[BACK]Return to Dmodule.texi CVS log [TXT][DIR] Up to [local] / OpenXM / src / asir-contrib / packages / doc

Annotation of OpenXM/src/asir-contrib/packages/doc/Dmodule.texi, Revision 1.5

1.5     ! takayama    1: @c $OpenXM: OpenXM/src/asir-contrib/packages/doc/Dmodule.texi,v 1.4 2000/02/20 11:30:44 okutani Exp $
        !             2: @node D-module (library by Okutani),,, Top
        !             3: @section D-module (library by Okutani)
1.1       takayama    4: $B%U%!%$%k(B @file{gr}, @file{xm}, @file{Matrix}, @file{Diff} $B$,I,MW$G$9(B.
1.5     ! takayama    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:
1.1       takayama    9: @menu
1.5     ! takayama   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::
1.1       takayama   36: @end menu
                     37:
1.5     ! takayama   38: @node odmodule_d_op_tosm1,,, D-module (library by Okutani)
        !            39: @subsection @code{odmodule_d_op_tosm1}
        !            40: @findex odmodule_d_op_tosm1
1.1       takayama   41: @table @t
1.5     ! takayama   42: @item odmodule_d_op_tosm1(@var{LL},@var{V})
1.1       takayama   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.
1.4       okutani    55: @item  $B$3$N4X?t$O(B@code{diff_op_tosm1}$B$HEy2A$G$9(B.
1.5     ! takayama   56: @item  @code{odmodule_d_op_tosm1}$B$NNc(B
1.1       takayama   57: @end itemize
                     58: @example
1.5     ! takayama   59: [299] odmodule_d_op_tosm1([[[x,[2,0]],[-1,[0,0]]],
1.3       okutani    60:                           [[y,[0,2]],[-1,[0,0]]]],[x,y]);
1.1       takayama   61: [ + ( + (1) x) dx^2 + ( + (-1)), + ( + (1) y) dy^2 + ( + (-1))]
                     62:
1.5     ! takayama   63: [300] odmodule_d_op_tosm1([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],
1.3       okutani    64:                           [[1,[2,0]],[1,[0,2]]]],[x,y]);
1.1       takayama   65: [ + ( + (1) x) dx + ( + (1) y) dy + ( + (1)), + ( + (1)) dx^2 + ( + (1)) dy^2]
                     66:
1.5     ! takayama   67: [301] odmodule_d_op_tosm1([[[1/2,[1,0]],[1,[0,0]]],
1.3       okutani    68:                           [[1/3,[0,1]],[1/4,[0,0]]]],[x,y]);
1.1       takayama   69: [ + ( + (6)) dx + ( + (12)), + ( + (4)) dy + ( + (3))]
                     70:
1.5     ! takayama   71: [302] odmodule_d_op_tosm1([[[1/2*x,[1,0]],[1,[0,0]]],
1.3       okutani    72:                           [[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
1.1       takayama   73: [ + ( + (6) x) dx + ( + (12)), + ( + (4) y) dy + ( + (3))]
                     74: @end example
                     75:
1.5     ! takayama   76: @node odmodule_d_op_toasir,,, D-module (library by Okutani)
        !            77: @subsection @code{odmodule_d_op_toasir}
        !            78: @findex odmodule_d_op_toasir
1.1       takayama   79: @table @t
1.5     ! takayama   80: @item odmodule_d_op_toasir(@var{LL},@var{V})
1.2       okutani    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.
1.1       takayama   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
1.4       okutani    92: @item  $B$3$N4X?t$O(B@code{diff_op_toasir}$B$HEy2A$G$9(B.
1.5     ! takayama   93: @item  @code{odmodule_d_op_toasir}$B$NNc(B
1.1       takayama   94: @end itemize
                     95: @example
1.5     ! takayama   96: [303] odmodule_d_op_toasir([[[1/2*x,[1,0]],[1,[0,0]]],
1.3       okutani    97:                            [[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
1.1       takayama   98: [1/2*x*dx+1,1/3*y*dy+1/4]
                     99:
1.5     ! takayama  100: [304] odmodule_d_op_toasir([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],
1.3       okutani   101:                            [[1,[2,0]],[1,[0,2]]]],[x,y]);
1.1       takayama  102: [x*dx+y*dy+1,dx^2+dy^2]
                    103: @end example
                    104:
1.5     ! takayama  105: @node odmodule_d_op_fromasir,,, D-module (library by Okutani)
        !           106: @subsection @code{odmodule_d_op_fromasir}
        !           107: @findex odmodule_d_op_fromasir
1.1       takayama  108: @table @t
1.5     ! takayama  109: @item odmodule_d_op_fromasir(@var{D_list},@var{V})
1.2       okutani   110: ::  @code{asir} $B$NB?9`<0$+$i%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$KJQ49$7$^$9(B.
1.1       takayama  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
1.4       okutani   121: @item  $B$3$N4X?t$O(B@code{diff_op_fromasir}$B$HEy2A$G$9(B.
1.5     ! takayama  122: @item  @code{odmodule_d_op_fromasir}$B$NNc(B
1.1       takayama  123: @end itemize
                    124: @example
1.5     ! takayama  125: [305] odmodule_d_op_fromasir([1/2*x*dx+1,1/3*y*dy+1/4],[x,y]);
