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