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 e$ e8 }4 x1 f8 d
参考：
http://www.forcal.net/sysm/forcal9/fchtm/fcopt.htm
4 K! E6 X6 C: K; R& x
- L! J8 c+ l+ U4 f
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;
3 F" H" m$ q1 k) o- g' p+ w
f(x)=x^6-5*x^5+3*x^4+x^3-7*x^2+7*x-20;
8 G1 o7 o2 t* x! z* b' E! ~& A
fcopt::isolve[HFor("f")];
3 Z. J& b# `' U% }, p0 R' j( F+ e- `
复制代码
-1.402463030422577 3.552713678800501e-015
8 N" {3 C/ T! J
4.333755446919994 -2.984279490192421e-013
( t* m, Z* i0 I" I
2.
/ m* V( S4 S7 {- v/ ^9 o
" A3 ]; r( W o
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。
! {) j- Z# X8 M% E
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;
! J/ A9 o' H1 G* ?& w
!using("fcopt");
' o2 L |7 r3 X% D8 Y0 M
f(x,y)=(x^2+y^2)^3-36*(x^2-y^2)^2;
% N* o) |8 M1 {+ f1 Z
isolve[HFor("f"),optpara,1];
1 z6 X5 n! `7 f( A! v% @
复制代码
-5.530393535267971 1. -3.637978807091713e-012
; }- g- @# m, P% T, F* |
-1.32936186218296 1. -7.105427357601002e-015
. g* e" b$ k2 [' F2 j& c. i; a
-0.8047014256478491 1. -1.776356839400251e-015
6 {1 `$ ^8 W! f- i
0.8047014256478491 1. -1.776356839400251e-015
2 Z6 R- l6 v& |2 A; M% O ^% q" @3 g" A
1.32936186218296 1. -7.105427357601002e-015
0 U0 D" Q; S& [$ H4 ^% Q. k
5.530393535267971 1. -3.637978807091713e-012
+ E: _: K% i1 A6 r3 r$ P
6.
: C: v) e. I9 g: e4 l
1 H/ _. Z! w( V [: M: r4 N7 v
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;
% P/ d# |6 {0 R& j; k
!using("fcopt");
5 v3 I' ^$ [% f3 k3 i. }* D3 {8 m
f(x,y)=(x^2+y^2)^3-36*(x^2-y^2)^2;
0 l9 Q8 }+ a/ K3 U5 Y: c
isolve[HFor("f"), optthis,1, optpara,1.1];
& l) G4 D& P# o3 K6 @; P
复制代码
1.1 -5.413569621185505 0.
! r# h5 c* m' Y( _" l' W% s' Z
1.1 -1.52029233271966 0.
% p( m: _, h G
1.1 -0.8671650244626143 8.881784197001252e-016
. h- r6 ~1 d: [8 M! ?
1.1 0.8671650244626143 8.881784197001252e-016
# `2 w- b" _; u+ P6 u8 q0 t7 P
1.1 1.52029233271966 0.
+ }/ d, P. M2 Y. K# }
1.1 5.413569621185504 0.
" e: f& C% S$ h6 k5 ]% x+ a
6.
5 y- B1 x- p' P4 ?
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;
# e7 D8 y/ ?* S' e
!using("fcopt");
* p6 a/ @* F+ @
f(x,y,z)=(x+y+z)*(x*y+x*z+y*z)-10*x*y*z;
5 o6 ~2 y+ b6 `3 _, B4 w9 J
init(:x,y,i)={
. \: f' A& m) ]1 Y# q8 |: x+ q
i=0,
1 J2 G0 a. m, |( U
x=1,while{x<=10,
* D6 Z0 x u4 L) q' f
y=1,while{y<=10,
8 q) p2 e; ]( }
i=i+isolve[HFor("f"), optrange,1,10, optthis,2, optpara,x,y],
9 ~0 y3 Q: R: [; f$ }
y=y+0.5
% H! P7 f% ?' A. L5 {; l, z
},
" V2 F' P8 |) u) o, ]1 b0 j, Q
x=x+0.5
0 G# v5 } j O- W
},
, l8 c$ m7 K; V* a
i
) G2 x5 H9 _' p2 C' l5 k1 t( Z$ c
};
9 |7 f S f, r
复制代码
1. 1. 2. 0.
. N6 f4 _1 W0 Q) {1 n1 {& d1 f( [
1. 1.5 2.226208734813002 0.
' `8 |4 E( ?3 M3 Z3 `9 o1 B
1. 2. 1. 0.
, d% [6 M4 g4 x! G
1. 2. 1.999999999999999 0.
8 Q' M3 X7 ]( f: c
1.5 1. 2.226208734813 0.
" l8 S) U" {5 F& @; [7 P4 a
1.5 1.5 3. 0.
7 b" T8 ~: W5 |0 h! C! U
1.5 2. 3.30716411545796 0.
2 I( B. i! [- U0 T
1.5 2.5 1.135767284302283 0.
% I4 g9 K. l0 q, b4 J; m
1.5 2.5 3.301732715697718 0.
! N( t. T' I& v* C
1.5 3. 1.499999999999999 0.
9 x- ~3 b5 d% `' A5 Z3 f
1.5 3. 3.000000000000004 0.
! |5 e' P" D" u5 @) {
2. 1. 1. 0.
% ~7 @6 A$ ?; J. a& ?, Q+ U% C
2. 1. 1.999999999999996 0.
. ~% w* O! A0 s5 {
2. 1.5 3.30716411545796 0.
/ B" J+ O( U; c: c4 Z
2. 2. 1. 0.
7 v0 C9 q) _+ g$ ?, j6 M
2. 2. 4.000000000000001 0.
, \9 f _5 U7 c' ~2 \
2. 2.5 1.149218940641788 0.
; A d, R, R" `7 P- G5 I; @
2. 2.5 4.350781059358212 0.
( N# L" {' a/ H
2. 3. 1.347582530373998 0.
9 H! x+ v2 K) m( ~' S- c0 m7 M/ k
2. 3. 4.452417469626003 0.
! Z: M( v6 }1 O! W* C6 `# `
2. 3.5 1.611932882193128 0.
; C5 Z9 ?* @- C0 t; {# l l; @
2. 3.5 4.342612572352325 0.
' P1 y6 \: t8 C% W1 a6 M" R
2. 4. 1.999999999999999 0.
( l8 e$ ~/ ~+ ]# z
2. 4. 3.999999999999999 0.
) i: l" j2 w& F e
2.5 1.5 1.135767284302283 0.
$ d0 _$ S0 F! G- z
2.5 1.5 3.301732715697717 0.
$ m: V# J% D3 B- N7 G4 J3 [9 }
2.5 2. 1.149218940641788 0.
1 b" {) e8 v& U% A* N X$ q* d* u
2.5 2. 4.350781059358212 0.
8 f2 y% y5 n, l
2.5 2.5 1.25 0.
4 X/ |! C) e5 u; s! f! G
2.5 2.5 4.999999999999998 0.
/ a& s4 r: z6 w% A K
2.5 3. 1.39451558049041 0.
. a8 o. d* k7 q. w- T% R0 R
2.5 3. 5.378211692236864 5.684341886080802e-014
2 z. o; _: ^2 }9 A" P* M
2.5 3.5 1.577202478216426 0.
# W6 N6 R& i |5 \ B: e2 R* a
2.5 3.5 5.547797521783575 0.
8 m7 q: s5 I% i5 h% g* Z" N& S
2.5 4. 1.804522914534426 0.
0 \8 w* y3 v. D4 {4 ]
2.5 4. 5.541630931619419 0.
- P! p7 g& Y9 F6 k& E- l, p/ X
2.5 4.5 2.09541126457111 0.
2 }; x0 d% N7 O0 `& O& G* h" C* M
2.5 4.5 5.368874449714605 0.
& q: F2 |! \$ |0 x/ J
2.5 5. 2.5 0.
5 F: `( {& S0 m9 K4 e( ^0 ?2 b
2.5 5. 4.999999999999998 0.
4 U5 M: g4 k( }# K) |$ G
2.5 5.5 3.292157134434847 0.
6 b, x* c% ^, s
2.5 5.5 4.176592865565161 0.
, F& g/ T9 L ~! \- {3 S
3. 1.5 1.499999999999999 0.
5 R( S! `' ?( n- M# u% a& R1 D) }
3. 1.5 3.000000000000004 0.
$ R' B3 i( c" L* d) ~
3. 2. 1.347582530373997 0.
6 v2 H$ i- F" [- ?% E
3. 2. 4.452417469626003 0.
2 V8 N. g8 f. s2 e: [
3. 2.5 1.39451558049041 0.
3 a- [# A' ^, p \5 ^1 }
3. 2.5 5.378211692236861 -5.684341886080802e-014
- i+ w i1 u' F6 D
3. 3. 1.5 0.
# p& ]; ~- t) | q2 F
3. 3. 6.000000000000001 0.
/ M$ ]- {4 G3 m- U3 u4 g! e
3. 3.5 1.641371232518948 0.
1 ~& J5 H: j2 \1 B" U7 |/ b
3. 3.5 6.397090305942587 0.
6 y0 \5 b# x+ f' ?
3. 4. 1.814243197655509 -2.842170943040401e-014
' w6 w; v9 v9 ]5 E( p) M
3. 4. 6.614328230915922 0.
0 B1 K. K6 n e( i# \6 q4 F
3. 4.5 2.021373795560996 0.
+ r$ H: b) c% V% `; N$ j
3. 4.5 6.678626204439006 0.
' M: I' l1 I) v3 G7 K2 W' {+ P6 B
3. 5. 2.271534568604568 0.
7 q* Y9 |6 J$ B" [) ` W
3. 5. 6.603465431395431 0.
. x3 J1 C# F+ [, a, m% z
3. 5.5 2.583225948048685 0.
8 ]2 t. `% |6 t2 h1 |. x! S" I
3. 5.5 6.387362287245431 0.
9 J: }$ S, F& w& m) D: T
3. 6. 3. 0.
7 t( T ]" ]# ^
3. 6. 6.000000000000004 0.
5 S& p$ m4 W. Q, J9 z' f
3. 6.5 3.692013773129524 0.
0 I) E* C- W. o. L. |
3. 6.5 5.281670437396789 0.
6 V' V' V/ U- G* t6 w9 V( Q+ @
3.5 2. 1.611932882193128 0.
" G$ }4 b) z2 A0 }( o7 K
3.5 2. 4.342612572352325 0.
' E. I/ v! d \4 w" a
3.5 2.5 1.577202478216427 0.
/ Q9 ]3 M& ?4 G' F( F5 J6 A
3.5 2.5 5.547797521783575 0.
; X( V! y0 N' h5 ?% a
3.5 3. 1.641371232518947 0.
4 D* Q# M+ k; m9 G, _
3.5 3. 6.397090305942591 0.
& e4 N# g$ L6 l) l, i4 { m
3.5 3.5 1.75 0.
( J4 ?1 M& K. ?
3.5 3.5 7. 0.
5 D- I8 F4 A8 {0 O, O
3.5 4. 1.889112461544294 0.
; r- l& S5 A8 R
3.5 4. 7.410887538455708 0.
: Y2 U3 f+ n4 S
3.5 4.5 2.055177184113076 0.
) u/ R2 D A: g3 U8 x5 v
3.5 4.5 7.663572815886926 0.
- r! Y( @' x: s' k, K, `
3.5 5. 2.249335186315033 0.
; K( y0 B2 a3 T: A
3.5 5. 7.78007657839085 0.
; H7 u4 v7 g1 U+ @+ t: L; s/ `5 W
3.5 5.5 2.476297487447864 0.
% V4 w" U7 Z6 I0 Q: {) U: }
3.5 5.5 7.773702512552139 0.
+ ?; Y+ |% Q# D% I, E# D6 @! @" e& D" g
3.5 6. 2.745300211529267 0.
" e7 P* O1 y6 w0 F- W7 {/ A6 j4 o; {
3.5 6. 7.649436630576002 0.
7 I7 X* e! b& V, ]( Y: y' k
3.5 6.5 3.073844239487252 0.
; g. {8 K) Q, Z2 L N# H% u5 @
3.5 6.5 7.401155760512754 0.
h9 g" U2 d9 x0 ?! {2 a7 M
3.5 7. 3.5 0.
2 ]' o% d& @% H5 }" [0 ~# S
3.5 7. 7. 0.
6 T2 z# `2 t3 H
3.5 7.5 4.146248634662254 0.
$ R; f. a! p3 o( g# O# K
3.5 7.5 6.331024092610477 0.
" I5 K# x& C# ^4 H- h7 E1 f% B
4. 2. 2.000000000000001 0.
7 r' R# Q; S( |6 J% a
4. 2. 3.999999999999997 0.
2 Q# h2 O; ~) [- ~4 }
4. 2.5 1.804522914534426 0.
7 B( o6 J6 O* E$ N7 Q" I
4. 2.5 5.541630931619421 0.
, w% h; v7 s9 n7 b( n* J
4. 3. 1.814243197655509 0.
7 p/ b2 F; Y# x8 h1 o1 Y
4. 3. 6.614328230915922 0.
+ {9 U( K! D" Y6 U! i
4. 3.5 1.889112461544296 0.
, _* f; X( a$ B/ u2 X
4. 3.5 7.410887538455708 0.
]0 d+ ~/ f) ~7 g( c: q
4. 4. 2. 0.
$ v2 u* \& s$ `1 d9 J+ y
4. 4. 8. 0.
3 b/ H8 q1 f& {
4. 4.5 2.137407852977751 0.
0 _3 g' b" U6 o9 E) E* G$ c. }- _
4. 4.5 8.421415676434013 0.
, i# B! Q0 a% V
4. 5. 2.298437881283576 0.
% [4 S3 N J! M7 \
4. 5. 8.701562118716424 0.
5 `& z0 d7 r7 i* v! A
4. 5.5 2.483445700017514 0.
& A' Q- v/ A; z
4. 5.5 8.858659563140384 0.
/ F c a& T: _: N6 n* V
4. 6. 2.695165060747996 0.
, J9 y V$ O7 z4 H, l
4. 6. 8.904834939252009 0.
) {2 |/ h* O$ R
4. 6.5 2.938916502606828 0.
6 h) ]. T5 o2 i1 n- s; P- o
4. 6.5 8.846797783107462 0.
% e. `- ?) U+ i6 V! v
4. 7. 3.223865764386256 0.
: @, S$ S& B# }2 G# X
4. 7. 8.685225144704656 0.
% D* x- s) ^% s
4. 7.5 3.566387492405245 0.
+ }5 c0 j4 H; B% w. T
4. 7.5 8.411873377159974 0.
, _0 n, c' Z. T, A) I& z, f
4. 8. 4.000000000000002 0.
% ?& J; b: N% U4 |8 E
4. 8. 7.999999999999995 0.
, o1 [4 g3 r1 N: j, H- ? L/ B+ ~
4. 8.5 4.618832614156824 0.
8 Y0 O/ L6 F2 o N8 O. r* ~8 s( z, P
4. 8.5 7.361167385843178 0.
: p! v! }, H+ I
4.5 2.5 2.095411264571111 0.
& p3 P, i6 }/ N7 [. F* k h+ }
4.5 2.5 5.368874449714603 0.
( P- x0 y, T4 l4 P4 V! Z) x
4.5 3. 2.021373795560996 0.
+ e* B) ?# y' p) H: y7 c
4.5 3. 6.678626204439004 0.
/ c. K. u0 G8 x2 S" Q4 q
4.5 3.5 2.055177184113076 0.
9 w7 c% H# o' M# `4 X7 C
4.5 3.5 7.663572815886925 0.
- d" l. f* @( Y* p/ d+ Z7 T& Q
4.5 4. 2.137407852977751 0.
9 }: Q0 t$ R! G( q: j
4.5 4. 8.421415676434013 0.
+ U, ~" D6 R3 D" ]. O4 Z
4.5 4.5 2.25 0.
- r4 E( ]+ L& Z) o3 I- f/ L
4.5 4.5 9. 0.
/ |1 M0 ^1 E6 |6 B/ v
4.5 5. 2.386074153449669 0.
' S, a, i6 V$ k! z# S$ g
4.5 5. 9.429715320234545 0.
2 M4 H/ G2 G0 \9 i# h0 n
4.5 5.5 2.543211996792689 0.
7 }3 U; A6 P! L7 M0 R
4.5 5.5 9.731788003207315 0.
M% O R- _8 P# |1 Y
4.5 6. 2.721364796483262 0.
$ q0 W- I! M" k5 X: E( b3 M
4.5 6. 9.92149234637388 0.
. Z( }4 ~& {7 a$ Z; n7 ]- ]
4.5 6.5 2.922185008548723 0.
1 C8 O) {5 u' E8 q1 s* q( W3 i
4.5 7. 3.149000780229209 0.
# k h2 Z" L) A+ J% D
4.5 7.5 3.407301852906852 0.
% q: E7 Q! q! }5 P& N' H2 I% t* j
4.5 7.5 9.905198147093154 0.
% a2 ~& q. M. A+ R
4.5 8. 3.705986018674346 0.
; F( z5 y# o+ e7 e
4.5 8. 9.714013981325651 0.
5 s+ M* \% A' z% n6 L
4.5 8.5 4.060312832145664 0.
4 g) q0 y# x( Y) c! o
4.5 8.5 9.420456398623564 0.
; ?- |) v1 E- g. n) `1 P, F- d
4.5 9. 4.5 0.
" {# _# L/ }/ {& Q# b+ v3 A
4.5 9. 9.000000000000005 0.
7 p5 [+ x$ B0 h7 f" m; E) [
4.5 9.5 5.100326474258905 0.
8 V; N. }! k8 ^! U
4.5 9.5 8.381816382883958 0.
