version 1.6, 2000/02/20 11:30:44 |
version 1.7, 2001/06/24 01:14:21 |
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@c $OpenXM: OpenXM/src/asir-contrib/packages/doc/Diff.texi,v 1.5 2000/01/31 11:01:00 okutani Exp $ |
@c $OpenXM: OpenXM/src/asir-contrib/packages/doc/Diff.texi,v 1.6 2000/02/20 11:30:44 okutani Exp $ |
@node Differential equations,,, $B$=$NB>$NH!?t(B |
@node Differential equations (library by Okutani),,, Top |
@section Differential equations |
@section Differential equations (library by Okutani) |
$B%U%!%$%k(B @file{gr}, @file{Matrix} $B$,I,MW$G$9(B. |
$B%U%!%$%k(B @file{gr}, @file{Matrix} $B$,I,MW$G$9(B. |
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Yukio Okutani $B;a$K$h$k(B Risa/Asir $B8@8l$G=q$+$l$?O"N)@~7AJPHyJ,J}Dx<0MQ(B |
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$B$N%i%$%V%i%j$G$9(B. |
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$B$9$Y$F$N4X?tL>$O(B odiff_ $B$G;O$^$j$^$9(B. |
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@tex |
@tex |
$B$3$N@a$G>R2p$5$l$k4X?t$G$OHyJ,:nMQAG$O%j%9%H$^$?$OB?9`<0$GI=8=$5$l$^$9(B. |
$B$3$N@a$G>R2p$5$l$k4X?t$G$OHyJ,:nMQAG$O%j%9%H$^$?$OB?9`<0$GI=8=$5$l$^$9(B. |
$B%j%9%H$K$h$kI=8=$O<!$N$h$&$K$J$j$^$9(B. |
$B%j%9%H$K$h$kI=8=$O<!$N$h$&$K$J$j$^$9(B. |
Line 24 $$ x*dx+y*dy+1 $$ |
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Line 28 $$ x*dx+y*dy+1 $$ |
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$B$HI=8=$5$l$^$9(B. |
$B$HI=8=$5$l$^$9(B. |
@end tex |
@end tex |
@menu |
@menu |
@c * diff_op_hg1:: |
@c * odiff_op_hg1:: |
@c * diff_op_appell1:: |
@c * odiff_op_appell1:: |
@c * diff_op_appell2:: |
@c * odiff_op_appell2:: |
@c * diff_op_appell3:: |
@c * odiff_op_appell3:: |
* diff_op_appell4:: |
* odiff_op_appell4:: |
@c * diff_op_selberg2:: |
@c * odiff_op_selberg2:: |
@c * diff_op_gkz:: |
@c * odiff_op_gkz:: |
* diff_op_tosm1:: |
* odiff_op_tosm1:: |
* diff_op_toasir:: |
* odiff_op_toasir:: |
* diff_op_fromasir:: |
* odiff_op_fromasir:: |
* diff_act:: |
* odiff_act:: |
@c * diff_act_hg1:: |
@c * odiff_act_hg1:: |
@c * diff_act_appell1:: |
@c * odiff_act_appell1:: |
@c * diff_act_appell2:: |
@c * odiff_act_appell2:: |
@c * diff_act_appell3:: |
@c * odiff_act_appell3:: |
* diff_act_appell4:: |
* odiff_act_appell4:: |
@c * diff_act_selberg2:: |
@c * odiff_act_selberg2:: |
@c * diff_act_gkz:: |
@c * odiff_act_gkz:: |
* diff_poly_solve:: |
* odiff_poly_solve:: |
* diff_poly_solve_hg1:: |
* odiff_poly_solve_hg1:: |
@c * diff_poly_solve_appell1:: |
@c * odiff_poly_solve_appell1:: |
@c * diff_poly_solve_appell2:: |
@c * odiff_poly_solve_appell2:: |
@c * diff_poly_solve_appell3:: |
@c * odiff_poly_solve_appell3:: |
* diff_poly_solve_appell4:: |
* odiff_poly_solve_appell4:: |
@c * diff_poly_solve_selberg2:: |
@c * odiff_poly_solve_selberg2:: |
@c * diff_poly_solve_gkz:: |
@c * odiff_poly_solve_gkz:: |
* diff_rat_solve:: |
* odiff_rat_solve:: |
@c * diff_pseries_appell4:: |
@c * odiff_pseries_appell4:: |
@end menu |
@end menu |
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@node diff_op_appell4,,, Differential equations |
@node odiff_op_appell4,,, Differential equations (library by Okutani) |
@subsection @code{diff_op_appell4} |
@subsection @code{odiff_op_appell4} |
