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

1.1       takayama    1: @c $OpenXM: OpenXM/src/asir99/lib/contrib/packages/doc/Diff.texi,v 1.4 1999/11/24 10:24:36 okutani Exp $
                      2: @node Differential equations,,, $B$=$NB>$NH!?t(B
                      3: @section Differential equations
                      4: $B%U%!%$%k(B @file{gr}, @file{Matrix} $B$,I,MW$G$9(B.
                      5:
                      6: @tex
                      7: $B$3$N@a$G>R2p$5$l$k4X?t$G$OHyJ,:nMQAG$O<!$N$h$&$J%j%9%H$GI=8=$7$^$9(B.
                      8: $$ [ [f_{\alpha},[\alpha_{1},\ldots,\alpha_{n}]],\ldots ] $$
                      9: $B$3$l$O(B
                     10: $$ \sum_{\alpha}f_{\alpha}\partial^{\alpha} $$
                     11: $B$H$$$&0UL#$G$9(B. $B@~7?JPHyJ,J}Dx<07O(B
                     12: $$ (\sum_{\alpha^{(i)}}f_{\alpha^{(i)}}\partial^{\alpha^{(i)}})\bullet u = 0 \quad (i = 1,\ldots,s) $$
                     13: $B$J$I$N$h$&$KJ#?t$NHyJ,:nMQAG$rI=8=$9$k$H$-$OHyJ,:nMQAG$N%j%9%H$r;H$$$^$9(B.
                     14: $$ [ [ [f_{\alpha^{(1)}},[\alpha_{1}^{(1)},\ldots,\alpha_{n}^{(1)}]],\ldots ],\ldots,[ [f_{\alpha^{(s)}},[\alpha_{1}^{(s)},\ldots,\alpha_{n}^{(s)}]],\ldots ] ] $$
                     15: $BNc$($PHyJ,:nMQAG(B$x dx + y dy + 1$$B$N>l9g$O(B
                     16: $$ [ [x,[1,0]],[y,[0,1]],[1,[0,0]] ] $$
                     17: $B$H$J$j$^$9(B. $B$^$?HyJ,:nMQAG$N%j%9%H$G(B$x dx + y dy + 1, dx^2 + dy^2$$B$rI=$9$H(B
                     18: $$ [ [ [x,[1,0]],[y,[0,1]],[1,[0,0]] ],[ [1,[2,0]],[1,[0,2]] ] ] $$
                     19: $B$H$J$j$^$9(B.
                     20: @end tex
                     21: @menu
                     22: @c * diff_op_hg1::
                     23: @c * diff_op_appell1::
                     24: @c * diff_op_appell2::
                     25: @c * diff_op_appell3::
                     26: * diff_op_appell4::
                     27: @c * diff_op_selberg2::
                     28: @c * diff_op_gkz::
                     29: * diff_act::
                     30: @c * diff_act_hg1::
                     31: @c * diff_act_appell1::
                     32: @c * diff_act_appell2::
                     33: @c * diff_act_appell3::
                     34: * diff_act_appell4::
                     35: @c * diff_act_selberg2::
                     36: @c * diff_act_gkz::
                     37: * diff_poly_solve::
                     38: @c * diff_poly_solve_hg1::
                     39: @c * diff_poly_solve_appell1::
                     40: @c * diff_poly_solve_appell2::
                     41: @c * diff_poly_solve_appell3::
                     42: @c * diff_poly_solve_appell4::
                     43: @c * diff_poly_solve_selberg2::
                     44: @c * diff_poly_solve_gkz::
                     45: @end menu
                     46:
                     47: @node diff_op_appell4,,, Differential equations
                     48: @subsection @code{diff_op_appell4}
                     49: @findex diff_op_appell4
                     50: @table @t
                     51: @item diff_op_appell4(@var{a},@var{b},@var{c1},@var{c2},@var{V})
                     52: ::  appell $B$N(B F_4 $B$rNm2=$9$kHyJ,:nMQAG$r@8@.$7$^$9(B.
                     53: @end table
                     54: @table @var
                     55: @item return
                     56: $B%j%9%H(B
                     57: @item a, b, c1, c2
                     58: $BM-M}<0(B
                     59: @item V
                     60: $B%j%9%H(B
                     61: @end table
                     62: @itemize @bullet
                     63: @item  @code{diff_op_appell4}$B$NNc(B.