- r' j2 n! P. _: e3 ?3 \/ V& a- N; [
4.5 10. 6.402193416458818 0.
* C- A) i9 d( A
4.5 10. 7.028841066299776 4.547473508864641e-013
6 r7 e* t+ W: {& n4 W( k
5. 2.5 2.499999999999997 0.
1 J' R6 g5 Y5 O) O j9 ~( f
5. 2.5 4.999999999999998 0.
6 [" f! K6 L2 s% Q& z
5. 3. 2.271534568604568 0.
0 n# }0 ^6 y( R; \; X
5. 3. 6.603465431395431 0.
. Y5 ~% g9 I8 B5 K! P
5. 3.5 2.249335186315031 0.
3 n" l) |/ p v9 ^# E6 c
5. 3.5 7.78007657839085 0.
; ^# |, M. \- b' ~+ ~4 k
5. 4. 2.298437881283576 0.
[+ l3 X- F2 w) H& M& x: D
5. 4. 8.701562118716424 0.
7 t8 Y" [: U4 m( D
5. 4.5 2.386074153449668 0.
2 h U6 @+ V% @' P
5. 4.5 9.429715320234545 0.
$ L. S) ?3 m- y. G1 T% w: x
5. 5. 2.5 0.
4 ~4 l p l5 K
5. 5. 9.999999999999993 0.
+ n: E2 [8 x- D1 {
5. 5.5 2.635001373375082 0.
& f Q+ T8 P5 Z4 v F
5. 6. 2.789031160980821 0.
# K7 F( P. Z0 j2 v! h N" q* Q$ }
5. 6.5 2.961827475384206 0.
/ x1 N. D K$ i/ c
5. 7. 3.154404956432853 0.
, o7 J7 _) Y' }. e- c" b% F0 T8 g
5. 7.5 3.368956325934996 0.
* b/ r! g2 ]% n" `, r# @" r
5. 8. 3.609045829068848 0.
+ O8 j' u6 |* n# v* ^8 j
5. 8.5 3.880150804346176 0.
; c# b5 F5 a5 ] i9 a" W0 k$ v& j
5. 9. 4.190822529142221 0.
0 h8 A% S. i6 \( H* {5 K
5. 9.5 4.555265557190405 0.
/ B& v& }" |( a+ t/ ?% a0 b
5. 10. 4.999999999999997 0.
" C1 M7 w4 W1 z: d
5. 10. 10. 0.
; p* G+ H2 Z- h
5.5 2.5 3.292157134434847 0.
' F2 o4 ~) m: {# d8 x
5.5 2.5 4.176592865565167 0.
0 Q6 K P. }9 R+ y2 |/ W
5.5 3. 2.583225948048685 0.
- n3 T z5 T* M3 ~( J2 }
5.5 3. 6.387362287245431 0.
7 ?* `* k8 k: c2 S0 u5 Y+ L
5.5 3.5 2.476297487447864 0.
! `" p+ L/ E O0 Q X9 q! a6 S
5.5 3.5 7.773702512552133 0.
6 H2 M, R2 z- R3 w
5.5 4. 2.483445700017513 0.
5 e% o2 w/ u* o0 {. l5 }) Q
5.5 4. 8.858659563140384 0.
0 a) w ~7 V# ]. j# T* H9 X
5.5 4.5 2.543211996792689 0.
d& p2 d% }! o
5.5 4.5 9.731788003207313 0.
- s# t \ q; e9 D1 }
5.5 5. 2.635001373375081 0.
6 w# ~; K- s5 B0 b: ]- Q
5.5 5.5 2.749999999999999 0.
3 ^0 x! M2 D. M m
5.5 6. 2.884119329429114 0.
4 V* R! U) P; @2 @
5.5 6.5 3.035604845963815 0.
* f9 B8 U4 D4 H
5.5 7. 3.204083523261024 0.
( c1 h. r5 C- i; G3 `
5.5 7.5 3.390173520212255 0.
9 g$ \* ~# h1 |9 M, q4 A
5.5 8. 3.595369279178611 0.
. g' e0 s, ~8 w* D1 ]
5.5 8.5 3.822111065390602 0.
: ^& |8 m7 f. d8 O- j
5.5 9. 4.074041860443781 0.
; q$ U; m/ g6 ~
5.5 9.5 4.356541541407054 0.
1 _" ], j2 @# y/ e* r6 \
5.5 10. 4.677786777828594 0.
4 H* g8 s ?2 ]# e: t7 B: `
6. 3. 3. 0.
: G& w# Z# A+ i% H* C. v
6. 3. 5.999999999999999 0.
