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Added contents about 'diff_rat_solve'.

@c $OpenXM: OpenXM/src/asir-contrib/packages/doc/Diff.texi,v 1.4 2000/01/21 12:54:39 okutani Exp $
@node Differential equations,,, $B$=$NB>$NH!?t(B
@section Differential equations
$B%U%!%$%k(B @file{gr}, @file{Matrix} $B$,I,MW$G$9(B.

@tex
$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.
$$ [ [f_{\alpha},[\alpha_{1},\ldots,\alpha_{n}]],\ldots ] $$
$B$3$l$O(B
$$ \sum_{\alpha}f_{\alpha}\partial^{\alpha} $$
$B$H$$$&0UL#$G$9(B. $B@~7?JPHyJ,J}Dx<07O(B
$$ (\sum_{\alpha^{(i)}}f_{\alpha^{(i)}}\partial^{\alpha^{(i)}})\bullet u = 0 \quad (i = 1,\ldots,s) $$
$B$J$I$N$h$&$KJ#?t$NHyJ,:nMQAG$rI=8=$9$k$H$-$OHyJ,:nMQAG$N%j%9%H$r;H$$$^$9(B.
$$ [ [ [f_{\alpha^{(1)}},[\alpha_{1}^{(1)},\ldots,\alpha_{n}^{(1)}]],\ldots ],\ldots,[ [f_{\alpha^{(s)}},[\alpha_{1}^{(s)},\ldots,\alpha_{n}^{(s)}]],\ldots ] ] $$
$BNc$($PHyJ,:nMQAG(B$x dx + y dy + 1$$B$N>l9g$O(B
$$ [ [x,[1,0]],[y,[0,1]],[1,[0,0]] ] $$
$B$H$J$j$^$9(B. $B$^$?HyJ,:nMQAG$N%j%9%H$G(B$x dx + y dy + 1, dx^2 + dy^2$$B$rI=$9$H(B
$$ [ [ [x,[1,0]],[y,[0,1]],[1,[0,0]] ],[ [1,[2,0]],[1,[0,2]] ] ] $$
$B$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
@end tex
@menu
@c * diff_op_hg1::
@c * diff_op_appell1::
@c * diff_op_appell2::
@c * diff_op_appell3::
* diff_op_appell4::
@c * diff_op_selberg2::
@c * diff_op_gkz::
* diff_act::
@c * diff_act_hg1::
@c * diff_act_appell1::
@c * diff_act_appell2::
@c * diff_act_appell3::
* diff_act_appell4::
@c * diff_act_selberg2::
@c * diff_act_gkz::
* diff_poly_solve::
@c * diff_poly_solve_hg1::
@c * diff_poly_solve_appell1::
@c * diff_poly_solve_appell2::
@c * diff_poly_solve_appell3::
* diff_poly_solve_appell4::
@c * diff_poly_solve_selberg2::
@c * diff_poly_solve_gkz::
* diff_rat_solve::
@c * diff_pseries_appell4::
@end menu

@node diff_op_appell4,,, Differential equations
@subsection @code{diff_op_appell4}
@findex diff_op_appell4
@table @t
@item diff_op_appell4(@var{a},@var{b},@var{c1},@var{c2},@var{V})
::  appell $B$N(B F_4 $B$rNm2=$9$kHyJ,:nMQAG$r@8@.$7$^$9(B.
@end table
@table @var
@item return
$B%j%9%H(B
@item a, b, c1, c2
$BM-M}<0(B
@item V
$B%j%9%H(B
@end table
@itemize @bullet
@item  @code{diff_op_appell4}$B$NNc(B.
@end itemize
@example
[298] diff_op_appell4(a,b,c1,c2,[x,y]);
[ [ [-x^2+x,[2,0]], [-2*y*x,[1,1]], [-y^2,[0,2]],
    [(-a-b-1)*x+c1,[1,0]], [(-a-b-1)*y,[0,1]], [-b*a,[0,0]] ],
  [ [-y^2+y,[0,2]], [-2*y*x,[1,1]], [-x^2,[2,0]],
    [(-a-b-1)*y+c2,[0,1]], [(-a-b-1)*x,[1,0]], [-b*a,[0,0]] ] ]
@end example

@node diff_act,,, Differential equations
@subsection @code{diff_act}
@findex diff_act
@table @t
@item diff_act(@var{L},@var{F},@var{V})
::  $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.
@end table
@table @var
@item return
$BM-M}<0(B
@item L
$B%j%9%H(B
@item F
$BM-M}<0(B
@item V
$B%j%9%H(B
@end table
@itemize @bullet
@item  @code{diff_act}$B$NNc(B
@end itemize
@example
[302] diff_act([[1,[2]]],x^3+x^2+x+1,[x]);
6*x+2