                     64: @end itemize
                     65: @example
                     66: [298] diff_op_appell4(a,b,c1,c2,[x,y]);
                     67: [ [ [-x^2+x,[2,0]], [-2*y*x,[1,1]], [-y^2,[0,2]],
                     68:     [(-a-b-1)*x+c1,[1,0]], [(-a-b-1)*y,[0,1]], [-b*a,[0,0]] ],
                     69:   [ [-y^2+y,[0,2]], [-2*y*x,[1,1]], [-x^2,[2,0]],
                     70:     [(-a-b-1)*y+c2,[0,1]], [(-a-b-1)*x,[1,0]], [-b*a,[0,0]] ] ]
                     71: @end example
                     72:
                     73: @node diff_act,,, Differential equations
                     74: @subsection @code{diff_act}
                     75: @findex diff_act
                     76: @table @t
                     77: @item diff_act(@var{L},@var{F},@var{V})
                     78: ::  $BHyJ,:nMQAG(B @var{L} $B$rM-M}<0(B @var{F} $B$K:nMQ$5$;$k(B. @var{V} $B$OJQ?t%j%9%H(B.
                     79: @end table
                     80: @table @var
                     81: @item return
                     82: $BM-M}<0(B
                     83: @item L
                     84: $B%j%9%H(B
                     85: @item F
                     86: $BM-M}<0(B
                     87: @item V
                     88: $B%j%9%H(B
                     89: @end table
                     90: @itemize @bullet
                     91: @item  @code{diff_act}$B$NNc(B
                     92: @end itemize
                     93: @example
                     94: [302] diff_act([[1,[2]]],x^3+x^2+x+1,[x]);
                     95: 6*x+2
                     96:
                     97: [303] diff_act([[1,[1,0]],[1,[0,1]]],x^2+y^2,[x,y]);
                     98: 2*x+2*y
                     99: @end example
                    100:
                    101: @node diff_act_appell4,,, Differential equations
                    102: @subsection @code{diff_act_appell4}
                    103: @findex diff_act_appell4
                    104: @table @t
                    105: @item diff_act_appell4(@var{a},@var{b},@var{c1},@var{c2},@var{F},@var{V})
                    106: ::  $BHyJ,:nMQAG(B @code{diff_op_appell4} $B$rM-M}<0(B @var{F} $B$K:nMQ$5$;$k(B.
                    107: @end table
                    108: @table @var
                    109: @item return
                    110: $B%j%9%H(B
                    111: @item a, b, c1, c2
                    112: $BM-M}<0(B
                    113: @item F
                    114: $BM-M}<0(B
                    115: @item V
                    116: $B%j%9%H(B
                    117: @end table
                    118: @itemize @bullet
                    119: @item  @code{diff_act_appell4}$B$NNc(B
                    120: @end itemize
                    121: @example
                    122: [303] diff_act_appell4(1,0,1,1,x^2+y^2,[x,y]);
                    123: [-6*x^2+4*x-6*y^2,-6*x^2-6*y^2+4*y]
                    124:
                    125: [304] diff_act_appell4(0,0,1,1,x^2+y^2,[x,y]);
                    126: [-4*x^2+4*x-4*y^2,-4*x^2-4*y^2+4*y]
                    127:
                    128: [305] diff_act_appell4(-2,-2,-1,-1,x^2+y^2,[x,y]);
                    129: [0,0]
                    130: @end example
                    131:
                    132: @node diff_poly_solve,,, Differential equations
                    133: @subsection @code{diff_poly_solve}
                    134: @findex diff_poly_solve
                    135: @table @t
                    136: @item diff_poly_solve(@var{LL},@var{N},@var{V})
                    137: ::  $BM?$($i$l$?@~7?HyJ,J}Dx<07O$N(B @var{N} $B<!0J2<$NB?9`<02r$r5a$a$k(B.
                    138: @end table
                    139: @table @var
                    140: @item return
                    141: $B%j%9%H(B
                    142: @item LL
                    143: $B%j%9%H(B
                    144: @item N
                    145: $B@0?t(B
                    146: @item V
                    147: $B%j%9%H(B
                    148: @end table
                    149: @itemize @bullet
                    150: @item  @code{diff_poly_solve}$B$NNc(B.
                    151: @end itemize
                    152: @example
                    153: [297] diff_poly_solve([[[x,[1,0]],[-1,[0,0]]],[[y,[0,1]],[-1,[0,0]]]],5,[x,y]);
                    154: [_4*y*x,[_4]]
                    155:
                    156: [298] diff_poly_solve([[[x,[1,0]],[-2,[0,0]]],[[y,[0,1]],[-2,[0,0]]]],5,[x,y]);
                    157: [_33*y^2*x^2,[_33]]
                    158: @end example
                    159: