数学建模社区-数学中国
标题:
求方程的全部解
[打印本页]
作者:
forcal
时间:
2011-1-9 11:24
标题:
求方程的全部解
Forcal优化库FcOpt中新增函数fcopt::isolve，试图求解方程的全部解。正在测试修改，请大家多提意见。
7 Q) Y9 Z# F( R" c1 m2 _& ]
参考：
http://www.forcal.net/sysm/forcal9/fchtm/fcopt.htm
( |4 Z7 l) y! E' `; m
' {, B; G; t' i# _0 x/ e, g& S# s
例子1：求方程的全部解：f(x)=x^6-5*x^5+3*x^4+x^3-7*x^2+7*x-20;
$ i- i6 S' Q) X1 t5 @# f6 H
f(x)=x^6-5*x^5+3*x^4+x^3-7*x^2+7*x-20;
. H9 ?. A/ X+ p8 b( M3 ]# a' X
fcopt::isolve[HFor("f")];
[& U9 s T7 z/ O2 ~
复制代码
-1.402463030422577 3.552713678800501e-015
% Z) t9 e$ w, m$ V, b$ M4 v' t
4.333755446919994 -2.984279490192421e-013
3 S3 Y2 E! m% U+ P: Z
2.
# j7 W$ s8 P: v! |
7 {2 a: L2 J+ l/ m% E
说明：前面2行，每行中前一个数是解，后一个数是误差。最后的2说明有两个解。
+ {( E4 _; M- y
作者:
wgxzy_1015
时间:
2011-1-9 11:34
谢谢................
作者:
forcal
时间:
2011-1-9 11:35
例子2：求方程的全部解（当y为1时，求x的全部解）：f(x,y)=(x^2+y^2)^3-36*(x^2-y^2)^2;
/ a# _2 l1 Y- T, k. R' Q( Z
!using("fcopt");
4 |5 q* d; `4 S1 e! I1 m
f(x,y)=(x^2+y^2)^3-36*(x^2-y^2)^2;
) m- ?8 x% b8 G0 L
isolve[HFor("f"),optpara,1];
x( V* T- W' B+ \0 |: c# ]3 y- E
复制代码
-5.530393535267971 1. -3.637978807091713e-012
8 g6 N$ W. G* D% H7 G$ A
-1.32936186218296 1. -7.105427357601002e-015
6 T3 V1 t# h7 Z8 o( s8 t
-0.8047014256478491 1. -1.776356839400251e-015
8 u5 t. y& r( d7 N/ H
0.8047014256478491 1. -1.776356839400251e-015
8 u3 t0 \& x2 K7 T% u& T7 @0 n# I
1.32936186218296 1. -7.105427357601002e-015
/ a7 \# u% e, N( U4 U& x
5.530393535267971 1. -3.637978807091713e-012
) k, c" Q/ h/ r$ z2 G- p+ o
6.
) G* y# B' r; j4 N* h7 G F! ^# q
0 `& U$ F7 C6 |" B
作者:
forcal
时间:
2011-1-9 11:37
例子3：求方程的全部解（x取1.1，求y的全部解）：f(x,y)=(x^2+y^2)^3-36*(x^2-y^2)^2;
; C; m0 U3 u9 {, n- F: h0 a
!using("fcopt");
6 @. j t8 B$ i1 C
f(x,y)=(x^2+y^2)^3-36*(x^2-y^2)^2;
$ `) D/ N. a2 y, G
isolve[HFor("f"), optthis,1, optpara,1.1];
" m7 j& T5 [& R) T
复制代码
1.1 -5.413569621185505 0.
, P' G. G/ ~6 A' W/ M, Y* S! L! P
1.1 -1.52029233271966 0.
; D/ U" @3 {) P8 h8 a
1.1 -0.8671650244626143 8.881784197001252e-016
2 ~8 D! e4 `! z9 K8 v
1.1 0.8671650244626143 8.881784197001252e-016
" s4 U( {) w5 B8 s6 j
1.1 1.52029233271966 0.
9 a0 _ I _* ^' J& k
1.1 5.413569621185504 0.
% C3 _- D2 q9 v+ q; Q" M5 I
6.
