Return to Diff-ja.texi CVS log

Up to [local] / OpenXM / src / asir-contrib / packages / doc

Annotation of OpenXM/src/asir-contrib/packages/doc/Diff-ja.texi, Revision 1.1

1.1     ! takayama    1: @c $OpenXM$
        !             2: @node Differential equations (library by Okutani),,, Top
        !             3: @chapter Differential equations (library by Okutani)
        !             4: $B%U%!%$%k(B @file{gr}, @file{Matrix} $B$,I,MW$G$9(B.
        !             5:
        !             6: Yukio Okutani $B;a$K$h$k(B Risa/Asir $B8@8l$G=q$+$l$?O"N)@~7AJPHyJ,J}Dx<0MQ(B
        !             7: $B$N%i%$%V%i%j$G$9(B.
        !             8: $B$9$Y$F$N4X?tL>$O(B odiff_ $B$G;O$^$j$^$9(B.
        !             9:
        !            10: @tex
        !            11: $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.
        !            12: $B%j%9%H$K$h$kI=8=$O<!$N$h$&$K$J$j$^$9(B.
        !            13: $$ [ [f_{\alpha},[\alpha_{1},\ldots,\alpha_{n}]],\ldots ] $$
        !            14: $B$3$l$O(B
        !            15: $$ \sum_{\alpha}f_{\alpha}\partial^{\alpha} $$
        !            16: $B$H$$$&0UL#$G$9(B. $B@~7?JPHyJ,J}Dx<07O(B
        !            17: $$ (\sum_{\alpha^{(i)}}f_{\alpha^{(i)}}\partial^{\alpha^{(i)}})\bullet u = 0 \quad (i = 1,\ldots,s) $$
        !            18: $B$J$I$N$h$&$KJ#?t$NHyJ,:nMQAG$rI=8=$9$k$H$-$OHyJ,:nMQAG$N%j%9%H$r;H$$$^$9(B.
        !            19: $$ [ [ [f_{\alpha^{(1)}},[\alpha_{1}^{(1)},\ldots,\alpha_{n}^{(1)}]],\ldots ],\ldots,[ [f_{\alpha^{(s)}},[\alpha_{1}^{(s)},\ldots,\alpha_{n}^{(s)}]],\ldots ] ] $$
        !            20: $BNc$($PHyJ,:nMQAG(B$x \partial_{x} + y \partial_{y} + 1$$B$N>l9g$O(B
        !            21: $$ [ [x,[1,0]],[y,[0,1]],[1,[0,0]] ] $$
        !            22: $B$H$J$j$^$9(B. $B$^$?HyJ,:nMQAG$N%j%9%H$G(B$x \partial_{x} + y \partial_{y} + 1, {\partial_{x}}^{2} + {\partial_{y}}^{2}$$B$rI=$9$H(B
        !            23: $$ [ [ [x,[1,0]],[y,[0,1]],[1,[0,0]] ],[ [1,[2,0]],[1,[0,2]] ] ] $$
        !            24: $B$H$J$j$^$9(B. $B$^$?$3$NI=8=K!$r;H$&$H$-$OJQ?t%j%9%H$r>o$K0U<1$7$F$$$kI,MW$,$"$j$^$9(B.
        !            25: $B<!$KB?9`<0$K$h$kI=8=$K$D$$$F=R$Y$^$9(B. $BJQ?t(B$x$$B$KBP$9$kHyJ,$O(B$dx$$B$GI=8=$5$l$^$9(B.
        !            26: $BNc$($P(B$x \partial_{x} + y \partial_{y} + 1$$B$K$D$$$F$O(B
        !            27: $$ x*dx+y*dy+1 $$
        !            28: $B$HI=8=$5$l$^$9(B.