@findex diff_op_appell4 |
@findex odiff_op_appell4 |
@table @t |
@table @t |
@item diff_op_appell4(@var{a},@var{b},@var{c1},@var{c2},@var{V}) |
@item odiff_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. |
:: appell $B$N(B F_4 $B$rNm2=$9$kHyJ,:nMQAG$r@8@.$7$^$9(B. |
@end table |
@end table |
@table @var |
@table @var |
Line 70 $$ x*dx+y*dy+1 $$ |
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Line 74 $$ x*dx+y*dy+1 $$ |
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$B%j%9%H(B |
$B%j%9%H(B |
@end table |
@end table |
@itemize @bullet |
@itemize @bullet |
@item @code{diff_op_appell4}$B$NNc(B. |
@item @code{odiff_op_appell4}$B$NNc(B. |
@end itemize |
@end itemize |
@example |
@example |
[298] diff_op_appell4(a,b,c1,c2,[x,y]); |
[298] odiff_op_appell4(a,b,c1,c2,[x,y]); |
[ [ [-x^2+x,[2,0]], [-2*y*x,[1,1]], [-y^2,[0,2]], |
[ [ [-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]] ], |
[(-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]], |
[ [-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]] ] ] |
[(-a-b-1)*y+c2,[0,1]], [(-a-b-1)*x,[1,0]], [-b*a,[0,0]] ] ] |
@end example |
@end example |
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@node diff_op_tosm1,,, Differential equations |
@node odiff_op_tosm1,,, Differential equations (library by Okutani) |
@subsection @code{diff_op_tosm1} |
@subsection @code{odiff_op_tosm1} |
@findex diff_op_tosm1 |
@findex odiff_op_tosm1 |
@table @t |
@table @t |
@item diff_op_tosm1(@var{LL},@var{V}) |
@item odiff_op_tosm1(@var{LL},@var{V}) |
:: $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$r(B sm1 $B7A<0$KJQ49$7$^$9(B. |
:: $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$r(B sm1 $B7A<0$KJQ49$7$^$9(B. |
@end table |
@end table |
@table @var |
@table @var |
Line 97 $$ x*dx+y*dy+1 $$ |
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Line 101 $$ x*dx+y*dy+1 $$ |
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@end table |
@end table |
@itemize @bullet |
@itemize @bullet |
@item $BHyJ,:nMQAG$N78?t$O@0?tB?9`<0$KJQ49$5$l$^$9(B. |
@item $BHyJ,:nMQAG$N78?t$O@0?tB?9`<0$KJQ49$5$l$^$9(B. |
@item @code{diff_op_tosm1}$B$NNc(B |
@item @code{odiff_op_tosm1}$B$NNc(B |
@end itemize |
@end itemize |
@example |
@example |
[299] diff_op_tosm1([[[x,[2,0]],[-1,[0,0]]], |
[299] odiff_op_tosm1([[[x,[2,0]],[-1,[0,0]]], |
[[y,[0,2]],[-1,[0,0]]]],[x,y]); |
[[y,[0,2]],[-1,[0,0]]]],[x,y]); |
[ + ( + (1) x) dx^2 + ( + (-1)), + ( + (1) y) dy^2 + ( + (-1))] |
[ + ( + (1) x) dx^2 + ( + (-1)), + ( + (1) y) dy^2 + ( + (-1))] |
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[300] diff_op_tosm1([[[x,[1,0]],[y,[0,1]],[1,[0,0]]], |
[300] odiff_op_tosm1([[[x,[1,0]],[y,[0,1]],[1,[0,0]]], |
[[1,[2,0]],[1,[0,2]]]],[x,y]); |
[[1,[2,0]],[1,[0,2]]]],[x,y]); |
[ + ( + (1) x) dx + ( + (1) y) dy + ( + (1)), + ( + (1)) dx^2 + ( + (1)) dy^2] |
[ + ( + (1) x) dx + ( + (1) y) dy + ( + (1)), + ( + (1)) dx^2 + ( + (1)) dy^2] |
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[301] diff_op_tosm1([[[1/2,[1,0]],[1,[0,0]]], |
[301] odiff_op_tosm1([[[1/2,[1,0]],[1,[0,0]]], |
[[1/3,[0,1]],[1/4,[0,0]]]],[x,y]); |
[[1/3,[0,1]],[1/4,[0,0]]]],[x,y]); |
[ + ( + (6)) dx + ( + (12)), + ( + (4)) dy + ( + (3))] |