+ |' Z+ j6 y+ @( B
作者:
forcal
时间:
2011-1-9 12:08
例子4：为隐函数绘图准备数据（x取1～10，y取1～10，z取1～10）：f(x,y,z)=(x+y+z)*(x*y+x*z+y*z)-10*x*y*z;
5 @8 j2 V/ W. g0 v
!using("fcopt");
% ?. G* X6 }- ?! B1 s
f(x,y,z)=(x+y+z)*(x*y+x*z+y*z)-10*x*y*z;
- d& N1 E3 ^) Y: l
init(:x,y,i)={
3 Y* b) d* M! x0 ^7 J
i=0,
# ~7 Q X& B7 Q4 I C0 m
x=1,while{x<=10,
& Y, p6 w' \9 ~$ R6 L* }, g; f: ~
y=1,while{y<=10,
, J# ?+ E- s: S8 y# U; B# e
i=i+isolve[HFor("f"), optrange,1,10, optthis,2, optpara,x,y],
" x0 o. M" z! a, b. k- M8 a9 \
y=y+0.5
* u4 @- \- X2 m
},
f+ D: l7 x4 Q0 Z+ e% i
x=x+0.5
8 \$ f3 \. D' K: O' M
},
% Z; Z" O; ^* B2 d9 Y2 n, i1 F
i
9 X2 U3 |$ q9 t7 ~' Y% a- x* }2 v
};
/ R! \- Q2 G V6 }
复制代码
1. 1. 2. 0.
) T* l* v V7 K- p
1. 1.5 2.226208734813002 0.
, y' W' W" x, A3 h& d
1. 2. 1. 0.
, v, q9 e' d- t7 a' p3 ^
1. 2. 1.999999999999999 0.
* H! t! G) X0 _0 D+ ]
1.5 1. 2.226208734813 0.
# i& l5 @ |) D: p" L% X1 g7 s" ]
1.5 1.5 3. 0.
/ ]9 N( ^! s$ l7 w$ m0 Z
1.5 2. 3.30716411545796 0.
9 H6 D4 N7 C5 {7 l( S$ Q
1.5 2.5 1.135767284302283 0.
+ L: h x& d$ f5 y( b' y
1.5 2.5 3.301732715697718 0.
1 _* J, ?: d' i
1.5 3. 1.499999999999999 0.
' C/ O: |+ {# Y( K5 N
1.5 3. 3.000000000000004 0.
5 Z, |! d' e+ N9 D) j) s
2. 1. 1. 0.
; F/ O- C2 ?# A; l# F
2. 1. 1.999999999999996 0.
9 F/ \4 w. r X
2. 1.5 3.30716411545796 0.
/ ], M4 ]; |' {: g/ {
2. 2. 1. 0.
D% ~! }' m$ q1 u. b
2. 2. 4.000000000000001 0.
1 ~% o4 H8 J+ e/ [; h6 l
2. 2.5 1.149218940641788 0.
/ `9 m R* o0 [7 m) C, R
2. 2.5 4.350781059358212 0.
( S& E2 G5 M# T; @6 t; r
2. 3. 1.347582530373998 0.
+ }/ b$ l9 l- u2 @% R9 A! F8 d" @9 m
2. 3. 4.452417469626003 0.
- \+ C. R/ {0 Q( q
2. 3.5 1.611932882193128 0.
7 J* e. B; J1 `1 Z# k& S) w
2. 3.5 4.342612572352325 0.
$ C5 u- p# }5 x2 R
2. 4. 1.999999999999999 0.
5 d7 O2 X5 v y) @/ H
2. 4. 3.999999999999999 0.
[6 m. O. g# q. v; B" a
2.5 1.5 1.135767284302283 0.
7 O3 P b( G; S: m4 V
2.5 1.5 3.301732715697717 0.
$ Q4 ^: ]. l* ~
2.5 2. 1.149218940641788 0.
7 l; O* _* C0 d
2.5 2. 4.350781059358212 0.
4 R `% {2 @6 `
2.5 2.5 1.25 0.
& i! Y" R1 J2 ?7 y
2.5 2.5 4.999999999999998 0.
9 v( Q+ a$ B- e5 N. M6 j
2.5 3. 1.39451558049041 0.
- I+ b" p0 U' k& I H; ?5 i
2.5 3. 5.378211692236864 5.684341886080802e-014
5 d/ W! R: R) M- R4 j; g6 [. j1 n9 o
2.5 3.5 1.577202478216426 0.
1 c5 t- g/ S( x% }, ~
2.5 3.5 5.547797521783575 0.
: t3 ` b! W5 @+ t% z4 f) L- r' ^
2.5 4. 1.804522914534426 0.
+ g0 k+ J+ t9 \+ Y! A o4 z
2.5 4. 5.541630931619419 0.
3 f" x4 g: |- {% e1 @; j: @% l
2.5 4.5 2.09541126457111 0.
. j6 W! o7 R$ ~ g. r5 e- ]! H
2.5 4.5 5.368874449714605 0.
7 o1 o5 \1 _; f" M
2.5 5. 2.5 0.
' D! E$ W. m# P+ P: E8 w
2.5 5. 4.999999999999998 0.
+ ~% A- M9 H/ Q( ?
2.5 5.5 3.292157134434847 0.
0 B, C( E1 ]0 ?: N" z/ j% q% H5 h; I
2.5 5.5 4.176592865565161 0.
W2 \; K' B4 a$ d; K! \
3. 1.5 1.499999999999999 0.
; N# B& B9 A k& E. K$ T
3. 1.5 3.000000000000004 0.
$ ]3 G! R2 \1 f. C/ p
3. 2. 1.347582530373997 0.
1 B0 Z4 O/ R) L* D2 m
3. 2. 4.452417469626003 0.
; P Y# O4 }8 r! R( N* p1 s& [4 j
3. 2.5 1.39451558049041 0.
* t8 y d( z" U5 g6 l& ~+ E
3. 2.5 5.378211692236861 -5.684341886080802e-014
" R' H/ j. o! {2 X! b
3. 3. 1.5 0.
3 Z; {7 Q, y- \* x6 t7 U
3. 3. 6.000000000000001 0.
* T6 A2 X! U4 o: V: o- i
3. 3.5 1.641371232518948 0.
6 {: X; S6 G& ^' m5 e- T% ^: _" F! w5 I
3. 3.5 6.397090305942587 0.
; B: H/ G$ @5 \* d" x$ f" g
3. 4. 1.814243197655509 -2.842170943040401e-014
0 m- f/ C f6 q) o) [$ u
3. 4. 6.614328230915922 0.
, `: G# D- ^0 y
3. 4.5 2.021373795560996 0.
{) K* m* A0 R+ y
3. 4.5 6.678626204439006 0.
1 h/ j+ m% p; J. E: r; h* B' W
3. 5. 2.271534568604568 0.
) Y' M# X: M7 q$ R8 |
3. 5. 6.603465431395431 0.
( x: S6 [0 `. |; B O
3. 5.5 2.583225948048685 0.
7 w% I! l# _# H& h1 Q. x0 O
3. 5.5 6.387362287245431 0.
0 i# l2 d6 h$ T& _( V: g
3. 6. 3. 0.
7 D3 ]3 ~. S6 \5 {6 E
3. 6. 6.000000000000004 0.
+ h' K3 B5 V: h- c
3. 6.5 3.692013773129524 0.
, e- Y% P# C' h2 i5 I
3. 6.5 5.281670437396789 0.
0 L( }6 \0 X$ f# s; W
3.5 2. 1.611932882193128 0.
) b" `0 Y! Z8 U1 K c0 ^
3.5 2. 4.342612572352325 0.
, I8 l7 m. c8 t5 _; W, }
3.5 2.5 1.577202478216427 0.
7 }4 k7 ~5 A) A( f+ W+ r
3.5 2.5 5.547797521783575 0.
- k' T3 s3 T9 d" ^9 {
3.5 3. 1.641371232518947 0.
2 i$ |5 Z B8 X2 C
3.5 3. 6.397090305942591 0.
+ L/ Y9 s) v2 l5 U- n# b- Y- c( a% Z
3.5 3.5 1.75 0.
$ m6 @( `( X0 [4 Q/ N( L+ [
3.5 3.5 7. 0.
# r4 N, g3 n0 o
3.5 4. 1.889112461544294 0.
2 ?4 x: b5 q. `( L
3.5 4. 7.410887538455708 0.
2 q2 [4 y1 K: k& }. @- q" k
3.5 4.5 2.055177184113076 0.
/ M# T4 G. s0 t. i$ w% ~+ B
3.5 4.5 7.663572815886926 0.
; _5 [: r& K# \7 N, E
3.5 5. 2.249335186315033 0.
' R8 G* s0 r: T% I2 V7 d9 P
3.5 5. 7.78007657839085 0.
0 d3 G: `! M3 A+ f9 O
3.5 5.5 2.476297487447864 0.
7 K/ W9 L8 }# r/ o
3.5 5.5 7.773702512552139 0.
( b- P. n6 f8 q- B# J. \. Q5 z3 U
3.5 6. 2.745300211529267 0.
, q- g) \: O& i8 E$ C4 [5 J
3.5 6. 7.649436630576002 0.
* F) Y' U# p/ p) e
3.5 6.5 3.073844239487252 0.
$ ], N- j ~2 |+ ?( y
3.5 6.5 7.401155760512754 0.
+ G, R8 k) c) p& J; C% I8 A2 B1 }
3.5 7. 3.5 0.
; L9 b' V5 {9 `, I
3.5 7. 7. 0.
, t$ K, U7 y5 P2 q/ I, v# `( S
3.5 7.5 4.146248634662254 0.
" n( |- W8 l4 H8 ~
3.5 7.5 6.331024092610477 0.
) e. I2 y) ]5 {1 q3 S3 n' J$ B
4. 2. 2.000000000000001 0.
# }" v/ c$ A- X* J
4. 2. 3.999999999999997 0.