5 Q! u) M6 t# S& ^2 f& D; l
6. 3.5 2.745300211529266 0.
3 X4 B8 a2 i" @) g# l
6. 3.5 7.649436630575996 0.
! {* `, T" @2 }; F
6. 4. 2.695165060747994 0.
+ _& @+ Q+ c3 B6 e7 b5 n& A# o' q
6. 4. 8.904834939252005 0.
6 T3 }5 b- g2 C8 _% `
6. 4.5 2.721364796483262 0.
7 v: Q8 T$ x* H, J! J+ j
6. 4.5 9.92149234637388 0.
( F ]; M+ I9 w! X$ [9 @' L$ y; |
6. 5. 2.78903116098082 0.
1 _; p. ^/ |5 ?8 P5 H a
6. 5.5 2.884119329429112 0.
, K1 B1 b# H0 t
6. 6. 3. 0.
* N! K) {% ?% r+ a" b* d* E4 b& K5 P3 ]
6. 6.5 3.133381054885423 0.
. ?$ t' }9 v8 Y, r# R) W3 r& n, W. A
6. 7. 3.282742465037893 0.
; x! |0 K: d5 \7 h, {0 W
6. 7.5 3.447656821925362 2.273736754432321e-013
# c; K* X. J- i) a% ^, {# U
6. 8. 3.628486395311015 0.
. ^( A0 r# i/ w" n
6. 8.5 3.826272163735232 0.
) e9 R3 X0 k7 u' e
6. 9. 4.042747591121993 0.
t) _+ m6 h5 X7 ?& E( n
6. 9.5 4.280465505524228 0.
$ D6 H1 }) x' \, |- \; h7 f
6. 10. 4.543069137209136 0.
; s; a! x, Z, D; l
6.5 3. 3.692013773129525 0.
* q% S( u0 K2 z/ O: t
6.5 3. 5.281670437396786 0.
. ~$ d0 @) v. A9 L
6.5 3.5 3.073844239487251 0.
/ E* l$ p, O- U3 f# M3 G
6.5 3.5 7.401155760512746 0.
& ~7 R3 s, |% e* _& R7 \
6.5 4. 2.938916502606827 0.
, } f$ r0 l# N- G: Z3 m' L5 U
6.5 4. 8.846797783107464 0.
0 F D2 J3 f5 q/ C% X# L
6.5 4.5 2.922185008548724 0.
- U& A& t) z" z" l2 V
6.5 5. 2.961827475384206 0.
7 H0 N0 z' ?+ C5 ^
6.5 5.5 3.035604845963813 0.
2 G! e0 D. I" L S; t, }9 f
6.5 6. 3.133381054885422 0.
4 i7 C' y- Y7 `" {
6.5 6.5 3.25 0.
4 E: s% A4 D( G3 p
6.5 7. 3.382753896487015 0.
& } K" \9 ?' t+ L3 k) J
6.5 7.5 3.530313399868478 0.
3 ?) e7 w ^8 i9 T
6.5 8. 3.692229149874506 0.
1 S: Q& X6 ~, z$ G) b, W4 j$ D. \
6.5 8.5 3.868693727795107 0.
7 q) n1 G, J6 K" H) {4 Q
6.5 9. 4.060441442861232 0.
' c2 d5 s; ]# m, _' C0 n
6.5 9.5 4.268736592110795 0.
1 l- @& a5 ~8 B. j2 g
6.5 10. 4.495435882583067 0.
% o, n" \6 I' H* Q* i9 @; O4 q& G
7. 3.5 3.500000000000001 0.
5 x8 a' @4 p# ]
7. 3.5 7. 0.
' l+ E9 b, F/ W c( V
7. 4. 3.223865764386255 0.
0 w/ G6 A4 i, _" n2 j
7. 4. 8.685225144704656 0.
" L* s W! E- ?& F" a+ U, v
7. 4.5 3.14900078022921 0.
# v) j2 {1 R g6 q: u
7. 5. 3.154404956432853 0.
4 m7 D2 n3 ^/ L3 S$ q
7. 5.5 3.204083523261021 0.
9 E6 @) H( O$ r! L
7. 6. 3.282742465037893 0.
' P8 I& e9 \0 X3 }2 ?
7. 6.5 3.382753896487015 0.
6 d B4 ?5 e7 _/ W; ~
7. 7. 3.5 0.
0 ^4 g/ @9 C+ O- C4 ^* Q, I
7. 7.5 3.632214429249618 0.
7 g9 O. G6 W! N$ C% F
7. 8. 3.778224923088592 0.