[ + ( + (6)) dx + ( + (12)), + ( + (4)) dy + ( + (3))] |
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[302] diff_op_tosm1([[[1/2*x,[1,0]],[1,[0,0]]], |
[302] odiff_op_tosm1([[[1/2*x,[1,0]],[1,[0,0]]], |
[[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]); |
[[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]); |
[ + ( + (6) x) dx + ( + (12)), + ( + (4) y) dy + ( + (3))] |
[ + ( + (6) x) dx + ( + (12)), + ( + (4) y) dy + ( + (3))] |
@end example |
@end example |
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@node diff_op_toasir,,, Differential equations |
@node odiff_op_toasir,,, Differential equations (library by Okutani) |
@subsection @code{diff_op_toasir} |
@subsection @code{odiff_op_toasir} |
@findex diff_op_toasir |
@findex odiff_op_toasir |
@table @t |
@table @t |
@item diff_op_toasir(@var{LL},@var{V}) |
@item odiff_op_toasir(@var{LL},@var{V}) |
:: $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H(B @var{LL} $B$r(B @code{asir} $B$NB?9`<0$KJQ49$7$^$9(B. |
:: $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H(B @var{LL} $B$r(B @code{asir} $B$NB?9`<0$KJQ49$7$^$9(B. |
@end table |
@end table |
@table @var |
@table @var |
Line 133 $$ x*dx+y*dy+1 $$ |
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Line 137 $$ x*dx+y*dy+1 $$ |
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$B%j%9%H(B |
$B%j%9%H(B |
@end table |
@end table |
@itemize @bullet |
@itemize @bullet |
@item @code{diff_op_toasir}$B$NNc(B |
@item @code{odiff_op_toasir}$B$NNc(B |
@end itemize |
@end itemize |
@example |
@example |
[303] diff_op_toasir([[[1/2*x,[1,0]],[1,[0,0]]], |
[303] odiff_op_toasir([[[1/2*x,[1,0]],[1,[0,0]]], |
[[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]); |
[[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]); |
[1/2*x*dx+1,1/3*y*dy+1/4] |
[1/2*x*dx+1,1/3*y*dy+1/4] |
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[304] diff_op_toasir([[[x,[1,0]],[y,[0,1]],[1,[0,0]]], |
[304] odiff_op_toasir([[[x,[1,0]],[y,[0,1]],[1,[0,0]]], |
[[1,[2,0]],[1,[0,2]]]],[x,y]); |
[[1,[2,0]],[1,[0,2]]]],[x,y]); |
[x*dx+y*dy+1,dx^2+dy^2] |
[x*dx+y*dy+1,dx^2+dy^2] |
@end example |
@end example |
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@node diff_op_fromasir,,, Differential equations |
@node odiff_op_fromasir,,, Differential equations (library by Okutani) |
@subsection @code{diff_op_fromasir} |
@subsection @code{odiff_op_fromasir} |
@findex diff_op_fromasir |
@findex odiff_op_fromasir |
@table @t |
@table @t |
@item diff_op_fromasir(@var{D_list},@var{V}) |
@item odiff_op_fromasir(@var{D_list},@var{V}) |
:: @code{asir} $B$NB?9`<0$+$i%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$KJQ49$7$^$9(B. |
:: @code{asir} $B$NB?9`<0$+$i%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$KJQ49$7$^$9(B. |
@end table |
@end table |
@table @var |
@table @var |
Line 161 $$ x*dx+y*dy+1 $$ |
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Line 165 $$ x*dx+y*dy+1 $$ |
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$B%j%9%H(B |
$B%j%9%H(B |
@end table |
@end table |
@itemize @bullet |
@itemize @bullet |
@item @code{diff_op_fromasir}$B$NNc(B |
@item @code{odiff_op_fromasir}$B$NNc(B |
@end itemize |
@end itemize |
