Annotation of OpenXM/src/asir-contrib/packages/doc/Diff-ja.texi, Revision 1.3
1.3 ! takayama 1: @c $OpenXM: OpenXM/src/asir-contrib/packages/doc/Diff-ja.texi,v 1.2 2002/08/04 07:37:46 takayama Exp $
1.1 takayama 2: @node Differential equations (library by Okutani),,, Top
3: @chapter Differential equations (library by Okutani)
1.2 takayama 4: $B%U%!%$%k(B @file{gr}, @file{Matrix}, @file{Diff} $B$,I,MW$G$9(B.
1.3 ! takayama 5:
! 6: OpenXM/Risa/Asir $B$G$NMxMQ$K$"$?$C$F$O(B,
! 7: @example
! 8: load("Diff")$
! 9: @end example
! 10: $B$,;O$a$KI,MW(B.
! 11:
1.1 takayama 12:
13: Yukio Okutani $B;a$K$h$k(B Risa/Asir $B8@8l$G=q$+$l$?O"N)@~7AJPHyJ,J}Dx<0MQ(B
14: $B$N%i%$%V%i%j$G$9(B.
15: $B$9$Y$F$N4X?tL>$O(B odiff_ $B$G;O$^$j$^$9(B.
16:
17: @tex
18: $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.
19: $B%j%9%H$K$h$kI=8=$O<!$N$h$&$K$J$j$^$9(B.
20: $$ [ [f_{\alpha},[\alpha_{1},\ldots,\alpha_{n}]],\ldots ] $$
21: $B$3$l$O(B
22: $$ \sum_{\alpha}f_{\alpha}\partial^{\alpha} $$
23: $B$H$$$&0UL#$G$9(B. $B@~7?JPHyJ,J}Dx<07O(B
24: $$ (\sum_{\alpha^{(i)}}f_{\alpha^{(i)}}\partial^{\alpha^{(i)}})\bullet u = 0 \quad (i = 1,\ldots,s) $$
25: $B$J$I$N$h$&$KJ#?t$NHyJ,:nMQAG$rI=8=$9$k$H$-$OHyJ,:nMQAG$N%j%9%H$r;H$$$^$9(B.
26: $$ [ [ [f_{\alpha^{(1)}},[\alpha_{1}^{(1)},\ldots,\alpha_{n}^{(1)}]],\ldots ],\ldots,[ [f_{\alpha^{(s)}},[\alpha_{1}^{(s)},\ldots,\alpha_{n}^{(s)}]],\ldots ] ] $$
27: $BNc$($PHyJ,:nMQAG(B$x \partial_{x} + y \partial_{y} + 1$$B$N>l9g$O(B
28: $$ [ [x,[1,0]],[y,[0,1]],[1,[0,0]] ] $$
29: $B$H$J$j$^$9(B. $B$^$?HyJ,:nMQAG$N%j%9%H$G(B$x \partial_{x} + y \partial_{y} + 1, {\partial_{x}}^{2} + {\partial_{y}}^{2}$$B$rI=$9$H(B
30: $$ [ [ [x,[1,0]],[y,[0,1]],[1,[0,0]] ],[ [1,[2,0]],[1,[0,2]] ] ] $$
31: $B$H$J$j$^$9(B. $B$^$?$3$NI=8=K!$r;H$&$H$-$OJQ?t%j%9%H$r>o$K0U<1$7$F$$$kI,MW$,$"$j$^$9(B.
32: $B<!$KB?9`<0$K$h$kI=8=$K$D$$$F=R$Y$^$9(B. $BJQ?t(B$x$$B$KBP$9$kHyJ,$O(B$dx$$B$GI=8=$5$l$^$9(B.
33: $BNc$($P(B$x \partial_{x} + y \partial_{y} + 1$$B$K$D$$$F$O(B
34: $$ x*dx+y*dy+1 $$
35: $B$HI=8=$5$l$^$9(B.
36: @end tex
37: @menu
38: @c * odiff_op_hg1::
39: @c * odiff_op_appell1::
40: @c * odiff_op_appell2::
41: @c * odiff_op_appell3::
42: * odiff_op_appell4::
43: @c * odiff_op_selberg2::
44: @c * odiff_op_gkz::
45: * odiff_op_tosm1::
46: * odiff_op_toasir::
47: * odiff_op_fromasir::
48: * odiff_act::
49: @c * odiff_act_hg1::
50: @c * odiff_act_appell1::
51: @c * odiff_act_appell2::
52: @c * odiff_act_appell3::
53: * odiff_act_appell4::
54: @c * odiff_act_selberg2::
55: @c * odiff_act_gkz::
56: * odiff_poly_solve::
57: * odiff_poly_solve_hg1::
58: @c * odiff_poly_solve_appell1::
59: @c * odiff_poly_solve_appell2::
60: @c * odiff_poly_solve_appell3::
61: * odiff_poly_solve_appell4::
62: @c * odiff_poly_solve_selberg2::
63: @c * odiff_poly_solve_gkz::
64: * odiff_rat_solve::
65: @c * odiff_pseries_appell4::
66: @end menu
67:
68: @node odiff_op_appell4,,, Differential equations (library by Okutani)
69: @subsection @code{odiff_op_appell4}
70: @findex odiff_op_appell4
71: @table @t
72: @item odiff_op_appell4(@var{a},@var{b},@var{c1},@var{c2},@var{V})
73: :: appell $B$N(B F_4 $B$rNm2=$9$kHyJ,:nMQAG$r@8@.$7$^$9(B.