        !            29: @end tex
        !            30: @menu
        !            31: @c * odiff_op_hg1::
        !            32: @c * odiff_op_appell1::
        !            33: @c * odiff_op_appell2::
        !            34: @c * odiff_op_appell3::
        !            35: * odiff_op_appell4::
        !            36: @c * odiff_op_selberg2::
        !            37: @c * odiff_op_gkz::
        !            38: * odiff_op_tosm1::
        !            39: * odiff_op_toasir::
        !            40: * odiff_op_fromasir::
        !            41: * odiff_act::
        !            42: @c * odiff_act_hg1::
        !            43: @c * odiff_act_appell1::
        !            44: @c * odiff_act_appell2::
        !            45: @c * odiff_act_appell3::
        !            46: * odiff_act_appell4::
        !            47: @c * odiff_act_selberg2::
        !            48: @c * odiff_act_gkz::
        !            49: * odiff_poly_solve::
        !            50: * odiff_poly_solve_hg1::
        !            51: @c * odiff_poly_solve_appell1::
        !            52: @c * odiff_poly_solve_appell2::
        !            53: @c * odiff_poly_solve_appell3::
        !            54: * odiff_poly_solve_appell4::
        !            55: @c * odiff_poly_solve_selberg2::
        !            56: @c * odiff_poly_solve_gkz::
        !            57: * odiff_rat_solve::
        !            58: @c * odiff_pseries_appell4::
        !            59: @end menu
        !            60:
        !            61: @node odiff_op_appell4,,, Differential equations (library by Okutani)
        !            62: @subsection @code{odiff_op_appell4}
        !            63: @findex odiff_op_appell4
        !            64: @table @t
        !            65: @item odiff_op_appell4(@var{a},@var{b},@var{c1},@var{c2},@var{V})
        !            66: ::  appell $B$N(B F_4 $B$rNm2=$9$kHyJ,:nMQAG$r@8@.$7$^$9(B.
        !            67: @end table
        !            68: @table @var
        !            69: @item return
        !            70: $B%j%9%H(B
        !            71: @item a, b, c1, c2
        !            72: $BM-M}<0(B
        !            73: @item V
        !            74: $B%j%9%H(B
        !            75: @end table
        !            76: @itemize @bullet
        !            77: @item  @code{odiff_op_appell4}$B$NNc(B.
        !            78: @end itemize
        !            79: @example
        !            80: [298] odiff_op_appell4(a,b,c1,c2,[x,y]);
        !            81: [ [ [-x^2+x,[2,0]], [-2*y*x,[1,1]], [-y^2,[0,2]],
        !            82:     [(-a-b-1)*x+c1,[1,0]], [(-a-b-1)*y,[0,1]], [-b*a,[0,0]] ],
        !            83:   [ [-y^2+y,[0,2]], [-2*y*x,[1,1]], [-x^2,[2,0]],
        !            84:     [(-a-b-1)*y+c2,[0,1]], [(-a-b-1)*x,[1,0]], [-b*a,[0,0]] ] ]
        !            85: @end example
        !            86:
        !            87: @node odiff_op_tosm1,,, Differential equations (library by Okutani)
        !            88: @subsection @code{odiff_op_tosm1}
        !            89: @findex odiff_op_tosm1
        !            90: @table @t
        !            91: @item odiff_op_tosm1(@var{LL},@var{V})
        !            92: ::  $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$r(B sm1 $B7A<0$KJQ49$7$^$9(B.
        !            93: @end table
        !            94: @table @var
        !            95: @item return
        !            96: $B%j%9%H(B
        !            97: @item LL
        !            98: $B%j%9%H(B
        !            99: @item V
        !           100: $B%j%9%H(B
        !           101: @end table
        !           102: @itemize @bullet
        !           103: @item  $BHyJ,:nMQAG$N78?t$O@0?tB?9`<0$KJQ49$5$l$^$9(B.