5 ~3 Z" d8 u' R5 m! Y/ a3 q/ g
4. 2.5 1.804522914534426 0.
; I8 e' {/ L# ^! S
4. 2.5 5.541630931619421 0.
& g0 p) f% X* p7 ^9 V! U" y
4. 3. 1.814243197655509 0.
& A7 ~# { _9 y5 ~, t
4. 3. 6.614328230915922 0.
/ N* r8 _ N# e0 g" U9 o
4. 3.5 1.889112461544296 0.
% M; ^/ o8 v- L( p$ ^
4. 3.5 7.410887538455708 0.
' K& S. I# u; w% M! a8 {5 ^
4. 4. 2. 0.
J1 r" v' v I! g
4. 4. 8. 0.
* \; v2 g+ ?' s* J6 S
4. 4.5 2.137407852977751 0.
$ m/ f6 D, x. [6 j& v
4. 4.5 8.421415676434013 0.
% d. L+ G6 x4 |5 |
4. 5. 2.298437881283576 0.
& c3 C; [8 x+ v; G" J5 I$ X6 c* v2 e
4. 5. 8.701562118716424 0.
2 a* ]' L; o Q% F7 z5 g9 ^; @5 T
4. 5.5 2.483445700017514 0.
# s x8 d: e- z8 W: I. `! h% C' E
4. 5.5 8.858659563140384 0.
: N4 b# R1 Z- y1 t' p
4. 6. 2.695165060747996 0.
3 W5 J. Z: @5 r2 o
4. 6. 8.904834939252009 0.
3 h1 t& Q, i7 A" _$ C/ a" \
4. 6.5 2.938916502606828 0.
2 \7 O5 H; i9 _3 D8 N
4. 6.5 8.846797783107462 0.
9 K3 J/ H/ _% u6 P- ]4 K% Z
4. 7. 3.223865764386256 0.
$ z. x4 C/ y5 E! N* [8 m* ]" l: b
4. 7. 8.685225144704656 0.
8 G7 W- @1 |" `. B c$ p. K
4. 7.5 3.566387492405245 0.
* U: _' v/ {/ o2 T
4. 7.5 8.411873377159974 0.
* D, f3 m- ~7 e$ ^# [4 h3 q* ?# J9 B
4. 8. 4.000000000000002 0.
4 G0 Z: m* n$ z; M
4. 8. 7.999999999999995 0.
+ P9 W6 ]; C E$ L7 y: r1 u
4. 8.5 4.618832614156824 0.
1 u% P% _) H& g0 t4 T
4. 8.5 7.361167385843178 0.
% Z3 c+ d$ U i) \4 f8 H2 K* O: T2 I
4.5 2.5 2.095411264571111 0.
) z! J1 d% I W* G. W
4.5 2.5 5.368874449714603 0.
, N# f* M( i( Y
4.5 3. 2.021373795560996 0.
# q$ N& Z4 i9 ~9 R/ Y
4.5 3. 6.678626204439004 0.
+ a l7 t8 T7 _
4.5 3.5 2.055177184113076 0.
, p, h% v4 K4 |5 |' P
4.5 3.5 7.663572815886925 0.
1 o/ }0 s E! O2 H- F& V
4.5 4. 2.137407852977751 0.
& a F6 U& i3 y: X0 W5 U
4.5 4. 8.421415676434013 0.
- Q+ H/ G1 U# p) b! s4 b
4.5 4.5 2.25 0.
7 t# F; G& G; }- n" Q5 c
4.5 4.5 9. 0.
+ I( @6 H/ ~5 H# \% p
4.5 5. 2.386074153449669 0.
. {/ {0 M2 {# {. b4 Q4 t
4.5 5. 9.429715320234545 0.
+ _5 N1 j* @: d2 T5 Y2 ]# e/ Q' Q
4.5 5.5 2.543211996792689 0.
3 g- [. E( m9 y
4.5 5.5 9.731788003207315 0.
9 G2 e; q0 C! e
4.5 6. 2.721364796483262 0.
' q; I3 e8 u' j: ^6 z
4.5 6. 9.92149234637388 0.
6 [6 y' I. P+ C( e7 c2 B% ]' i) p
4.5 6.5 2.922185008548723 0.
8 y1 N5 Y; `! ]* X& I* ]
4.5 7. 3.149000780229209 0.
. I+ v8 ^- w' m3 f
4.5 7.5 3.407301852906852 0.
' b2 j8 a5 B3 }, j% R- `
4.5 7.5 9.905198147093154 0.
+ g8 c( r$ P5 @, g1 @1 @' L9 K
4.5 8. 3.705986018674346 0.
* R) w+ r+ ~: o; @- L
4.5 8. 9.714013981325651 0.
5 J, Y6 T6 X7 K# X
4.5 8.5 4.060312832145664 0.