; b* K" L$ R( }) k' C
7. 8.5 3.93757894317775 0.
- }. t) V% W, b& `
7. 9. 4.110354368226149 0.
# Q6 M6 A) x5 q+ s
7. 9.5 4.297071556823225 0.
! _- n& @% f: K% X0 M& X- p
7. 10. 4.498670372630065 0.
9 Y2 ]9 O/ Z/ K
7.5 3.5 4.146248634662252 0.
- i# j. g3 O3 y3 o, y1 `7 M
7.5 3.5 6.331024092610478 0.
/ d- ]/ T8 x) s% |+ r" p
7.5 4. 3.566387492405242 0.
- `' u6 f) s/ s$ ^! n: w) e
7.5 4. 8.411873377159969 0.
9 Q8 \( ^0 I3 E1 J* ]" Z
7.5 4.5 3.407301852906851 0.
( r. [. c3 n9 |
7.5 4.5 9.905198147093145 0.
8 j% x# f3 k5 U' g" @
7.5 5. 3.368956325934993 0.
- } {: q3 B6 w3 n6 R+ ? ~
7.5 5.5 3.390173520212255 0.
6 }' ^: C% g4 V0 O9 Z* E; C9 a* {5 k
7.5 6. 3.447656821925362 0.
, @! j* V3 Z+ |: b
7.5 6.5 3.530313399868477 0.
0 T" x, F" Y0 q3 G; M& O
7.5 7. 3.632214429249618 0.
2 Z5 d) E; B8 ~2 E0 m: S' l
7.5 7.5 3.750000000000003 0.
G4 @9 Q! H! C% _$ _5 ^0 ^
7.5 8. 3.881745401569135 0.
9 q2 _$ \$ `% b$ Y5 S) T/ ^6 n
7.5 8.5 4.026409271112575 0.
2 P1 [1 ]* E% D6 p6 J0 C
7.5 9. 4.183546741471229 0.
; C& r) v9 c# p: M, ^+ s0 `
7.5 9.5 4.353157178625922 0.
1 W! D$ O# D& P- H1 p8 I
7.5 10. 4.535607994138771 0.
. v5 n6 X# c) Y; j+ R1 `: K7 ]) z
8. 4. 4.000000000000002 0.
4 X; O% e" a' t; v+ p% l
8. 4. 8. 0.
; O8 B8 @" Z) m4 e( ?
8. 4.5 3.705986018674347 0.
0 l' ?8 ^+ ^8 |! L; C5 X
8. 4.5 9.714013981325657 0.
5 q' n) E+ g: c+ ^8 O
8. 5. 3.609045829068849 0.
0 B; I4 h" S: L
8. 5.5 3.595369279178607 0.
U4 I' |5 _7 x% B2 M- @' H" j0 \9 q7 S
8. 6. 3.628486395311016 0.
8 H8 q* s# S* Y# s8 @
8. 6.5 3.692229149874504 0.
; s, V: f$ K3 i" U; O
8. 7. 3.77822492308859 0.
5 M y: h* [, k% K) I% P
8. 7.5 3.881745401569135 0.
5 ^& z/ C' P; T3 N7 F$ l, T2 L
8. 8. 4.000000000000003 0.
& R2 M" n$ R1 t7 J2 S, Y
8. 8.5 4.131333821659408 0.
% M8 Q5 ]8 R* W, |5 a
8. 9. 4.274815705955503 0.
7 f9 G1 m2 g( n! T; O9 J
8. 9.5 4.430014593640446 0.
. Y: X0 a8 ?1 H
8. 10. 4.596875762567152 0.
( \8 i& o0 u9 b9 T. w
8.5 4. 4.618832614156823 0.
! e9 Y' A( b* p
8.5 4. 7.361167385843172 0.
7 j- W: P; b1 r4 {: J+ t1 V9 K
8.5 4.5 4.060312832145666 0.
8 ?, x3 L9 \* |# m4 c. [. \& `
8.5 4.5 9.420456398623564 0.
9 q' a3 `/ J8 T- S, i# b) f
8.5 5. 3.880150804346178 0.
: F1 J ^( Z7 p0 W3 E& u6 I
8.5 5.5 3.822111065390603 0.
/ I$ X$ L9 _* y3 E: W) \' A
8.5 6. 3.826272163735231 0.
v" g, v7 ^1 q
8.5 6.5 3.868693727795108 0.
) ?: Z# O& R! e u4 E
8.5 7. 3.937578943177748 0.
& I8 u0 L Y0 `! L9 D, ~# K5 m
8.5 7.5 4.026409271112575 0.
