayama 63: [ + ( + (6)) dx + ( + (12)), + ( + (4)) dy + ( + (3))]
64:
1.3 ! okutani 65: [302] dmodule_d_op_tosm1([[[1/2*x,[1,0]],[1,[0,0]]],
! 66: [[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
1.1 takayama 67: [ + ( + (6) x) dx + ( + (12)), + ( + (4) y) dy + ( + (3))]
68: @end example
69:
1.3 ! okutani 70: @node dmodule_d_op_toasir,,, D-module
! 71: @subsection @code{dmodule_d_op_toasir}
! 72: @findex dmodule_d_op_toasir
1.1 takayama 73: @table @t
1.3 ! okutani 74: @item dmodule_d_op_toasir(@var{LL},@var{V})
1.2 okutani 75: :: $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H(B @var{LL} $B$r(B @code{asir} $B$NB?9`<0$KJQ49$7$^$9(B.
1.1 takayama 76: @end table
77: @table @var
78: @item return
79: $B%j%9%H(B
80: @item LL
81: $B%j%9%H(B
82: @item V
83: $B%j%9%H(B
84: @end table
85: @itemize @bullet
1.3 ! okutani 86: @item @code{dmodule_d_op_toasir}$B$NNc(B
1.1 takayama 87: @end itemize
88: @example
1.3 ! okutani 89: [303] dmodule_d_op_toasir([[[1/2*x,[1,0]],[1,[0,0]]],
! 90: [[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
1.1 takayama 91: [1/2*x*dx+1,1/3*y*dy+1/4]
92:
1.3 ! okutani 93: [304] dmodule_d_op_toasir([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],
! 94: [[1,[2,0]],[1,[0,2]]]],[x,y]);
1.1 takayama 95: [x*dx+y*dy+1,dx^2+dy^2]
96: @end example
97:
1.3 ! okutani 98: @node dmodule_d_op_fromasir,,, D-module
! 99: @subsection @code{dmodule_d_op_fromasir}
! 100: @findex dmodule_d_op_fromasir
1.1 takayama 101: @table @t
1.3 ! okutani 102: @item dmodule_d_op_fromasir(@var{D_list},@var{V})
1.2 okutani 103: :: @code{asir} $B$NB?9`<0$+$i%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$KJQ49$7$^$9(B.
1.1 takayama 104: @end table
105: @table @var
106: @item return
107: $B%j%9%H(B
108: @item D_list
109: $B%j%9%H(B
110: @item V
111: $B%j%9%H(B
112: @end table
113: @itemize @bullet
1.3 ! okutani 114: @item @code{dmodule_d_op_fromasir}$B$NNc(B
1.1 takayama 115: @end itemize
116: @example
1.3 ! okutani 117: [305] dmodule_d_op_fromasir([1/2*x*dx+1,1/3*y*dy+1/4],[x,y]);
1.1 takayama 118: [[[1/2*x,[1,0]],[1,[0,0]]],[[1/3*y,[0,1]],[1/4,[0,0]]]]
119:
1.3 ! okutani 120: [306] dmodule_d_op_fromasir([x*dx+y*dy+1,dx^2+dy^2],[x,y]);
1.1 takayama 121: [[[x,[1,0]],[y,[0,1]],[1,[0,0]]],[[1,[2,0]],[1,[0,2]]]]
122: @end example
123:
1.3 ! okutani 124: @node dmodule_ch_ideal,,, D-module
! 125: @subsection @code{dmodule_ch_ideal}
! 126: @findex dmodule_ch_ideal
1.1 takayama 127: @table @t
1.3 ! okutani 128: @item dmodule_ch_ideal(@var{D_ideal},@var{V})
1.1 takayama 129: :: @var{D_ideal}$B$N(Bcharacteristic ideal$B$r5a$a$^$9(B.