74: @end table
75: @table @var
76: @item return
77: $B%j%9%H(B
78: @item a, b, c1, c2
79: $BM-M}<0(B
80: @item V
81: $B%j%9%H(B
82: @end table
83: @itemize @bullet
84: @item @code{odiff_op_appell4}$B$NNc(B.
85: @end itemize
86: @example
87: [298] odiff_op_appell4(a,b,c1,c2,[x,y]);
88: [ [ [-x^2+x,[2,0]], [-2*y*x,[1,1]], [-y^2,[0,2]],
89: [(-a-b-1)*x+c1,[1,0]], [(-a-b-1)*y,[0,1]], [-b*a,[0,0]] ],
90: [ [-y^2+y,[0,2]], [-2*y*x,[1,1]], [-x^2,[2,0]],
91: [(-a-b-1)*y+c2,[0,1]], [(-a-b-1)*x,[1,0]], [-b*a,[0,0]] ] ]
92: @end example
93:
94: @node odiff_op_tosm1,,, Differential equations (library by Okutani)
95: @subsection @code{odiff_op_tosm1}
96: @findex odiff_op_tosm1
97: @table @t
98: @item odiff_op_tosm1(@var{LL},@var{V})
99: :: $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$r(B sm1 $B7A<0$KJQ49$7$^$9(B.
100: @end table
101: @table @var
102: @item return
103: $B%j%9%H(B
104: @item LL
105: $B%j%9%H(B
106: @item V
107: $B%j%9%H(B
108: @end table
109: @itemize @bullet
110: @item $BHyJ,:nMQAG$N78?t$O@0?tB?9`<0$KJQ49$5$l$^$9(B.
111: @item @code{odiff_op_tosm1}$B$NNc(B
112: @end itemize
113: @example
114: [299] odiff_op_tosm1([[[x,[2,0]],[-1,[0,0]]],
115: [[y,[0,2]],[-1,[0,0]]]],[x,y]);
116: [ + ( + (1) x) dx^2 + ( + (-1)), + ( + (1) y) dy^2 + ( + (-1))]
117:
118: [300] odiff_op_tosm1([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],
119: [[1,[2,0]],[1,[0,2]]]],[x,y]);
120: [ + ( + (1) x) dx + ( + (1) y) dy + ( + (1)), + ( + (1)) dx^2 + ( + (1)) dy^2]
121:
122: [301] odiff_op_tosm1([[[1/2,[1,0]],[1,[0,0]]],
123: [[1/3,[0,1]],[1/4,[0,0]]]],[x,y]);
124: [ + ( + (6)) dx + ( + (12)), + ( + (4)) dy + ( + (3))]
125:
126: [302] odiff_op_tosm1([[[1/2*x,[1,0]],[1,[0,0]]],
127: [[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
128: [ + ( + (6) x) dx + ( + (12)), + ( + (4) y) dy + ( + (3))]
129: @end example
130:
131: @node odiff_op_toasir,,, Differential equations (library by Okutani)
132: @subsection @code{odiff_op_toasir}
133: @findex odiff_op_toasir
134: @table @t
135: @item odiff_op_toasir(@var{LL},@var{V})
136: :: $B%j%9%H7A<0$NHyJ,:nMQAG%j%9%H(B @var{LL} $B$r(B @code{asir} $B$NB?9`<0$KJQ49$7$^$9(B.
137: @end table
138: @table @var
139: @item return
140: $B%j%9%H(B
141: @item LL
142: $B%j%9%H(B
143: @item V
144: $B%j%9%H(B
145: @end table
146: @itemize @bullet
147: @item @code{odiff_op_toasir}$B$NNc(B
148: @end itemize
149: @example
150: [303] odiff_op_toasir([[[1/2*x,[1,0]],[1,[0,0]]],
151: [[1/3*y,[0,1]],[1/4,[0,0]]]],[x,y]);
152: [1/2*x*dx+1,1/3*y*dy+1/4]
153:
154: [304] odiff_op_toasir([[[x,[1,0]],[y,[0,1]],[1,[0,0]]],
155: [[1,[2,0]],[1,[0,2]]]],[x,y]);
156: [x*dx+y*dy+1,dx^2+dy^2]
157: @end example
158:
159: @node odiff_op_fromasir,,, Differential equations (library by Okutani)
160: @subsection @code{odiff_op_fromasir}
161: @findex odiff_op_fromasir
162: @table @t
163: @item odiff_op_fromasir(@var{D_list},@var{V})
164: :: @code{asir} $B$NB?9`<0$+$i%j%9%H7A<0$NHyJ,:nMQAG%j%9%H$KJQ49$7$^$9(B.