4 a7 C. |( p/ t' s& J
4.5 8.5 9.420456398623564 0.
- h Q9 h( ?9 s$ [4 q2 T
4.5 9. 4.5 0.
0 x7 a4 q) v/ Y; m; ~& r9 ?- q# v
4.5 9. 9.000000000000005 0.
. o1 y% @4 w5 Q E% u0 S
4.5 9.5 5.100326474258905 0.
6 {- S4 B0 T0 e+ X
4.5 9.5 8.381816382883958 0.
& y% @+ n% Q/ C$ g# C S( `' c$ |
4.5 10. 6.402193416458818 0.
' c! p. j# `! j8 w" h+ g, F" _
4.5 10. 7.028841066299776 4.547473508864641e-013
5 F/ G3 X# m6 S, m/ ?1 K
5. 2.5 2.499999999999997 0.
4 r; q" D: w U5 o* Q" f- _! t
5. 2.5 4.999999999999998 0.
0 i- P& v) \/ A6 o
5. 3. 2.271534568604568 0.
( P s4 \5 \/ a! y: M% r! |" Y
5. 3. 6.603465431395431 0.
" y3 G+ i: m# x: Q1 Q
5. 3.5 2.249335186315031 0.
) c, z% [: r+ {6 Y3 {- c4 L7 p. J
5. 3.5 7.78007657839085 0.
5 x7 i2 M; v. O: I& _! e1 m' t
5. 4. 2.298437881283576 0.
7 v. E* C$ g1 e9 t# J, q, b
5. 4. 8.701562118716424 0.
; Y* \" U7 n( b2 v- A1 O! N. P
5. 4.5 2.386074153449668 0.
+ ^, c% X- X$ O! U
5. 4.5 9.429715320234545 0.
* H0 x* P9 J# @$ q
5. 5. 2.5 0.
- ~ q" G1 c, ?
5. 5. 9.999999999999993 0.
& h5 N+ u" e' e
5. 5.5 2.635001373375082 0.
5 f% O/ g8 `) C( m( h0 N5 D$ e
5. 6. 2.789031160980821 0.
' w: P- c P% m
5. 6.5 2.961827475384206 0.
: ^) m9 t4 A- n& F) k; r) H
5. 7. 3.154404956432853 0.
5 ]8 _$ b0 F: o/ G+ l
5. 7.5 3.368956325934996 0.
. Y( C5 e, z- P" R8 |0 [5 O
5. 8. 3.609045829068848 0.
' v9 Z* _% z0 N v" M
5. 8.5 3.880150804346176 0.
0 n3 t6 Y/ F7 Z$ p# f/ i
5. 9. 4.190822529142221 0.
" v* i# o& x. ^! V) v7 m6 X5 K
5. 9.5 4.555265557190405 0.
" Y* |2 t2 r7 g) ~: N4 z# F5 B
5. 10. 4.999999999999997 0.
- S: b' S# \' U! R* {5 y
5. 10. 10. 0.
% G% R8 f; \7 q x
5.5 2.5 3.292157134434847 0.
5 \- E7 p3 k9 @# ?( z1 S
5.5 2.5 4.176592865565167 0.
6 I) q# S" f4 Q, A! y& K$ \
5.5 3. 2.583225948048685 0.
& ^& [9 @" |8 E; U) b( u
5.5 3. 6.387362287245431 0.
4 C+ w4 d+ V2 Q; [7 Q5 i; v( z
5.5 3.5 2.476297487447864 0.
8 B! q9 e6 M4 D
5.5 3.5 7.773702512552133 0.
, R* f% i, o# W M
5.5 4. 2.483445700017513 0.
+ ^% a& r3 C* u% |9 {0 [
5.5 4. 8.858659563140384 0.
! A% A& z5 J3 a6 L! i* j3 [. H* m) J
5.5 4.5 2.543211996792689 0.
* }6 P' z0 _7 S, U# o2 |
5.5 4.5 9.731788003207313 0.
L( d, C& W- A
5.5 5. 2.635001373375081 0.
& c: K+ I, I g
5.5 5.5 2.749999999999999 0.
6 a0 r/ M: [+ _
5.5 6. 2.884119329429114 0.
3 c9 y1 H. h# `' g
5.5 6.5 3.035604845963815 0.
4 R( ]1 V( K6 H. g9 R
5.5 7. 3.204083523261024 0.
8 q6 v) q D' \* j1 A
5.5 7.5 3.390173520212255 0.
5 j/ h2 Z# s9 D" @
5.5 8. 3.595369279178611 0.
& Z4 d2 ^4 x9 l+ E7 J7 e
5.5 8.5 3.822111065390602 0.
5 i. g1 G* R$ t) S, j2 E
5.5 9. 4.074041860443781 0.