1.1       takayama  126: [[[1/2*x,[1,0]],[1,[0,0]]],[[1/3*y,[0,1]],[1/4,[0,0]]]]
                    127:
1.5     ! takayama  128: [306] odmodule_d_op_fromasir([x*dx+y*dy+1,dx^2+dy^2],[x,y]);
1.1       takayama  129: [[[x,[1,0]],[y,[0,1]],[1,[0,0]]],[[1,[2,0]],[1,[0,2]]]]
                    130: @end example
                    131:
1.5     ! takayama  132: @node odmodule_ch_ideal,,, D-module (library by Okutani)
        !           133: @subsection @code{odmodule_ch_ideal}
        !           134: @findex odmodule_ch_ideal
1.1       takayama  135: @table @t
1.5     ! takayama  136: @item odmodule_ch_ideal(@var{D_ideal},@var{V})
1.1       takayama  137: ::  @var{D_ideal}$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: $B%j%9%H(B
                    146: @end table
                    147: @itemize @bullet
1.4       okutani   148: @item  @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
1.5     ! takayama  149: @item  @code{odmodule_ch_ideal}$B$NNc(B
1.1       takayama  150: @end itemize
                    151: @example
1.5     ! takayama  152: [344] odmodule_ch_ideal([x*dx+y*dy+a,dx^2+dy^2],[x,y]);
1.1       takayama  153: [x*dx+y*dy,dx^2+dy^2,y*dy*dx-x*dy^2,(x^2+y^2)*dy^2]
                    154:
1.5     ! takayama  155: [348] odmodule_ch_ideal(diff_op_appell4(a,b,c1,c2,[x,y]),[x,y]);
1.4       okutani   156: [-x*dx^2+y*dy^2,2*y*x*dy*dx+(y*x+y^2-y)*dy^2,
                    157:  (2*y^2-2*y)*dy^2*dx+(-y*x+3*y^2+y)*dy^3,
                    158:  2*y*x*dy^2*dx+(y*x^2+(-2*y^2-y)*x+y^3-y^2)*dy^3]
                    159: @end example
                    160:
1.5     ! takayama  161: @node odmodule_singular_locus,,, D-module (library by Okutani)
        !           162: @subsection @code{odmodule_singular_locus}
        !           163: @findex odmodule_singular_locus
1.4       okutani   164: @table @t
1.5     ! takayama  165: @item odmodule_singular_locus(@var{D_ideal},@var{V})
1.4       okutani   166: ::  @var{D_ideal}$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$-$^$9(B.
1.5     ! takayama  178: @item  @code{odmodule_singular_locus}$B$NNc(B
1.4       okutani   179: @end itemize
                    180: @example
                    181: [356] D = diff_op_appell4(a,b,c1,c2,[x,y])$
1.5     ! takayama  182: [357] odmodule_singular_locus(D,[x,y]);
1.4       okutani   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])$
1.5     ! takayama  186: [359] odmodule_singular_locus(D,[x]);
1.4       okutani   187: [x^2-x]
1.1       takayama  188: @end example
                    189:
1.5     ! takayama  190: @node odmodule_restriction,,, D-module (library by Okutani)
        !           191: @subsection @code{odmodule_restriction}
        !           192: @findex odmodule_restriction
1.1       takayama  193: @table @t
1.5     ! takayama  194: @item odmodule_restriction(@var{D_ideal},@var{V},@var{Rest})
1.1       takayama  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: $B%j%9%H(B
                    206: @end table
                    207: @itemize @bullet
1.4       okutani   208: @item  @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
1.5     ! takayama  209: @item  @code{odmodule_restriction}$B$NNc(B.
1.1       takayama  210: @end itemize
                    211: @example
1.5     ! takayama  212: [345] odmodule_restriction([x*dx+y*dy+a,dx^2+dy^2],[x,y],[y]);
1.4       okutani   213: [[2,[-x*dx-a,-e0*x*dx-e0*a-e0]]]
1.1       takayama  214: @end example
                    215:
1.5     ! takayama  216: @node odmodule_elimination,,, D-module (library by Okutani)
        !           217: @subsection @code{odmodule_elimination}
        !           218: @findex odmodule_elimination
1.1       takayama  219: @table @t
1.5     ! takayama  220: @item odmodule_elimination(@var{D_ideal},@var{V},@var{Elim})
1.1       takayama  221: ::  @var{D_ideal}$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: $B%j%9%H(B
                    232: @end table
                    233: @itemize @bullet
1.4       okutani   234: @item  @var{D_ideal}$B$O(Bgeneric parameter$B$r4^$`$3$H$,$G$-$^$9(B.
1.5     ! takayama  235: @item  @code{odmodule_elimination}$B$NNc(B.
1.1       takayama  236: @end itemize
                    237: @example
1.5     ! takayama  238: [346] odmodule_elimination([x*dx+y*dy+a,dx^2+dy^2],[x,y],[[y],[0]]);
1.4       okutani   239: [x^2*dx^2+(2*a+2)*x*dx+a^2+a]
1.3       okutani   240:
1.5     ! takayama  241: [347] odmodule_elimination([x*dx+y*dy+a,dx^2+dy^2],[x,y],[[y],[b]]);
1.4       okutani   242: [(x^2+b^2)*dx^2+(2*a+2)*x*dx+a^2+a]
1.1       takayama  243: @end example

FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>