        !           104: @item  @code{odiff_op_tosm1}$B$NNc(B
        !           105: @end itemize
        !           106: @example
        !           107: [299] odiff_op_tosm1([[[x,[2,0]],[-1,[0,0]]],
        !           108:                           [[y,[0,2]],[-1,[0,0]]]],[x,y]);
        !           109: [ + ( + (1) x) dx^2 + ( + (-1)), + ( + (1) y) dy^2 + ( + (-1))]
        !           110:
        !           111: [300] odiff_op_tosm1([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],
        !           112:                           [[1,[2,0]],[1,[0,2]]]],[x,y]);
        !           113: [ + ( + (1) x) dx + ( + (1) y) dy + ( + (1)), + ( + (1)) dx^2 + ( + (1)) dy^2]
        !           114:
        !           115: [301] odiff_op_tosm1([[[1/2,[1,0]],[1,[0,0]]],
        !           116:                           [[1/3,[0,1]],[1/4,[0,0]]]],[x,y]);
        !           117: [ + ( + (6)) dx + ( + (12)), + ( + (4)) dy + ( + (3))]
        !           118:
        !           119: [302] odiff_op_tosm1([[[1/2*x,[1,0]],[1,[0,0]]],
        !           120:                           [[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
        !           121: [ + ( + (6) x) dx + ( + (12)), + ( + (4) y) dy + ( + (3))]
        !           122: @end example
        !           123:
        !           124: @node odiff_op_toasir,,, Differential equations (library by Okutani)
        !           125: @subsection @code{odiff_op_toasir}
        !           126: @findex odiff_op_toasir
        !           127: @table @t
        !           128: @item odiff_op_toasir(@var{LL},@var{V})
        !           129: ::  $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H(B @var{LL} $B$r(B @code{asir} $B$NB?9`<0$KJQ49$7$^$9(B.
        !           130: @end table
        !           131: @table @var
        !           132: @item return
        !           133: $B%j%9%H(B
        !           134: @item LL
        !           135: $B%j%9%H(B
        !           136: @item V
        !           137: $B%j%9%H(B
        !           138: @end table
        !           139: @itemize @bullet
        !           140: @item  @code{odiff_op_toasir}$B$NNc(B
        !           141: @end itemize
        !           142: @example
        !           143: [303] odiff_op_toasir([[[1/2*x,[1,0]],[1,[0,0]]],
        !           144:                            [[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
        !           145: [1/2*x*dx+1,1/3*y*dy+1/4]
        !           146:
        !           147: [304] odiff_op_toasir([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],
        !           148:                            [[1,[2,0]],[1,[0,2]]]],[x,y]);
        !           149: [x*dx+y*dy+1,dx^2+dy^2]
        !           150: @end example
        !           151:
        !           152: @node odiff_op_fromasir,,, Differential equations (library by Okutani)
        !           153: @subsection @code{odiff_op_fromasir}
        !           154: @findex odiff_op_fromasir
        !           155: @table @t
        !           156: @item odiff_op_fromasir(@var{D_list},@var{V})
        !           157: ::  @code{asir} $B$NB?9`<0$+$i%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$KJQ49$7$^$9(B.
        !           158: @end table
        !           159: @table @var
        !           160: @item return
        !           161: $B%j%9%H(B
        !           162: @item D_list
        !           163: $B%j%9%H(B
        !           164: @item V
        !           165: $B%j%9%H(B
        !           166: @end table
        !           167: @itemize @bullet
        !           168: @item  @code{odiff_op_fromasir}$B$NNc(B
        !           169: @end itemize
        !           170: @example
        !           171: [305] odiff_op_fromasir([1/2*x*dx+1,1/3*y*dy+1/4],[x,y]);
        !           172: [[[1/2*x,[1,0]],[1,[0,0]]],[[1/3*y,[0,1]],[1/4,[0,0]]]]
        !           173:
        !           174: [306] odiff_op_fromasir([x*dx+y*dy+1,dx^2+dy^2],[x,y]);
        !           175: [[[x,[1,0]],[y,[0,1]],[1,[0,0]]],[[1,[2,0]],[1,[0,2]]]]
        !           176: @end example
        !           177:
        !           178: @node odiff_act,,, Differential equations (library by Okutani)
        !           179: @subsection @code{odiff_act}
        !           180: @findex odiff_act
        !           181: @table @t
        !           182: @item odiff_act(@var{L},@var{F},@var{V})
        !           183: ::  $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.