@example |
@example |
[305] diff_op_fromasir([1/2*x*dx+1,1/3*y*dy+1/4],[x,y]); |
[305] odiff_op_fromasir([1/2*x*dx+1,1/3*y*dy+1/4],[x,y]); |
[[[1/2*x,[1,0]],[1,[0,0]]],[[1/3*y,[0,1]],[1/4,[0,0]]]] |
[[[1/2*x,[1,0]],[1,[0,0]]],[[1/3*y,[0,1]],[1/4,[0,0]]]] |
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[306] diff_op_fromasir([x*dx+y*dy+1,dx^2+dy^2],[x,y]); |
[306] odiff_op_fromasir([x*dx+y*dy+1,dx^2+dy^2],[x,y]); |
[[[x,[1,0]],[y,[0,1]],[1,[0,0]]],[[1,[2,0]],[1,[0,2]]]] |
[[[x,[1,0]],[y,[0,1]],[1,[0,0]]],[[1,[2,0]],[1,[0,2]]]] |
@end example |
@end example |
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@node diff_act,,, Differential equations |
@node odiff_act,,, Differential equations (library by Okutani) |
@subsection @code{diff_act} |
@subsection @code{odiff_act} |
@findex diff_act |
@findex odiff_act |
@table @t |
@table @t |
@item diff_act(@var{L},@var{F},@var{V}) |
@item odiff_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. |
:: $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 |
@end table |
@table @var |
@table @var |
Line 189 $$ x*dx+y*dy+1 $$ |
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Line 193 $$ x*dx+y*dy+1 $$ |
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$B%j%9%H(B |
$B%j%9%H(B |
@end table |
@end table |
@itemize @bullet |
@itemize @bullet |
@item @code{diff_act}$B$NNc(B |
@item @code{odiff_act}$B$NNc(B |
@end itemize |
@end itemize |
@example |
@example |
[302] diff_act([[1,[2]]],x^3+x^2+x+1,[x]); |
[302] odiff_act([[1,[2]]],x^3+x^2+x+1,[x]); |
6*x+2 |
6*x+2 |
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[303] diff_act([[1,[1,0]],[1,[0,1]]],x^2+y^2,[x,y]); |
[303] odiff_act([[1,[1,0]],[1,[0,1]]],x^2+y^2,[x,y]); |
2*x+2*y |
2*x+2*y |
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[349] diff_act(x*dx+y*dy, x^2+x*y+y^2, [x,y]); |
[349] odiff_act(x*dx+y*dy, x^2+x*y+y^2, [x,y]); |
2*x^2+2*y*x+2*y^2 |
2*x^2+2*y*x+2*y^2 |
@end example |
@end example |
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@node diff_act_appell4,,, Differential equations |
@node odiff_act_appell4,,, Differential equations (library by Okutani) |
@subsection @code{diff_act_appell4} |
@subsection @code{odiff_act_appell4} |
@findex diff_act_appell4 |
@findex odiff_act_appell4 |
@table @t |
@table @t |
@item diff_act_appell4(@var{a},@var{b},@var{c1},@var{c2},@var{F},@var{V}) |
@item odiff_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. |
:: $BHyJ,:nMQAG(B @code{odiff_op_appell4} $B$rM-M}<0(B @var{F} $B$K:nMQ$5$;$k(B. |
@end table |
@end table |
@table @var |
@table @var |
@item return |
@item return |
Line 220 $$ x*dx+y*dy+1 $$ |
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Line 224 $$ x*dx+y*dy+1 $$ |
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$B%j%9%H(B |
$B%j%9%H(B |
@end table |
@end table |
@itemize @bullet |
@itemize @bullet |
@item @code{diff_act_appell4}$B$NNc(B |
@item @code{odiff_act_appell4}$B$NNc(B |
@end itemize |
@end itemize |
@example |
@example |
[303] diff_act_appell4(1,0,1,1,x^2+y^2,[x,y]); |
[303] odiff_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] |
[-6*x^2+4*x-6*y^2,-6*x^2-6*y^2+4*y] |
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[304] diff_act_appell4(0,0,1,1,x^2+y^2,[x,y]); |