1 f6 D; F$ T* @4 r$ c3 h! _7 y
5.5 9.5 4.356541541407054 0.
0 Z1 x$ Y! h( W) {1 G6 |
5.5 10. 4.677786777828594 0.
. H9 B0 u3 d2 n" i
6. 3. 3. 0.
8 u) [( n8 q) r' B- n/ t3 x
6. 3. 5.999999999999999 0.
( `1 D3 y/ K3 e
6. 3.5 2.745300211529266 0.
8 a1 r) Y6 `/ \8 i
6. 3.5 7.649436630575996 0.
' b7 T% l* J8 z. A$ ?
6. 4. 2.695165060747994 0.
& U* l# t( t; Y: z+ V0 x: f. V
6. 4. 8.904834939252005 0.
) G% D2 R& b5 s+ I$ H$ w
6. 4.5 2.721364796483262 0.
4 c. Z+ m- g s4 M$ r
6. 4.5 9.92149234637388 0.
3 ]0 s& N, [0 z& [7 U' ?+ B% W
6. 5. 2.78903116098082 0.
L6 H' J' c8 l6 J# R Q
6. 5.5 2.884119329429112 0.
/ W+ F" Q* Z& c. ^0 s/ z( {
6. 6. 3. 0.
4 t! h! l1 P8 W: p
6. 6.5 3.133381054885423 0.
( K) k5 U- Q- }# n: ^6 B
6. 7. 3.282742465037893 0.
4 b4 S6 z* e4 \9 ^
6. 7.5 3.447656821925362 2.273736754432321e-013
! \) t6 Z7 `- e
6. 8. 3.628486395311015 0.
1 F* D: G1 e$ p% H5 q! ^0 B2 @( d
6. 8.5 3.826272163735232 0.
) o, {. d ]3 f6 U5 G6 b
6. 9. 4.042747591121993 0.
) q/ \1 y% g9 i
6. 9.5 4.280465505524228 0.
5 @9 [ i- `) J1 H* j/ ^& d
6. 10. 4.543069137209136 0.
; D$ Z% S E! C& g4 e
6.5 3. 3.692013773129525 0.
6 U1 b- g8 X; R0 B! {- P
6.5 3. 5.281670437396786 0.
- v5 W: e2 Q4 A& |
6.5 3.5 3.073844239487251 0.
/ g! ^6 I' F, d
6.5 3.5 7.401155760512746 0.
% w$ Y! h) w8 G8 o$ ~! w1 o1 p
6.5 4. 2.938916502606827 0.
& s6 v1 Z* M$ I
6.5 4. 8.846797783107464 0.
1 Y: C: u6 e' v. a
6.5 4.5 2.922185008548724 0.
4 t- e; n! ^: ^/ _$ v* ?% X
6.5 5. 2.961827475384206 0.
% a9 m1 x: ?6 R& {; d
6.5 5.5 3.035604845963813 0.
2 Y; K/ W1 A& ~/ Y! G' t7 |- m" B$ N
6.5 6. 3.133381054885422 0.
8 I4 _" v& N( M. i, m
6.5 6.5 3.25 0.
% \+ ^$ L# l: f/ b3 K
6.5 7. 3.382753896487015 0.
7 ` ~" n1 A6 z0 h8 L1 W
6.5 7.5 3.530313399868478 0.
8 r4 s/ K4 g9 Q- I
6.5 8. 3.692229149874506 0.
, _5 m* k! u3 a; R, U: {3 L1 {
6.5 8.5 3.868693727795107 0.
' Z3 e4 T6 A- T! n; P
6.5 9. 4.060441442861232 0.
; A( g! O/ P5 y9 [) Y
6.5 9.5 4.268736592110795 0.
, b" x! I% @8 {5 }- R
6.5 10. 4.495435882583067 0.
0 v* I' c: ?. P/ p J& B( M% j
7. 3.5 3.500000000000001 0.
7 }- \' R& F+ P: y6 J1 s6 B
7. 3.5 7. 0.
8 ^1 l7 Q- m0 @( [
7. 4. 3.223865764386255 0.
% K+ p3 g! ?4 q! @: U9 K2 y) [) x
7. 4. 8.685225144704656 0.
1 K" ]( ~, N( |7 E# C" f% x
7. 4.5 3.14900078022921 0.
# {2 l; s7 T: d) l/ |+ t- x4 ~
7. 5. 3.154404956432853 0.
. t4 Z6 U2 J1 a) M( T6 [
7. 5.5 3.204083523261021 0.
& {+ H; y. ]5 x) ? P
7. 6. 3.282742465037893 0.
& ~7 r3 S& K% t7 B
7. 6.5 3.382753896487015 0.
9 O3 X1 K, Z4 @& P& _
7. 7. 3.5 0.