165: @end table
166: @table @var
167: @item return
168: $B%j%9%H(B
169: @item D_list
170: $B%j%9%H(B
171: @item V
172: $B%j%9%H(B
173: @end table
174: @itemize @bullet
175: @item @code{odiff_op_fromasir}$B$NNc(B
176: @end itemize
177: @example
178: [305] odiff_op_fromasir([1/2*x*dx+1,1/3*y*dy+1/4],[x,y]);
179: [[[1/2*x,[1,0]],[1,[0,0]]],[[1/3*y,[0,1]],[1/4,[0,0]]]]
180:
181: [306] odiff_op_fromasir([x*dx+y*dy+1,dx^2+dy^2],[x,y]);
182: [[[x,[1,0]],[y,[0,1]],[1,[0,0]]],[[1,[2,0]],[1,[0,2]]]]
183: @end example
184:
185: @node odiff_act,,, Differential equations (library by Okutani)
186: @subsection @code{odiff_act}
187: @findex odiff_act
188: @table @t
189: @item odiff_act(@var{L},@var{F},@var{V})
190: :: $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.
191: @end table
192: @table @var
193: @item return
194: $BM-M}<0(B
195: @item L
196: $B%j%9%H(B or $BB?9`<0(B
197: @item F
198: $BM-M}<0(B
199: @item V
200: $B%j%9%H(B
201: @end table
202: @itemize @bullet
203: @item @code{odiff_act}$B$NNc(B
204: @end itemize
205: @example
206: [302] odiff_act([[1,[2]]],x^3+x^2+x+1,[x]);
207: 6*x+2
208:
209: [303] odiff_act([[1,[1,0]],[1,[0,1]]],x^2+y^2,[x,y]);
210: 2*x+2*y
211:
212: [349] odiff_act(x*dx+y*dy, x^2+x*y+y^2, [x,y]);
213: 2*x^2+2*y*x+2*y^2
214: @end example
215:
216: @node odiff_act_appell4,,, Differential equations (library by Okutani)
217: @subsection @code{odiff_act_appell4}
218: @findex odiff_act_appell4
219: @table @t
220: @item odiff_act_appell4(@var{a},@var{b},@var{c1},@var{c2},@var{F},@var{V})
221: :: $BHyJ,:nMQAG(B @code{odiff_op_appell4} $B$rM-M}<0(B @var{F} $B$K:nMQ$5$;$k(B.
222: @end table
223: @table @var
224: @item return
225: $B%j%9%H(B
226: @item a, b, c1, c2
227: $BM-M}<0(B
228: @item F
229: $BM-M}<0(B
230: @item V
231: $B%j%9%H(B
232: @end table
233: @itemize @bullet
234: @item @code{odiff_act_appell4}$B$NNc(B
235: @end itemize
236: @example
237: [303] odiff_act_appell4(1,0,1,1,x^2+y^2,[x,y]);
238: [-6*x^2+4*x-6*y^2,-6*x^2-6*y^2+4*y]
239:
240: [304] odiff_act_appell4(0,0,1,1,x^2+y^2,[x,y]);
241: [-4*x^2+4*x-4*y^2,-4*x^2-4*y^2+4*y]
242:
243: [305] odiff_act_appell4(-2,-2,-1,-1,x^2+y^2,[x,y]);
244: [0,0]
245: @end example
246:
247: @node odiff_poly_solve,,, Differential equations (library by Okutani)
248: @subsection @code{odiff_poly_solve}
249: @findex odiff_poly_solve
250: @table @t
251: @item odiff_poly_solve(@var{LL},@var{N},@var{V})
252: :: $BM?$($i$l$?@~7?HyJ,J}Dx<07O$N(B @var{N} $B<!0J2<$NB?9`<02r$r5a$a$k(B.
253: @end table
254: @table @var
255: @item return
256: $B%j%9%H(B
257: @item LL
258: $B%j%9%H(B
259: @item N
260: $B@0?t(B
261: @item V
262: $B%j%9%H(B
263: @end table
264: @itemize @bullet
265: @item @code{odiff_poly_solve}$B$NNc(B.