        !           184: @end table
        !           185: @table @var
        !           186: @item return
        !           187: $BM-M}<0(B
        !           188: @item L
        !           189: $B%j%9%H(B or $BB?9`<0(B
        !           190: @item F
        !           191: $BM-M}<0(B
        !           192: @item V
        !           193: $B%j%9%H(B
        !           194: @end table
        !           195: @itemize @bullet
        !           196: @item  @code{odiff_act}$B$NNc(B
        !           197: @end itemize
        !           198: @example
        !           199: [302] odiff_act([[1,[2]]],x^3+x^2+x+1,[x]);
        !           200: 6*x+2
        !           201:
        !           202: [303] odiff_act([[1,[1,0]],[1,[0,1]]],x^2+y^2,[x,y]);
        !           203: 2*x+2*y
        !           204:
        !           205: [349] odiff_act(x*dx+y*dy, x^2+x*y+y^2, [x,y]);
        !           206: 2*x^2+2*y*x+2*y^2
        !           207: @end example
        !           208:
        !           209: @node odiff_act_appell4,,, Differential equations (library by Okutani)
        !           210: @subsection @code{odiff_act_appell4}
        !           211: @findex odiff_act_appell4
        !           212: @table @t
        !           213: @item odiff_act_appell4(@var{a},@var{b},@var{c1},@var{c2},@var{F},@var{V})
        !           214: ::  $BHyJ,:nMQAG(B @code{odiff_op_appell4} $B$rM-M}<0(B @var{F} $B$K:nMQ$5$;$k(B.
        !           215: @end table
        !           216: @table @var
        !           217: @item return
        !           218: $B%j%9%H(B
        !           219: @item a, b, c1, c2
        !           220: $BM-M}<0(B
        !           221: @item F
        !           222: $BM-M}<0(B
        !           223: @item V
        !           224: $B%j%9%H(B
        !           225: @end table
        !           226: @itemize @bullet
        !           227: @item  @code{odiff_act_appell4}$B$NNc(B
        !           228: @end itemize
        !           229: @example
        !           230: [303] odiff_act_appell4(1,0,1,1,x^2+y^2,[x,y]);
        !           231: [-6*x^2+4*x-6*y^2,-6*x^2-6*y^2+4*y]
        !           232:
        !           233: [304] odiff_act_appell4(0,0,1,1,x^2+y^2,[x,y]);
        !           234: [-4*x^2+4*x-4*y^2,-4*x^2-4*y^2+4*y]
        !           235:
        !           236: [305] odiff_act_appell4(-2,-2,-1,-1,x^2+y^2,[x,y]);
        !           237: [0,0]
        !           238: @end example
        !           239:
        !           240: @node odiff_poly_solve,,, Differential equations (library by Okutani)
        !           241: @subsection @code{odiff_poly_solve}
        !           242: @findex odiff_poly_solve
        !           243: @table @t
        !           244: @item odiff_poly_solve(@var{LL},@var{N},@var{V})
        !           245: ::  $BM?$($i$l$?@~7?HyJ,J}Dx<07O$N(B @var{N} $B<!0J2<$NB?9`<02r$r5a$a$k(B.
        !           246: @end table
        !           247: @table @var
        !           248: @item return
        !           249: $B%j%9%H(B
        !           250: @item LL
        !           251: $B%j%9%H(B
        !           252: @item N
        !           253: $B@0?t(B
        !           254: @item V
        !           255: $B%j%9%H(B
        !           256: @end table
        !           257: @itemize @bullet
        !           258: @item  @code{odiff_poly_solve}$B$NNc(B.
        !           259: @end itemize
        !           260: @example
        !           261: [297] odiff_poly_solve([[[x,[1,0]],[-1,[0,0]]],[[y,[0,1]],[-1,[0,0]]]],5,[x,y]);
        !           262: [_4*y*x,[_4]]
        !           263:
        !           264: [298] odiff_poly_solve([[[x,[1,0]],[-2,[0,0]]],[[y,[0,1]],[-2,[0,0]]]],5,[x,y]);
        !           265: [_33*y^2*x^2,[_33]]
        !           266:
        !           267: [356] odiff_poly_solve([x*dx+y*dy-3,dx+dy],4,[x,y]);
        !           268: [-_126*x^3+3*_126*y*x^2-3*_126*y^2*x+_126*y^3,[_126]]
        !           269: @end example
        !           270:
        !           271: @node odiff_poly_solve_hg1,,, Differential equations (library by Okutani)
        !           272: @subsection @code{odiff_poly_solve_hg1}
        !           273: @findex odiff_poly_solve_hg1
        !           274: @table @t
        !           275: @item odiff_poly_solve_hg1(@var{a},@var{b},@var{c},@var{V})
        !           276: ::  $B%,%&%9$ND64v2?HyJ,J}Dx<0$NB?9`<02r$r5a$a$k(B.