) o. E2 Y& B5 }. L. E7 ^5 u1 G& H' D* ^
7. 7.5 3.632214429249618 0.
* Z% k) X: E4 U+ W& V7 v+ R, j/ l
7. 8. 3.778224923088592 0.
" ~, W8 H' F( L- [
7. 8.5 3.93757894317775 0.
0 s5 h/ j% _9 v' ]
7. 9. 4.110354368226149 0.
' W4 F( w5 p" ^" _: ?% x7 f4 A
7. 9.5 4.297071556823225 0.
5 @" l. v/ l) F% S8 s& _# F
7. 10. 4.498670372630065 0.
9 t! e9 M/ S$ v5 ^. g7 h
7.5 3.5 4.146248634662252 0.
" t j6 s8 I5 T* ]+ J: W
7.5 3.5 6.331024092610478 0.
" }* e4 T2 ~6 [: }4 V6 C
7.5 4. 3.566387492405242 0.
, M1 Q5 W3 o% Y! g, `9 B( q% k
7.5 4. 8.411873377159969 0.
/ k3 s3 T! @4 p8 \5 u
7.5 4.5 3.407301852906851 0.
2 i# z9 M6 c0 t+ X; s1 V
7.5 4.5 9.905198147093145 0.
- r7 T2 Q8 x! H$ u8 g- W
7.5 5. 3.368956325934993 0.
% F! F5 m1 t: p S' v& `
7.5 5.5 3.390173520212255 0.
8 H6 l6 {) E3 S3 S8 P" z1 w
7.5 6. 3.447656821925362 0.
& c3 t$ C. u8 W% Y+ s& j4 @
7.5 6.5 3.530313399868477 0.
6 W# L% Y+ D6 F
7.5 7. 3.632214429249618 0.
1 e& j$ f- k# ^- F) k7 t
7.5 7.5 3.750000000000003 0.
) P# O. }8 h$ w' w5 u6 }; N" z0 y. q
7.5 8. 3.881745401569135 0.
# A$ X) u/ J1 b, {- ]
7.5 8.5 4.026409271112575 0.
# K8 d9 `7 z5 r. C
7.5 9. 4.183546741471229 0.
K9 z0 q1 u6 V/ r5 W6 T
7.5 9.5 4.353157178625922 0.
: c$ S; X: z' q6 p, _
7.5 10. 4.535607994138771 0.
( M, [1 H; F9 c9 `9 v3 b$ P0 ^
8. 4. 4.000000000000002 0.
3 _7 c: j0 g: N! N' A8 f- S
8. 4. 8. 0.
. h" l6 d' b( H6 B2 L- o: \
8. 4.5 3.705986018674347 0.
9 o+ S; t* r1 O" y
8. 4.5 9.714013981325657 0.
- q. P; @" P' W' j% S
8. 5. 3.609045829068849 0.
' I+ U3 W' s# g' D" s g
8. 5.5 3.595369279178607 0.
/ w2 Z6 t/ u- s) s
8. 6. 3.628486395311016 0.
r9 f# g& y" P0 [
8. 6.5 3.692229149874504 0.
6 Q2 {" M" @9 E- E$ `* d0 k7 {
8. 7. 3.77822492308859 0.
9 z# m" a% B2 v( R
8. 7.5 3.881745401569135 0.
, {: h b7 ^/ d+ H7 o' {
8. 8. 4.000000000000003 0.
) K3 T3 f: {6 Z9 `+ @4 {* b
8. 8.5 4.131333821659408 0.
6 m) S1 e: ?4 d; @6 j P; b
8. 9. 4.274815705955503 0.
) Y% o5 m4 Q( W3 V
8. 9.5 4.430014593640446 0.
b) q1 Y% z# h' k3 a! y. p# K
8. 10. 4.596875762567152 0.
; O; i3 X$ y; ?0 I7 k! ?; H
8.5 4. 4.618832614156823 0.
. f5 E: k1 T! u" p
8.5 4. 7.361167385843172 0.
# E; {, O& v& _. [% n0 H( V0 n U
8.5 4.5 4.060312832145666 0.
# z! t6 G2 P- Z, s* a! R Z
8.5 4.5 9.420456398623564 0.
: E. r# `7 J4 a0 }* v
8.5 5. 3.880150804346178 0.
) O$ _. H# i/ }
8.5 5.5 3.822111065390603 0.
, n& t" ~$ _% q& j( G
8.5 6. 3.826272163735231 0.
1 ~7 B* d+ z9 T8 i' r2 R- G
8.5 6.5 3.868693727795108 0.
+ t2 g$ R6 k r) w( c/ P
8.5 7. 3.937578943177748 0.
' B0 Y0 P1 @# J& O; B5 l' ~3 m0 M
8.5 7.5 4.026409271112575 0.
