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Annotation of OpenXM/src/asir-contrib/packages/doc/Diff.texi, Revision 1.3

1.2       okutani     1: @c $OpenXM$
1.1       takayama    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: $$ [ [ [x,[1,0]],[y,[0,1]],[1,[0,0]] ],[ [1,[2,0]],[1,[0,2]] ] ] $$
1.2       okutani    19: $B$H$J$j$^$9(B. $B$^$?$3$l$i$NI=8=K!$r;H$&$H$-$OJQ?t%j%9%H$r>o$K0U<1$7$F$$$kI,MW$,$"$j$^$9!#(B
1.1       takayama   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::
1.2       okutani    42: * diff_poly_solve_appell4::
1.1       takayama   43: @c * diff_poly_solve_selberg2::
                     44: @c * diff_poly_solve_gkz::
1.3     ! okutani    45: * diff_rat_solve::
1.2       okutani    46: @c * diff_pseries_appell4::
1.1       takayama   47: @end menu
                     48:
                     49: @node diff_op_appell4,,, Differential equations
                     50: @subsection @code{diff_op_appell4}
                     51: @findex diff_op_appell4
                     52: @table @t
                     53: @item diff_op_appell4(@var{a},@var{b},@var{c1},@var{c2},@var{V})
                     54: ::  appell $B$N(B F_4 $B$rNm2=$9$kHyJ,:nMQAG$r@8@.$7$^$9(B.
                     55: @end table
                     56: @table @var
                     57: @item return
                     58: $B%j%9%H(B
                     59: @item a, b, c1, c2
                     60: $BM-M}<0(B
                     61: @item V
                     62: $B%j%9%H(B
                     63: @end table
                     64: @itemize @bullet
                     65: @item  @code{diff_op_appell4}$B$NNc(B.
                     66: @end itemize
                     67: @example
                     68: [298] diff_op_appell4(a,b,c1,c2,[x,y]);
                     69: [ [ [-x^2+x,[2,0]], [-2*y*x,[1,1]], [-y^2,[0,2]],
                     70:     [(-a-b-1)*x+c1,[1,0]], [(-a-b-1)*y,[0,1]], [-b*a,[0,0]] ],
                     71:   [ [-y^2+y,[0,2]], [-2*y*x,[1,1]], [-x^2,[2,0]],
                     72:     [(-a-b-1)*y+c2,[0,1]], [(-a-b-1)*x,[1,0]], [-b*a,[0,0]] ] ]
                     73: @end example
                     74:
                     75: @node diff_act,,, Differential equations
                     76: @subsection @code{diff_act}
                     77: @findex diff_act
                     78: @table @t
                     79: @item diff_act(@var{L},@var{F},@var{V})
                     80: ::  $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.
                     81: @end table
                     82: @table @var
                     83: @item return
                     84: $BM-M}<0(B
                     85: @item L
                     86: $B%j%9%H(B
                     87: @item F
                     88: $BM-M}<0(B
                     89: @item V
                     90: $B%j%9%H(B
                     91: @end table
                     92: @itemize @bullet
                     93: @item  @code{diff_act}$B$NNc(B
                     94: @end itemize
                     95: @example
                     96: [302] diff_act([[1,[2]]],x^3+x^2+x+1,[x]);
                     97: 6*x+2
                     98:
                     99: [303] diff_act([[1,[1,0]],[1,[0,1]]],x^2+y^2,[x,y]);
                    100: 2*x+2*y
                    101: @end example
                    102:
                    103: @node diff_act_appell4,,, Differential equations
                    104: @subsection @code{diff_act_appell4}
                    105: @findex diff_act_appell4
                    106: @table @t
                    107: @item diff_act_appell4(@var{a},@var{b},@var{c1},@var{c2},@var{F},@var{V})
                    108: ::  $BHyJ,:nMQAG(B @code{diff_op_appell4} $B$rM-M}<0(B @var{F} $B$K:nMQ$5$;$k(B.