266: @end itemize
267: @example
268: [297] odiff_poly_solve([[[x,[1,0]],[-1,[0,0]]],[[y,[0,1]],[-1,[0,0]]]],5,[x,y]);
269: [_4*y*x,[_4]]
270:
271: [298] odiff_poly_solve([[[x,[1,0]],[-2,[0,0]]],[[y,[0,1]],[-2,[0,0]]]],5,[x,y]);
272: [_33*y^2*x^2,[_33]]
273:
274: [356] odiff_poly_solve([x*dx+y*dy-3,dx+dy],4,[x,y]);
275: [-_126*x^3+3*_126*y*x^2-3*_126*y^2*x+_126*y^3,[_126]]
276: @end example
277:
278: @node odiff_poly_solve_hg1,,, Differential equations (library by Okutani)
279: @subsection @code{odiff_poly_solve_hg1}
280: @findex odiff_poly_solve_hg1
281: @table @t
282: @item odiff_poly_solve_hg1(@var{a},@var{b},@var{c},@var{V})
283: :: $B%,%&%9$ND64v2?HyJ,J}Dx<0$NB?9`<02r$r5a$a$k(B.
284: @end table
285: @table @var
286: @item return
287: $B%j%9%H(B
288: @item a, b, c
289: $BM-M}<0(B
290: @item V
291: $B%j%9%H(B
292: @end table
293: @itemize @bullet
294: @item @code{odiff_poly_solve_hg1}$B$NNc(B.
295: @end itemize
296: @example
297: [334] odiff_poly_solve_hg1(-3,-6,-5,[x]);
298: [_1*x^6-2*_0*x^3+9/2*_0*x^2-18/5*_0*x+_0,[_0,_1]]
299:
300: [335] odiff_poly_solve_hg1(-3,-6,-7,[x]);
301: [-4/7*_2*x^3+15/7*_2*x^2-18/7*_2*x+_2,[_2]]
302: @end example
303:
304: @node odiff_poly_solve_appell4,,, Differential equations (library by Okutani)
305: @subsection @code{odiff_poly_solve_appell4}
306: @findex odiff_poly_solve_appell4
307: @table @t
308: @item odiff_poly_solve_appell4(@var{a},@var{b},@var{c1},@var{c2},@var{V})
309: :: F_4$B$,$_$?$9@~7?HyJ,J}Dx<07O$NB?9`<02r$r5a$a$k(B.
310: @end table
311: @table @var
312: @item return
313: $B%j%9%H(B
314: @item a, b, c1, c2
315: $BM-M}<0(B
316: @item V
317: $B%j%9%H(B
318: @end table
319: @itemize @bullet
320: @item @code{odiff_poly_solve_appell4}$B$NNc(B.
321: @end itemize
322: @example
323: [299] odiff_poly_solve_appell4(-3,1,-1,-1,[x,y]);
324: [-_26*x^3+(3*_26*y+_26)*x^2+3*_24*y^2*x-_24*y^3+_24*y^2,[_24,_26]]
325:
326: [300] odiff_poly_solve_appell4(-3,1,1,-1,[x,y]);
327: [-3*_45*y^2*x-_45*y^3+_45*y^2,[_45]]
328: @end example
329:
330: @node odiff_rat_solve,,, Differential equations (library by Okutani)
331: @subsection @code{odiff_rat_solve}
332: @findex odiff_rat_solve
333: @table @t
334: @item odiff_rat_solve(@var{LL},@var{Dn},@var{N},@var{V})
335: :: $BM?$($i$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.
336: @end table
337: @table @var
338: @item return
339: $B%j%9%H(B
340: @item LL
341: $B%j%9%H(B
342: @item Dn
343: $BM-M}<0(B
344: @item N
345: $B@0?t(B
346: @item V
347: $B%j%9%H(B
348: @end table
349: @itemize @bullet
350: @item @code{odiff_rat_solve}$B$NNc(B.
351: @end itemize
352: @example
353: [333] odiff_rat_solve([[[x,[1]],[1,[0]]]],x,1,[x]);
354: [(_8)/(x),[_8]]
355:
356: [361] odiff_rat_solve([x*(1-x)*dx^2+(1-3*x)*dx-1],1-x,2,[x]);
357: [(_180)/(-x+1),[_180]]
358:
359: [350] D = odiff_op_appell4(0,0,3,0,[x,y])$
360: [351] odiff_rat_solve(D,x^2,2,[x,y]);
361: [(_118*x^2-_114*y*x+1/2*_114*y^2+_114*y)/(x^2),[_114,_118]]
362: @end example
FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>
![[BACK]](/icons/cvsweb/back.gif){kind=icon}
Return to Diff-ja.texi CVS log ![[TXT]](/icons/cvsweb/text.gif){kind=icon}
![[DIR]](/icons/cvsweb/dir.gif){kind=icon}
Up to [local] / OpenXM / src / asir-contrib / packages / doc