[304] odiff_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] |
[-4*x^2+4*x-4*y^2,-4*x^2-4*y^2+4*y] |
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[305] diff_act_appell4(-2,-2,-1,-1,x^2+y^2,[x,y]); |
[305] odiff_act_appell4(-2,-2,-1,-1,x^2+y^2,[x,y]); |
[0,0] |
[0,0] |
@end example |
@end example |
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@node diff_poly_solve,,, Differential equations |
@node odiff_poly_solve,,, Differential equations (library by Okutani) |
@subsection @code{diff_poly_solve} |
@subsection @code{odiff_poly_solve} |
@findex diff_poly_solve |
@findex odiff_poly_solve |
@table @t |
@table @t |
@item diff_poly_solve(@var{LL},@var{N},@var{V}) |
@item odiff_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. |
:: $BM?$($i$l$?@~7?HyJ,J}Dx<07O$N(B @var{N} $B<!0J2<$NB?9`<02r$r5a$a$k(B. |
@end table |
@end table |
@table @var |
@table @var |
Line 251 $$ x*dx+y*dy+1 $$ |
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Line 255 $$ x*dx+y*dy+1 $$ |
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$B%j%9%H(B |
$B%j%9%H(B |
@end table |
@end table |
@itemize @bullet |
@itemize @bullet |
@item @code{diff_poly_solve}$B$NNc(B. |
@item @code{odiff_poly_solve}$B$NNc(B. |
@end itemize |
@end itemize |
@example |
@example |
[297] diff_poly_solve([[[x,[1,0]],[-1,[0,0]]],[[y,[0,1]],[-1,[0,0]]]],5,[x,y]); |
[297] odiff_poly_solve([[[x,[1,0]],[-1,[0,0]]],[[y,[0,1]],[-1,[0,0]]]],5,[x,y]); |
[_4*y*x,[_4]] |
[_4*y*x,[_4]] |
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[298] diff_poly_solve([[[x,[1,0]],[-2,[0,0]]],[[y,[0,1]],[-2,[0,0]]]],5,[x,y]); |
[298] odiff_poly_solve([[[x,[1,0]],[-2,[0,0]]],[[y,[0,1]],[-2,[0,0]]]],5,[x,y]); |
[_33*y^2*x^2,[_33]] |
[_33*y^2*x^2,[_33]] |
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[356] diff_poly_solve([x*dx+y*dy-3,dx+dy],4,[x,y]); |
[356] odiff_poly_solve([x*dx+y*dy-3,dx+dy],4,[x,y]); |
[-_126*x^3+3*_126*y*x^2-3*_126*y^2*x+_126*y^3,[_126]] |
[-_126*x^3+3*_126*y*x^2-3*_126*y^2*x+_126*y^3,[_126]] |
@end example |
@end example |
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@node diff_poly_solve_hg1,,, Differential equations |
@node odiff_poly_solve_hg1,,, Differential equations (library by Okutani) |
@subsection @code{diff_poly_solve_hg1} |
@subsection @code{odiff_poly_solve_hg1} |
@findex diff_poly_solve_hg1 |
@findex odiff_poly_solve_hg1 |
@table @t |
@table @t |
@item diff_poly_solve_hg1(@var{a},@var{b},@var{c},@var{V}) |
@item odiff_poly_solve_hg1(@var{a},@var{b},@var{c},@var{V}) |
:: $B%,%&%9$ND64v2?HyJ,J}Dx<0$NB?9`<02r$r5a$a$k(B. |
:: $B%,%&%9$ND64v2?HyJ,J}Dx<0$NB?9`<02r$r5a$a$k(B. |
@end table |
@end table |
@table @var |
@table @var |
Line 280 $$ x*dx+y*dy+1 $$ |
|
Line 284 $$ x*dx+y*dy+1 $$ |
|
$B%j%9%H(B |
$B%j%9%H(B |
@end table |
@end table |
@itemize @bullet |
@itemize @bullet |
@item @code{diff_poly_solve_hg1}$B$NNc(B. |
@item @code{odiff_poly_solve_hg1}$B$NNc(B. |
@end itemize |
@end itemize |
@example |
@example |
[334] diff_poly_solve_hg1(-3,-6,-5,[x]); |
[334] odiff_poly_solve_hg1(-3,-6,-5,[x]); |
[_1*x^6-2*_0*x^3+9/2*_0*x^2-18/5*_0*x+_0,[_0,_1]] |
[_1*x^6-2*_0*x^3+9/2*_0*x^2-18/5*_0*x+_0,[_0,_1]] |
|
|