! d5 ~- ?: R, u3 b
8.5 8. 4.13133382165941 0.
! N, L% ~4 ^6 R+ P. q+ ]. e
8.5 8.5 4.25 0.
8 Y/ h/ }' t* m' c0 s7 c- R2 H
8.5 9. 4.380969715903502 0.
% c0 O( S6 h9 l) [4 o
8.5 9.5 4.523405444098199 0.
9 Y$ c7 G* a H5 E/ T. E4 n
8.5 10. 4.676893219133843 0.
% z% }6 ]$ z, @" j7 O
9. 4.5 4.499999999999997 0.
) ?8 L6 V4 p% p+ g0 S3 E# P
9. 4.5 9.000000000000009 0.
% i0 u" f/ X( _9 N- O6 ~; u# H' A0 ]
9. 5. 4.190822529142222 0.
$ G* Y" s$ ^/ }$ m( O K1 B% L3 j
9. 5.5 4.074041860443781 0.
! m$ ^% t: x9 f5 |" P
9. 6. 4.042747591121993 0.
+ A' W9 Q. C8 Z" f7 P% X, U% u
9. 6.5 4.060441442861232 -4.547473508864641e-013
: O1 c0 R* s2 u( P2 {6 z B7 G
9. 7. 4.110354368226151 0.
8 T g8 @0 O t6 B N A: t8 J8 x
9. 7.5 4.183546741471229 0.
$ K# A$ Z) o7 S& ~4 o" E
9. 8. 4.274815705955503 0.
" q" m$ ?2 c; `7 \) O) I% C
9. 8.5 4.380969715903502 0.
. f% h, s& c: d+ C
9. 9. 4.5 0.
! p" Y; j& Q9 a1 e* o
9. 9.5 4.630645298521483 0.
- L: `( N$ E% K7 \, h/ t6 k1 ?0 G
9. 10. 4.772148306899336 0.
* `- {+ s9 x' G+ e
9.5 4.5 5.100326474258897 0.
: e U( {" \0 i; b3 T8 g8 m
9.5 4.5 8.381816382883978 0.
. G. x: k5 M1 e8 Y. M9 T* c; a
9.5 5. 4.555265557190406 0.
9 L J; s [. I
9.5 5.5 4.356541541407055 0.
( S! Y: M- M7 d* B
9.5 6. 4.280465505524228 0.
6 r! E5 K" n0 I2 J. a
9.5 6.5 4.268736592110795 0.
& A4 L6 D G9 d8 l5 t Q
9.5 7. 4.297071556823221 0.
& N8 h9 Y% U. v" o) c
9.5 7.5 4.353157178625922 0.
6 j4 C/ J5 G @* Y
9.5 8. 4.430014593640445 0.
/ K$ ~8 Y9 I+ b" }
9.5 8.5 4.523405444098199 0.
: x$ G) ~9 _% w
9.5 9. 4.630645298521484 0.
8 @5 M+ A3 n+ h
9.5 9.5 4.75 0.
7 G0 ^% i% P+ @( \ `' {# \( {
9.5 10. 4.880354401607461 0.
& L9 t. F$ h, `9 G# a! V
10. 4.5 6.402193416458861 0.
% ~/ E+ J0 q& |* m4 d1 \
10. 4.5 7.028841066299777 4.547473508864641e-013
# c7 h- t% _* g) b
10. 5. 4.999999999999997 0.
' M; F7 s9 }; y4 L: p8 D
10. 5. 10. 0.
4 I" V% j* L4 a4 `+ M
10. 5.5 4.67778677782859 0.
1 s$ p7 X+ [+ A- F
10. 6. 4.543069137209136 0.
3 J8 p# k& F5 w+ o6 a8 k; t# \
10. 6.5 4.495435882583067 0.
, L" {- F$ I2 g
10. 7. 4.498670372630065 0.
2 O; T% }3 F; o# f
10. 7.5 4.535607994138771 0.
- Q" V- T- P9 z
10. 8. 4.596875762567152 0.
) ]' Z* x* u9 n, m* ?0 Q
10. 8.5 4.676893219133843 0.
8 [7 @5 s; ~) ?' Z' z' S2 B5 q
10. 9. 4.772148306899336 0.
, |- e3 c m- R z% U7 P5 F* Z4 e
10. 9.5 4.880354401607461 0.
0 }& @1 |8 v# c
10. 10. 5. 0.
6 i$ p6 L" [6 u1 R5 N; @
330.
' j$ O3 j: l5 l7 z
& ~0 b$ p7 {. Q7 _% ^) f+ m3 w
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