[303] diff_act([[1,[1,0]],[1,[0,1]]],x^2+y^2,[x,y]);
2*x+2*y
@end example

@node diff_act_appell4,,, Differential equations
@subsection @code{diff_act_appell4}
@findex diff_act_appell4
@table @t
@item diff_act_appell4(@var{a},@var{b},@var{c1},@var{c2},@var{F},@var{V})
::  $BHyJ,:nMQAG(B @code{diff_op_appell4} $B$rM-M}<0(B @var{F} $B$K:nMQ$5$;$k(B.
@end table
@table @var
@item return
$B%j%9%H(B
@item a, b, c1, c2
$BM-M}<0(B
@item F
$BM-M}<0(B
@item V
$B%j%9%H(B
@end table
@itemize @bullet
@item  @code{diff_act_appell4}$B$NNc(B
@end itemize
@example
[303] diff_act_appell4(1,0,1,1,x^2+y^2,[x,y]);
[-6*x^2+4*x-6*y^2,-6*x^2-6*y^2+4*y]

[304] diff_act_appell4(0,0,1,1,x^2+y^2,[x,y]);
[-4*x^2+4*x-4*y^2,-4*x^2-4*y^2+4*y]

[305] diff_act_appell4(-2,-2,-1,-1,x^2+y^2,[x,y]);
[0,0]
@end example

@node diff_poly_solve,,, Differential equations
@subsection @code{diff_poly_solve}
@findex diff_poly_solve
@table @t
@item diff_poly_solve(@var{LL},@var{N},@var{V})
::  $BM?$($i$l$?@~7?HyJ,J}Dx<07O$N(B @var{N} $B<!0J2<$NB?9`<02r$r5a$a$k(B.
@end table
@table @var
@item return
$B%j%9%H(B
@item LL
$B%j%9%H(B
@item N
$B@0?t(B
@item V
$B%j%9%H(B
@end table
@itemize @bullet
@item  @code{diff_poly_solve}$B$NNc(B.
@end itemize
@example
[297] diff_poly_solve([[[x,[1,0]],[-1,[0,0]]],[[y,[0,1]],[-1,[0,0]]]],5,[x,y]);
[_4*y*x,[_4]]

[298] diff_poly_solve([[[x,[1,0]],[-2,[0,0]]],[[y,[0,1]],[-2,[0,0]]]],5,[x,y]);
[_33*y^2*x^2,[_33]]
@end example

@node diff_poly_solve_appell4,,, Differential equations
@subsection @code{diff_poly_solve_appell4}
@findex diff_poly_solve_appell4
@table @t
@item diff_poly_solve_appell4(@var{a},@var{b},@var{c1},@var{c2},@var{N},@var{V})
::  F_4$B$,$_$?$9@~7?HyJ,J}Dx<07O$N(B @var{N} $B<!0J2<$NB?9`<02r$r5a$a$k(B.
@end table
@table @var
@item return
$B%j%9%H(B
@item a, b, c1, c2
$BM-M}<0(B
@item N
$B@0?t(B
@item V
$B%j%9%H(B
@end table
@itemize @bullet
@item  @code{diff_poly_solve_appell4}$B$NNc(B.
@end itemize
@example
[299] diff_poly_solve_appell4(-3,1,-1,-1,5,[x,y]);
[-_26*x^3+(3*_26*y+_26)*x^2+3*_24*y^2*x-_24*y^3+_24*y^2,[_24,_26]]

[300] diff_poly_solve_appell4(-3,1,1,-1,5,[x,y]);
[-3*_45*y^2*x-_45*y^3+_45*y^2,[_45]]
@end example

@node diff_rat_solve,,, Differential equations
@subsection @code{diff_rat_solve}
@findex diff_rat_solve
@table @t
@item diff_rat_solve(@var{LL},@var{Dn},@var{N},@var{V})
::  $BM?$($i$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.
@end table
@table @var
@item return
$B%j%9%H(B
@item LL
$B%j%9%H(B
@item Dn
$BM-M}<0(B
@item N
$B@0?t(B
@item V
$B%j%9%H(B
@end table
@itemize @bullet
@item  @code{diff_rat_solve}$B$NNc(B.
@end itemize
@example
[333] diff_rat_solve([[[x,[1]],[1,[0]]]],x,1,[x]);
[(_8)/(x),[_8]]

[350] D = diff_op_appell4(0,0,3,0,[x,y])$
[351] diff_rat_solve(D,x^2,2,[x,y]);
[(_118*x^2-_114*y*x+1/2*_114*y^2+_114*y)/(x^2),[_114,_118]]
@end example