        !           277: @end table
        !           278: @table @var
        !           279: @item return
        !           280: $B%j%9%H(B
        !           281: @item a, b, c
        !           282: $BM-M}<0(B
        !           283: @item V
        !           284: $B%j%9%H(B
        !           285: @end table
        !           286: @itemize @bullet
        !           287: @item  @code{odiff_poly_solve_hg1}$B$NNc(B.
        !           288: @end itemize
        !           289: @example
        !           290: [334] odiff_poly_solve_hg1(-3,-6,-5,[x]);
        !           291: [_1*x^6-2*_0*x^3+9/2*_0*x^2-18/5*_0*x+_0,[_0,_1]]
        !           292:
        !           293: [335] odiff_poly_solve_hg1(-3,-6,-7,[x]);
        !           294: [-4/7*_2*x^3+15/7*_2*x^2-18/7*_2*x+_2,[_2]]
        !           295: @end example
        !           296:
        !           297: @node odiff_poly_solve_appell4,,, Differential equations (library by Okutani)
        !           298: @subsection @code{odiff_poly_solve_appell4}
        !           299: @findex odiff_poly_solve_appell4
        !           300: @table @t
        !           301: @item odiff_poly_solve_appell4(@var{a},@var{b},@var{c1},@var{c2},@var{V})
        !           302: ::  F_4$B$,$_$?$9@~7?HyJ,J}Dx<07O$NB?9`<02r$r5a$a$k(B.
        !           303: @end table
        !           304: @table @var
        !           305: @item return
        !           306: $B%j%9%H(B
        !           307: @item a, b, c1, c2
        !           308: $BM-M}<0(B
        !           309: @item V
        !           310: $B%j%9%H(B
        !           311: @end table
        !           312: @itemize @bullet
        !           313: @item  @code{odiff_poly_solve_appell4}$B$NNc(B.
        !           314: @end itemize
        !           315: @example
        !           316: [299] odiff_poly_solve_appell4(-3,1,-1,-1,[x,y]);
        !           317: [-_26*x^3+(3*_26*y+_26)*x^2+3*_24*y^2*x-_24*y^3+_24*y^2,[_24,_26]]
        !           318:
        !           319: [300] odiff_poly_solve_appell4(-3,1,1,-1,[x,y]);
        !           320: [-3*_45*y^2*x-_45*y^3+_45*y^2,[_45]]
        !           321: @end example
        !           322:
        !           323: @node odiff_rat_solve,,, Differential equations (library by Okutani)
        !           324: @subsection @code{odiff_rat_solve}
        !           325: @findex odiff_rat_solve
        !           326: @table @t
        !           327: @item odiff_rat_solve(@var{LL},@var{Dn},@var{N},@var{V})
        !           328: ::  $BM?$($i$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.
        !           329: @end table
        !           330: @table @var
        !           331: @item return
        !           332: $B%j%9%H(B
        !           333: @item LL
        !           334: $B%j%9%H(B
        !           335: @item Dn
        !           336: $BM-M}<0(B
        !           337: @item N
        !           338: $B@0?t(B
        !           339: @item V
        !           340: $B%j%9%H(B
        !           341: @end table
        !           342: @itemize @bullet
        !           343: @item  @code{odiff_rat_solve}$B$NNc(B.
        !           344: @end itemize
        !           345: @example
        !           346: [333] odiff_rat_solve([[[x,[1]],[1,[0]]]],x,1,[x]);
        !           347: [(_8)/(x),[_8]]
        !           348:
        !           349: [361] odiff_rat_solve([x*(1-x)*dx^2+(1-3*x)*dx-1],1-x,2,[x]);
        !           350: [(_180)/(-x+1),[_180]]
        !           351:
        !           352: [350] D = odiff_op_appell4(0,0,3,0,[x,y])$
        !           353: [351] odiff_rat_solve(D,x^2,2,[x,y]);
        !           354: [(_118*x^2-_114*y*x+1/2*_114*y^2+_114*y)/(x^2),[_114,_118]]
        !           355: @end example