                    109: @end table
                    110: @table @var
                    111: @item return
                    112: $B%j%9%H(B
                    113: @item a, b, c1, c2
                    114: $BM-M}<0(B
                    115: @item F
                    116: $BM-M}<0(B
                    117: @item V
                    118: $B%j%9%H(B
                    119: @end table
                    120: @itemize @bullet
                    121: @item  @code{diff_act_appell4}$B$NNc(B
                    122: @end itemize
                    123: @example
                    124: [303] diff_act_appell4(1,0,1,1,x^2+y^2,[x,y]);
                    125: [-6*x^2+4*x-6*y^2,-6*x^2-6*y^2+4*y]
                    126:
                    127: [304] diff_act_appell4(0,0,1,1,x^2+y^2,[x,y]);
                    128: [-4*x^2+4*x-4*y^2,-4*x^2-4*y^2+4*y]
                    129:
                    130: [305] diff_act_appell4(-2,-2,-1,-1,x^2+y^2,[x,y]);
                    131: [0,0]
                    132: @end example
                    133:
                    134: @node diff_poly_solve,,, Differential equations
                    135: @subsection @code{diff_poly_solve}
                    136: @findex diff_poly_solve
                    137: @table @t
                    138: @item diff_poly_solve(@var{LL},@var{N},@var{V})
                    139: ::  $BM?$($i$l$?@~7?HyJ,J}Dx<07O$N(B @var{N} $B<!0J2<$NB?9`<02r$r5a$a$k(B.
                    140: @end table
                    141: @table @var
                    142: @item return
                    143: $B%j%9%H(B
                    144: @item LL
                    145: $B%j%9%H(B
                    146: @item N
                    147: $B@0?t(B
                    148: @item V
                    149: $B%j%9%H(B
                    150: @end table
                    151: @itemize @bullet
                    152: @item  @code{diff_poly_solve}$B$NNc(B.
                    153: @end itemize
                    154: @example
                    155: [297] diff_poly_solve([[[x,[1,0]],[-1,[0,0]]],[[y,[0,1]],[-1,[0,0]]]],5,[x,y]);
                    156: [_4*y*x,[_4]]
                    157:
                    158: [298] diff_poly_solve([[[x,[1,0]],[-2,[0,0]]],[[y,[0,1]],[-2,[0,0]]]],5,[x,y]);
                    159: [_33*y^2*x^2,[_33]]
1.2       okutani   160: @end example
                    161:
                    162: @node diff_poly_solve_appell4,,, Differential equations
                    163: @subsection @code{diff_poly_solve_appell4}
                    164: @findex diff_poly_solve_appell4
                    165: @table @t
                    166: @item diff_poly_solve_appell4(@var{a},@var{b},@var{c1},@var{c2},@var{N},@var{V})
                    167: ::  F_4$B$,$_$?$9@~7?HyJ,J}Dx<07O$N(B @var{N} $B<!0J2<$NB?9`<02r$r5a$a$k(B.
                    168: @end table
                    169: @table @var
                    170: @item return
                    171: $B%j%9%H(B
                    172: @item a, b, c1, c2
                    173: $BM-M}<0(B
                    174: @item N
                    175: $B@0?t(B
                    176: @item V
                    177: $B%j%9%H(B
                    178: @end table
                    179: @itemize @bullet
                    180: @item  @code{diff_poly_solve_appell4}$B$NNc(B.
                    181: @end itemize
                    182: @example
                    183: [299] diff_poly_solve_appell4(-3,1,-1,-1,5,[x,y]);
                    184: [-_26*x^3+(3*_26*y+_26)*x^2+3*_24*y^2*x-_24*y^3+_24*y^2,[_24,_26]]
                    185:
                    186: [300] diff_poly_solve_appell4(-3,1,1,-1,5,[x,y]);
                    187: [-3*_45*y^2*x-_45*y^3+_45*y^2,[_45]]
1.3     ! okutani   188: @end example
        !           189:
        !           190: @node diff_rat_solve,,, Differential equations
        !           191: @subsection @code{diff_rat_solve}
        !           192: @findex diff_rat_solve
        !           193: @table @t
        !           194: @item diff_rat_solve(@var{LL},@var{Dn},@var{N},@var{V})
        !           195: ::  $BM?$($i$l$?@~7?HyJ,J}Dx<07O$NJ,Jl$,(B @var{Dn}, $BJ,;R$,(B @var{N} $B<!0J2<$NB?9`<0$G$"$k$h$&$J2r$r5a$a$k(B.
        !           196: @end table
        !           197: @table @var
        !           198: @item return
        !           199: $B%j%9%H(B
        !           200: @item LL
        !           201: $B%j%9%H(B
        !           202: @item Dn
        !           203: $BM-M}<0(B
        !           204: @item N
        !           205: $B@0?t(B
        !           206: @item V
        !           207: $B%j%9%H(B
        !           208: @end table
        !           209: @itemize @bullet
        !           210: @item  @code{diff_rat_solve}$B$NNc(B.
        !           211: @end itemize
        !           212: @example
1.1       takayama  213: @end example
                    214:

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