Annotation of OpenXM/src/asir-contrib/packages/doc/ok_dmodule/ok_dmodule.oxw, Revision 1.1
1.1 ! takayama 1: /*&en
! 2:
! 3: We need to load the files
! 4: @file{gr}, @file{xm}, @file{ok_matrix.rr}, @file{ok_diff.rr},
! 5: @file{ok_diff.rr}
! 6: to call functions in this manual.
! 7:
! 8: The document has not yet been written.
! 9:
! 10: Here are examples.
! 11: @example
! 12: [344] odmodule_ch_ideal([x*dx+y*dy+a,dx^2+dy^2],[x,y]);
! 13: [x*dx+y*dy,dx^2+dy^2,y*dy*dx-x*dy^2,(x^2+y^2)*dy^2]
! 14:
! 15: [348] odmodule_ch_ideal(odiff_op_appell4(a,b,c1,c2,[x,y]),[x,y]);
! 16: [-x*dx^2+y*dy^2,2*y*x*dy*dx+(y*x+y^2-y)*dy^2,
! 17: (2*y^2-2*y)*dy^2*dx+(-y*x+3*y^2+y)*dy^3,
! 18: 2*y*x*dy^2*dx+(y*x^2+(-2*y^2-y)*x+y^3-y^2)*dy^3]
! 19: @end example
! 20:
! 21: */
! 22:
! 23: /*&ja
! 24: @c $OpenXM$
! 25: @node D-module (library by Okutani),,, Top
! 26: @chapter D-module (library by Okutani)
! 27: $B%U%!%$%k(B @file{gr}, @file{xm}, @file{ok_matrix.rr}, @file{ok_diff.rr},
! 28: @file{ok_diff.rr}
! 29: $B$,I,MW$G$9(B.
! 30:
! 31: OpenXM/Risa/Asir $B$G$NMxMQ$K$"$?$C$F$O(B,
! 32: @example
! 33: load("ok_diff.rr")$ load("ok_dmodule.rr")$
! 34: @end example
! 35: $B$,;O$a$KI,MW(B.
! 36:
! 37: Yukio Okutani $B;a$K$h$k(B D-$B2C727W;;MQ$N(B sm1 $B%5!<%P$H$N%$%s%?%U%'!<%9(B
! 38: $B%i%$%V%i%j$G$9(B. $B$9$Y$F$N4X?tL>$O(B odmodule_ $B$G;O$^$j$^$9(B.
! 39:
! 40: @menu
! 41: @c * odmodule_make_dv::
! 42: * odmodule_d_op_tosm1::
! 43: * odmodule_d_op_toasir::
! 44: * odmodule_d_op_fromasir::
! 45: * odmodule_ch_ideal::
! 46: * odmodule_singular_locus::
! 47: @c * odmodule_ch_ideal_appell1::
! 48: @c * odmodule_ch_ideal_appell2::
! 49: @c * odmodule_ch_ideal_appell3::
! 50: @c * odmodule_ch_ideal_appell4::
! 51: @c * odmodule_ch_ideal_selberg2::
! 52: @c * odmodule_ch_ideal_gkz::
! 53: * odmodule_restriction::
! 54: @c * odmodule_restriction_appell1::
! 55: @c * odmodule_restriction_appell2::
! 56: @c * odmodule_restriction_appell3::
! 57: @c * odmodule_restriction_appell4::
! 58: @c * odmodule_restriction_selberg2::
! 59: @c * odmodule_restriction_gkz::
! 60: * odmodule_elimination::
! 61: @c * odmodule_elimination_appell1::
! 62: @c * odmodule_elimination_appell2::
! 63: @c * odmodule_elimination_appell3::
! 64: @c * odmodule_elimination_appell4::
! 65: @c * odmodule_elimination_selberg2::
! 66: @c * odmodule_elimination_gkz::
! 67: @end menu
! 68:
! 69: @node odmodule_d_op_tosm1,,, D-module (library by Okutani)
! 70: @subsection @code{odmodule_d_op_tosm1}
! 71: @findex odmodule_d_op_tosm1
! 72: @table @t
! 73: @item odmodule_d_op_tosm1(@var{LL},@var{V})
! 74: :: $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$r(B sm1 $B7A<0$KJQ49$7$^$9(B.
! 75: @end table
! 76: @table @var
! 77: @item return
! 78: $B%j%9%H(B
! 79: @item LL
! 80: $B%j%9%H(B
! 81: @item V
! 82: $B%j%9%H(B
! 83: @end table
! 84: @itemize @bullet
! 85: @item $BHyJ,:nMQAG$N78?t$O@0?tB?9`<0$KJQ49$5$l$^$9(B.
! 86: @item $B$3$N4X?t$O(B@code{odiff_op_tosm1}$B$HEy2A$G$9(B.
! 87: @item @code{odmodule_d_op_tosm1}$B$NNc(B
! 88: @end itemize
! 89: @example
! 90: [299] odmodule_d_op_tosm1([[[x,[2,0]],[-1,[0,0]]],
! 91: [[y,[0,2]],[-1,[0,0]]]],[x,y]);
! 92: [ + ( + (1) x) dx^2 + ( + (-1)), + ( + (1) y) dy^2 + ( + (-1))]
! 93:
! 94: [300] odmodule_d_op_tosm1([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],
! 95: [[1,[2,0]],[1,[0,2]]]],[x,y]);
! 96: [ + ( + (1) x) dx + ( + (1) y) dy + ( + (1)), + ( + (1)) dx^2 + ( + (1)) dy^2]
! 97:
! 98: [301] odmodule_d_op_tosm1([[[1/2,[1,0]],[1,[0,0]]],
! 99: [[1/3,[0,1]],[1/4,[0,0]]]],[x,y]);
! 100: [ + ( + (6)) dx + ( + (12)), + ( + (4)) dy + ( + (3))]
! 101:
! 102: [302] odmodule_d_op_tosm1([[[1/2*x,[1,0]],[1,[0,0]]],
! 103: [[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
! 104: [ + ( + (6) x) dx + ( + (12)), + ( + (4) y) dy + ( + (3))]
! 105: @end example
! 106:
! 107: @node odmodule_d_op_toasir,,, D-module (library by Okutani)
! 108: @subsection @code{odmodule_d_op_toasir}
! 109: @findex odmodule_d_op_toasir
! 110: @table @t
! 111: @item odmodule_d_op_toasir(@var{LL},@var{V})
! 112: :: $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H(B @var{LL} $B$r(B @code{asir} $B$NB?9`<0$KJQ49$7$^$9(B.
! 113: @end table
! 114: @table @var
! 115: @item return
! 116: $B%j%9%H(B
! 117: @item LL
! 118: $B%j%9%H(B
! 119: @item V
! 120: $B%j%9%H(B
! 121: @end table
! 122: @itemize @bullet
! 123: @item $B$3$N4X?t$O(B@code{odiff_op_toasir}$B$HEy2A$G$9(B.
! 124: @item @code{odmodule_d_op_toasir}$B$NNc(B
! 125: @end itemize
! 126: @example
! 127: [303] odmodule_d_op_toasir([[[1/2*x,[1,0]],[1,[0,0]]],
! 128: [[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
! 129: [1/2*x*dx+1,1/3*y*dy+1/4]
! 130:
! 131: [304] odmodule_d_op_toasir([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],
! 132: [[1,[2,0]],[1,[0,2]]]],[x,y]);
! 133: [x*dx+y*dy+1,dx^2+dy^2]
! 134: @end example
! 135:
! 136: @node odmodule_d_op_fromasir,,, D-module (library by Okutani)
! 137: @subsection @code{odmodule_d_op_fromasir}
! 138: @findex odmodule_d_op_fromasir
! 139: @table @t
! 140: @item odmodule_d_op_fromasir(@var{D_list},@var{V})
! 141: :: @code{asir} $B$NB?9`<0$+$i%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$KJQ49$7$^$9(B.
! 142: @end table
! 143: @table @var
! 144: @item return
! 145: $B%j%9%H(B
! 146: @item D_list
! 147: $B%j%9%H(B
! 148: @item V
! 149: $B%j%9%H(B
! 150: @end table
! 151: @itemize @bullet
! 152: @item $B$3$N4X?t$O(B@code{odiff_op_fromasir}$B$HEy2A$G$9(B.
! 153: @item @code{odmodule_d_op_fromasir}$B$NNc(B
! 154: @end itemize
! 155: @example
! 156: [305] odmodule_d_op_fromasir([1/2*x*dx+1,1/3*y*dy+1/4],[x,y]);
! 157: [[[1/2*x,[1,0]],[1,[0,0]]],[[1/3*y,[0,1]],[1/4,[0,0]]]]
! 158:
! 159: [306] odmodule_d_op_fromasir([x*dx+y*dy+1,dx^2+dy^2],[x,y]);
! 160: [[[x,[1,0]],[y,[0,1]],[1,[0,0]]],[[1,[2,0]],[1,[0,2]]]]
! 161: @end example
! 162:
! 163: @node odmodule_ch_ideal,,, D-module (library by Okutani)
! 164: @subsection @code{odmodule_ch_ideal}
! 165: @findex odmodule_ch_ideal
! 166: @table @t
! 167: @item odmodule_ch_ideal(@var{D_ideal},@var{V})
! 168: :: @var{D_ideal}$B$N(Bcharacteristic ideal$B$r5a$a$^$9(B.
! 169: @end table
! 170: @table @var
! 171: @item return
! 172: $B%j%9%H(B
! 173: @item D_ideal
! 174: $B%j%9%H(B
! 175: @item V
! 176: $B%j%9%H(B
! 177: @end table
! 178: @itemize @bullet
! 179: @item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
! 180: @item @code{odmodule_ch_ideal}$B$NNc(B
! 181: @end itemize
! 182: @example
! 183: [344] odmodule_ch_ideal([x*dx+y*dy+a,dx^2+dy^2],[x,y]);
! 184: [x*dx+y*dy,dx^2+dy^2,y*dy*dx-x*dy^2,(x^2+y^2)*dy^2]
! 185:
! 186: [348] odmodule_ch_ideal(odiff_op_appell4(a,b,c1,c2,[x,y]),[x,y]);
! 187: [-x*dx^2+y*dy^2,2*y*x*dy*dx+(y*x+y^2-y)*dy^2,
! 188: (2*y^2-2*y)*dy^2*dx+(-y*x+3*y^2+y)*dy^3,
! 189: 2*y*x*dy^2*dx+(y*x^2+(-2*y^2-y)*x+y^3-y^2)*dy^3]
! 190: @end example
! 191:
! 192: @node odmodule_singular_locus,,, D-module (library by Okutani)
! 193: @subsection @code{odmodule_singular_locus}
! 194: @findex odmodule_singular_locus
! 195: @table @t
! 196: @item odmodule_singular_locus(@var{D_ideal},@var{V})
! 197: :: @var{D_ideal}$B$N(Bsingular locus$B$r5a$a$^$9(B.
! 198: @end table
! 199: @table @var
! 200: @item return
! 201: $B%j%9%H(B
! 202: @item D_ideal
! 203: $B%j%9%H(B
! 204: @item V
! 205: $B%j%9%H(B
! 206: @end table
! 207: @itemize @bullet
! 208: @item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
! 209: @item @code{odmodule_singular_locus}$B$NNc(B
! 210: @end itemize
! 211: @example
! 212: [356] D = odiff_op_appell4(a,b,c1,c2,[x,y])$
! 213: [357] odmodule_singular_locus(D,[x,y]);
! 214: [-y*x^3+(2*y^2+2*y)*x^2+(-y^3+2*y^2-y)*x]
! 215:
! 216: [358] D = odiff_op_hg1(a,b,c,[x])$
! 217: [359] odmodule_singular_locus(D,[x]);
! 218: [x^2-x]
! 219: @end example
! 220:
! 221: @node odmodule_restriction,,, D-module (library by Okutani)
! 222: @subsection @code{odmodule_restriction}
! 223: @findex odmodule_restriction
! 224: @table @t
! 225: @item odmodule_restriction(@var{D_ideal},@var{V},@var{Rest})
! 226: :: @var{D_ideal}$B$N(B 0 $B<!$N(Brestriction$B$r5a$a$^$9(B.
! 227: @end table
! 228: @table @var
! 229: @item return
! 230: $B%j%9%H(B
! 231: @item @var{D_ideal}
! 232: $B%j%9%H(B
! 233: @item @var{V}
! 234: $B%j%9%H(B
! 235: @item @var{Rest}
! 236: $B%j%9%H(B
! 237: @end table
! 238: @itemize @bullet
! 239: @item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
! 240: @item @code{odmodule_restriction}$B$NNc(B.
! 241: @end itemize
! 242: @example
! 243: [345] odmodule_restriction([x*dx+y*dy+a,dx^2+dy^2],[x,y],[y]);
! 244: [[2,[-x*dx-a,-e0*x*dx-e0*a-e0]]]
! 245: @end example
! 246:
! 247: @node odmodule_elimination,,, D-module (library by Okutani)
! 248: @subsection @code{odmodule_elimination}
! 249: @findex odmodule_elimination
! 250: @table @t
! 251: @item odmodule_elimination(@var{D_ideal},@var{V},@var{Elim})
! 252: :: @var{D_ideal}$B$N(Belimination ideal$B$r5a$a$^$9(B.
! 253: @end table
! 254: @table @var
! 255: @item return
! 256: $B%j%9%H(B
! 257: @item @var{D_ideal}
! 258: $B%j%9%H(B
! 259: @item @var{V}
! 260: $B%j%9%H(B
! 261: @item @var{Elim}
! 262: $B%j%9%H(B
! 263: @end table
! 264: @itemize @bullet
! 265: @item @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
! 266: @item @code{odmodule_elimination}$B$NNc(B.
! 267: @end itemize
! 268: @example
! 269: [346] odmodule_elimination([x*dx+y*dy+a,dx^2+dy^2],[x,y],[[y],[0]]);
! 270: [x^2*dx^2+(2*a+2)*x*dx+a^2+a]
! 271:
! 272: [347] odmodule_elimination([x*dx+y*dy+a,dx^2+dy^2],[x,y],[[y],[b]]);
! 273: [(x^2+b^2)*dx^2+(2*a+2)*x*dx+a^2+a]
! 274: @end example
! 275: */
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