130: @end table
131: @table @var
132: @item return
133: $B%j%9%H(B
134: @item D_ideal
135: $B%j%9%H(B
136: @item V
137: $B%j%9%H(B
138: @end table
139: @itemize @bullet
1.3 ! okutani 140: @item @code{dmodule_ch_ideal}$B$NNc(B
1.1 takayama 141: @end itemize
142: @example
1.3 ! okutani 143: [301] dmodule_ch_ideal(["x dx + y dy + 1","dx^2 + dy^2"],[x,y]);
1.1 takayama 144: [x*dx+y*dy,dx^2+dy^2,y*dy*dx-x*dy^2,(x^2+y^2)*dy^2]
145:
1.3 ! okutani 146: [302] dmodule_ch_ideal(["x dx + 1","dx dy"],[x,y]);
1.1 takayama 147: [x*dx,dy]
148: @end example
149:
1.3 ! okutani 150: @node dmodule_restriction,,, D-module
! 151: @subsection @code{dmodule_restriction}
! 152: @findex dmodule_restriction
1.1 takayama 153: @table @t
1.3 ! okutani 154: @item dmodule_restriction(@var{D_ideal},@var{V},@var{Rest})
1.1 takayama 155: :: @var{D_ideal}$B$N(Brestriction$B$r5a$a$^$9(B.
156: @end table
157: @table @var
158: @item return
159: $B%j%9%H(B
160: @item @var{D_ideal}
161: $B%j%9%H(B
162: @item @var{V}
163: $B%j%9%H(B
164: @item @var{Rest}
165: $B%j%9%H(B
166: @end table
167: @itemize @bullet
1.3 ! okutani 168: @item @code{dmodule_restriction}$B$NNc(B.
1.1 takayama 169: @end itemize
170: @example
1.3 ! okutani 171: [303] dmodule_restriction(["x dx + y dy + 1","dx^2 + dy^2"],[x,y],[y]);
1.1 takayama 172: [[2,[-x*dx-1,-e0*x*dx-2*e0]]]
173: @end example
174:
1.3 ! okutani 175: @node dmodule_elimination,,, D-module
! 176: @subsection @code{dmodule_elimination}
! 177: @findex dmodule_elimination
1.1 takayama 178: @table @t
1.3 ! okutani 179: @item dmodule_elimination(@var{D_ideal},@var{V},@var{Elim})
1.1 takayama 180: :: @var{D_ideal}$B$N(Belimination ideal$B$r5a$a$^$9(B.
181: @end table
182: @table @var
183: @item return
184: $B%j%9%H(B
185: @item @var{D_ideal}
186: $B%j%9%H(B
187: @item @var{V}
188: $B%j%9%H(B
189: @item @var{Elim}
190: $B%j%9%H(B
191: @end table
192: @itemize @bullet
1.3 ! okutani 193: @item @code{dmodule_elimination}$B$NNc(B.
1.1 takayama 194: @end itemize
195: @example
1.3 ! okutani 196: [305] dmodule_elimination(["x dx + y dy + 1","dx^2 + dy^2"],[x,y],[[y],[0]]);
1.1 takayama 197: [x^2*dx^2+4*x*dx+2]
1.3 ! okutani 198:
! 199: [306] dmodule_elimination(["x dx + y dy + 1","dx^2 + dy^2"],[x,y],[[y],[a]]);
! 200: [(x^2+a^2)*dx^2+4*x*dx+2]
! 201: @end example
! 202:
! 203: @node dmodule_elimination_generic,,, D-module
! 204: @subsection @code{dmodule_elimination_generic}
! 205: @findex dmodule_elimination_generic
! 206: @table @t
! 207: @item dmodule_elimination_generic(@var{D_ideal},@var{Param},@var{V},@var{Elim})
! 208: :: generic parameter$B$r4^$`(B@var{D_ideal}$B$N(Belimination ideal$B$r5a$a$^$9(B.
! 209: @end table
! 210: @table @var
! 211: @item return
! 212: $B%j%9%H(B
! 213: @item @var{D_ideal}
! 214: $B%j%9%H(B
! 215: @item @var{Param}
! 216: $B%j%9%H(B
! 217: @item @var{V}
! 218: $B%j%9%H(B
! 219: @item @var{Elim}
! 220: $B%j%9%H(B
! 221: @end table
! 222: @itemize @bullet
! 223: @item @code{dmodule_elimination_generic}$B$NNc(B.
! 224: @end itemize
! 225: @example
! 226: [307] dmodule_elimination_generic(["x dx + y dy + 1","dx^2 + dy^2 + a"],
! 227: [a],[x,y],[[y],[s]]);
! 228: [(x^2+s^2)*dx^2+4*x*dx+a*s^2+2,2*a]
! 229:
1.1 takayama 230: @end example
231:
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