Annotation of OpenXM/src/asir-contrib/packages/doc/Dmodule.texi, Revision 1.1
1.1 ! takayama 1: @c $OpenXM: OpenXM/src/asir99/lib/contrib/packages/doc/Dmodule.texi,v 1.3 1999/11/23 05:57:47 okutani Exp $
! 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})
! 71: :: $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H(B @var{LL} $B$r(B asir $B$NB?9`<0$KJQ49$7$^$9(B.
! 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})
! 97: :: asir $B$NB?9`<0$+$i%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$KJQ49$7$^$9(B.
! 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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