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