- e7 C4 z3 F& E% ^
8.5 8. 4.13133382165941 0.
$ }- T0 i% H: y
8.5 8.5 4.25 0.
9 u* s- f. W$ y
8.5 9. 4.380969715903502 0.
" e/ G7 S5 C7 i f
8.5 9.5 4.523405444098199 0.
6 x- D ?; G; P. `4 k) x
8.5 10. 4.676893219133843 0.
" S0 X/ X1 c5 n
9. 4.5 4.499999999999997 0.
2 i2 t/ {' t. o# k5 O! u/ C% H9 l
9. 4.5 9.000000000000009 0.
: |2 Y# M4 Z3 r
9. 5. 4.190822529142222 0.
: T- g. @( y- `, a. P8 m- Y
9. 5.5 4.074041860443781 0.
7 a+ o! m9 Y1 y; V
9. 6. 4.042747591121993 0.
' n3 e2 ^. z7 q+ T6 g" h
9. 6.5 4.060441442861232 -4.547473508864641e-013
( c$ `9 ^$ i2 E; N& Z9 g# ?# Z
9. 7. 4.110354368226151 0.
. U, `# k n" {; ]# w
9. 7.5 4.183546741471229 0.
' z9 q8 O, W" m2 l" A2 e* c- E
9. 8. 4.274815705955503 0.
5 T/ w0 v6 f/ x; P+ |" @0 t6 f: p
9. 8.5 4.380969715903502 0.
2 W0 ]8 g g. Z8 m
9. 9. 4.5 0.
! W) c8 _+ I1 n# _
9. 9.5 4.630645298521483 0.
. J; P; f! J" V: g: s! P+ S
9. 10. 4.772148306899336 0.
# j: J4 G; c' c- }9 a& n' |3 e
9.5 4.5 5.100326474258897 0.
1 @8 r9 ?# x. o! Z A5 x; `
9.5 4.5 8.381816382883978 0.
; P8 W4 u( N6 _' @3 H
9.5 5. 4.555265557190406 0.
. W8 b) g2 O* T4 r+ f
9.5 5.5 4.356541541407055 0.
p9 ]4 v4 J# G5 E4 D9 k
9.5 6. 4.280465505524228 0.
0 N8 f8 }; W0 p" L) J
9.5 6.5 4.268736592110795 0.
! S8 o6 n: o2 X- w
9.5 7. 4.297071556823221 0.
- t1 z4 x" Y. _0 Z; d: e& G8 @
9.5 7.5 4.353157178625922 0.
0 I r- a. v4 d
9.5 8. 4.430014593640445 0.
' q' b% s" a* Y4 A8 o2 @
9.5 8.5 4.523405444098199 0.
' L) E! e7 t3 |, X& d
9.5 9. 4.630645298521484 0.
8 O; u6 s, r3 l+ j/ u
9.5 9.5 4.75 0.
, @& G9 F( C: e
9.5 10. 4.880354401607461 0.
2 n7 }4 a6 b0 O# a6 `
10. 4.5 6.402193416458861 0.
. Z0 x6 D$ r% g( ?5 x- d3 I) I
10. 4.5 7.028841066299777 4.547473508864641e-013
- t: ]6 s3 p( N5 z
10. 5. 4.999999999999997 0.
2 v. b$ P: Q4 ?: `/ e, m" l. H
10. 5. 10. 0.
2 i( Z2 h3 a& \" R' q5 q' u1 F
10. 5.5 4.67778677782859 0.
. f2 B3 u* a% f' p5 E, }
10. 6. 4.543069137209136 0.
* x# e- ]4 K# S B7 V" Z" c
10. 6.5 4.495435882583067 0.
4 G, V8 Q0 G& S" S: _; k: O' b
10. 7. 4.498670372630065 0.
- l# x" X4 V9 m
10. 7.5 4.535607994138771 0.
. W: g& Q' I u6 x
10. 8. 4.596875762567152 0.
& N |5 s. `) @4 w6 D
10. 8.5 4.676893219133843 0.
% U) e+ S1 e4 F* P! Z
10. 9. 4.772148306899336 0.
, e$ `: j0 R4 G5 t6 f: v
10. 9.5 4.880354401607461 0.
/ p* a3 F I9 p7 S3 i' P
10. 10. 5. 0.
3 z! r6 [) y/ q x
330.
! U5 e( w8 c. T2 K: m' V; C/ O/ X' g" Z
$ z A9 x- r9 p2 A
作者:
forcal
时间:
2011-1-11 06:30
isolve函数正在测试阶段，请大家赐题测试，以帮助改进。方程中可包含任意内容，包括积分、微分、微分方程等等。谢谢！
欢迎光临 数学建模社区-数学中国 (http://www.madio.net/)
Powered by Discuz! X2.5