[335] diff_poly_solve_hg1(-3,-6,-7,[x]); |
[335] odiff_poly_solve_hg1(-3,-6,-7,[x]); |
[-4/7*_2*x^3+15/7*_2*x^2-18/7*_2*x+_2,[_2]] |
[-4/7*_2*x^3+15/7*_2*x^2-18/7*_2*x+_2,[_2]] |
@end example |
@end example |
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|
@node diff_poly_solve_appell4,,, Differential equations |
@node odiff_poly_solve_appell4,,, Differential equations (library by Okutani) |
@subsection @code{diff_poly_solve_appell4} |
@subsection @code{odiff_poly_solve_appell4} |
@findex diff_poly_solve_appell4 |
@findex odiff_poly_solve_appell4 |
@table @t |
@table @t |
@item diff_poly_solve_appell4(@var{a},@var{b},@var{c1},@var{c2},@var{V}) |
@item odiff_poly_solve_appell4(@var{a},@var{b},@var{c1},@var{c2},@var{V}) |
:: F_4$B$,$_$?$9@~7?HyJ,J}Dx<07O$NB?9`<02r$r5a$a$k(B. |
:: F_4$B$,$_$?$9@~7?HyJ,J}Dx<07O$NB?9`<02r$r5a$a$k(B. |
@end table |
@end table |
@table @var |
@table @var |
Line 306 $$ x*dx+y*dy+1 $$ |
|
Line 310 $$ x*dx+y*dy+1 $$ |
|
$B%j%9%H(B |
$B%j%9%H(B |
@end table |
@end table |
@itemize @bullet |
@itemize @bullet |
@item @code{diff_poly_solve_appell4}$B$NNc(B. |
@item @code{odiff_poly_solve_appell4}$B$NNc(B. |
@end itemize |
@end itemize |
@example |
@example |
[299] diff_poly_solve_appell4(-3,1,-1,-1,[x,y]); |
[299] odiff_poly_solve_appell4(-3,1,-1,-1,[x,y]); |
[-_26*x^3+(3*_26*y+_26)*x^2+3*_24*y^2*x-_24*y^3+_24*y^2,[_24,_26]] |
[-_26*x^3+(3*_26*y+_26)*x^2+3*_24*y^2*x-_24*y^3+_24*y^2,[_24,_26]] |
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|
[300] diff_poly_solve_appell4(-3,1,1,-1,[x,y]); |
[300] odiff_poly_solve_appell4(-3,1,1,-1,[x,y]); |
[-3*_45*y^2*x-_45*y^3+_45*y^2,[_45]] |
[-3*_45*y^2*x-_45*y^3+_45*y^2,[_45]] |
@end example |
@end example |
|
|
@node diff_rat_solve,,, Differential equations |
@node odiff_rat_solve,,, Differential equations (library by Okutani) |
@subsection @code{diff_rat_solve} |
@subsection @code{odiff_rat_solve} |
@findex diff_rat_solve |
@findex odiff_rat_solve |
@table @t |
@table @t |
@item diff_rat_solve(@var{LL},@var{Dn},@var{N},@var{V}) |
@item odiff_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. |
:: $BM?$($i$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 |
@end table |
@table @var |
@table @var |
Line 336 $$ x*dx+y*dy+1 $$ |
|
Line 340 $$ x*dx+y*dy+1 $$ |
|
$B%j%9%H(B |
$B%j%9%H(B |
@end table |
@end table |
@itemize @bullet |
@itemize @bullet |
@item @code{diff_rat_solve}$B$NNc(B. |
@item @code{odiff_rat_solve}$B$NNc(B. |
@end itemize |
@end itemize |
@example |
@example |
[333] diff_rat_solve([[[x,[1]],[1,[0]]]],x,1,[x]); |
[333] odiff_rat_solve([[[x,[1]],[1,[0]]]],x,1,[x]); |
[(_8)/(x),[_8]] |
[(_8)/(x),[_8]] |
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|
[361] diff_rat_solve([x*(1-x)*dx^2+(1-3*x)*dx-1],1-x,2,[x]); |
[361] odiff_rat_solve([x*(1-x)*dx^2+(1-3*x)*dx-1],1-x,2,[x]); |
[(_180)/(-x+1),[_180]] |
[(_180)/(-x+1),[_180]] |
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|
[350] D = diff_op_appell4(0,0,3,0,[x,y])$ |
[350] D = odiff_op_appell4(0,0,3,0,[x,y])$ |
[351] diff_rat_solve(D,x^2,2,[x,y]); |
[351] odiff_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]] |
[(_118*x^2-_114*y*x+1/2*_114*y^2+_114*y)/(x^2),[_114,_118]] |
@end example |
@end example |