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Annotation of OpenXM/src/asir-contrib/packages/doc/Dmodule.texi, Revision 1.1.1.1

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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