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。
5 h6 A) c+ j9 m
参考：
http://www.forcal.net/sysm/forcal9/fchtm/fcopt.htm
! U7 E" h, F1 N z& y% ?6 Y, }1 h
2 |7 m; Q# T1 a7 x' 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;
9 J% i5 L1 z5 r$ V
f(x)=x^6-5*x^5+3*x^4+x^3-7*x^2+7*x-20;
1 A! T( R* `) N5 F! X
fcopt::isolve[HFor("f")];
- V1 I1 O2 D+ l. F7 r V- M
复制代码
-1.402463030422577 3.552713678800501e-015
: Q1 q( W& }5 O, a$ \( B
4.333755446919994 -2.984279490192421e-013
' U( _: z' A5 `7 U' N1 {
2.
8 [9 w8 J2 E' G) Q3 q3 Y
" n% Z. y7 D) P, r' x
说明：前面2行，每行中前一个数是解，后一个数是误差。最后的2说明有两个解。
; K! R9 C# t* L: L# ~9 y& L$ C, {3 d7 Y
作者:
wgxzy_1015
时间:
2011-1-9 11:34
谢谢................
作者:
forcal
时间:
2011-1-9 11:35
例子2：求方程的全部解（当y为1时，求x的全部解）：f(x,y)=(x^2+y^2)^3-36*(x^2-y^2)^2;
5 w0 F; P. F! b
!using("fcopt");
3 [5 g4 L( o$ R, v L
f(x,y)=(x^2+y^2)^3-36*(x^2-y^2)^2;
7 t4 T5 |0 z& N; X d- F
isolve[HFor("f"),optpara,1];
, A; @% N% ?: d- a ^
复制代码
-5.530393535267971 1. -3.637978807091713e-012
% U& H1 Z$ x2 H# P1 O6 s
-1.32936186218296 1. -7.105427357601002e-015
' `9 Q/ a% ^7 n; y7 p- g+ M& Q
-0.8047014256478491 1. -1.776356839400251e-015
% M# ~6 Y1 q5 B3 Z6 S
0.8047014256478491 1. -1.776356839400251e-015
. h0 I( Q7 m: C B; Q( ]/ o. R
1.32936186218296 1. -7.105427357601002e-015
! h: i8 y! U. w
5.530393535267971 1. -3.637978807091713e-012
8 r4 A) Y+ r6 x+ `7 Q
6.
, ~( s0 n, L! g
) X m# k4 @8 L$ L
作者:
forcal
时间:
2011-1-9 11:37
例子3：求方程的全部解（x取1.1，求y的全部解）：f(x,y)=(x^2+y^2)^3-36*(x^2-y^2)^2;
) R1 a% l# F; u% d' ]
!using("fcopt");
) y6 ~! q" }8 m5 k' V. v- Y
f(x,y)=(x^2+y^2)^3-36*(x^2-y^2)^2;
; `( d& {$ j/ I9 i
isolve[HFor("f"), optthis,1, optpara,1.1];
" Y4 }2 @6 f3 Y/ t1 X
复制代码
1.1 -5.413569621185505 0.
1 U3 d; y3 ]$ O3 f( Y# H
1.1 -1.52029233271966 0.
5 Q0 V3 E2 k" l6 v) C
1.1 -0.8671650244626143 8.881784197001252e-016
0 V: l3 `8 J, j( h$ Q
1.1 0.8671650244626143 8.881784197001252e-016
! w4 o: F6 m% A8 L8 g+ J2 |
1.1 1.52029233271966 0.
2 |, ?& n: E! y9 f% W: b" P! }
1.1 5.413569621185504 0.
2 X0 B# y2 ^* G% }# f, ?' R
6.
2 K n' Y6 K2 t$ ~1 }
作者:
forcal
时间:
2011-1-9 12:08
例子4：为隐函数绘图准备数据（x取1～10，y取1～10，z取1～10）：f(x,y,z)=(x+y+z)*(x*y+x*z+y*z)-10*x*y*z;
# b; W6 o+ u0 l9 r9 F
!using("fcopt");
- u# y8 z4 G5 J' G1 R7 r4 `
f(x,y,z)=(x+y+z)*(x*y+x*z+y*z)-10*x*y*z;
" X+ a" \3 W/ a3 K. e% S: i1 \" U
init(:x,y,i)={
1 \) V- S" ~5 |* X
i=0,
- {8 C# R% h! z2 b6 B
x=1,while{x<=10,
' m5 O! J) s$ u2 K: J
y=1,while{y<=10,
& m6 t% x0 M( c# V! Q
i=i+isolve[HFor("f"), optrange,1,10, optthis,2, optpara,x,y],
" X1 `9 t' y9 K! _' C z# h5 g( e
y=y+0.5
9 [2 g. g9 \7 ?- p+ m) K$ f$ _$ A
},
* A% e( o6 M. X# B s
x=x+0.5
5 g$ v a& @* l% V- w' X$ u
},
3 s& T2 v% m/ V0 \* Z
i
3 \0 G2 _1 M4 f' C; m
};
2 O3 A, e X4 x0 R1 N1 q
复制代码
1. 1. 2. 0.
( s% o9 k8 Z# t" J, s% {
1. 1.5 2.226208734813002 0.
( q% c) r# r4 }0 o
1. 2. 1. 0.
! N n3 \6 I1 K
1. 2. 1.999999999999999 0.
6 R3 N. m1 B0 O# }
1.5 1. 2.226208734813 0.
! p- a4 \% y& r" ?" N
1.5 1.5 3. 0.
8 _' I2 R2 A3 x# i, s" \
1.5 2. 3.30716411545796 0.
0 M6 m: p7 b+ e; Y" i( v0 W5 n
1.5 2.5 1.135767284302283 0.
h6 y) O; t. u0 c) v# m
1.5 2.5 3.301732715697718 0.
9 S# B6 U& O0 ]1 @
1.5 3. 1.499999999999999 0.
% z" k* G" X. [2 s
1.5 3. 3.000000000000004 0.
5 i [) w, s1 w+ V, X- Z k
2. 1. 1. 0.
i0 N0 [& c B+ s6 N8 |
2. 1. 1.999999999999996 0.
( O% \. ] v2 j0 t
2. 1.5 3.30716411545796 0.
" }3 m+ e4 M8 B# l6 |! W
2. 2. 1. 0.
) ~2 r* r' O! y7 P: B3 J
2. 2. 4.000000000000001 0.
, Y3 L }# c9 l! A
2. 2.5 1.149218940641788 0.
3 c" r( p$ ^; l% u
2. 2.5 4.350781059358212 0.
4 ^* z' g/ Y3 g2 p
2. 3. 1.347582530373998 0.
/ ~ w/ V8 ~0 ~# Q' ^
2. 3. 4.452417469626003 0.
) q4 H/ ]8 z# k( c% ~! H1 _9 z1 a
2. 3.5 1.611932882193128 0.
4 E! c1 F# p7 C* z) K2 _/ r% c
2. 3.5 4.342612572352325 0.
! c2 e0 D8 U, z$ q) _0 i( s1 l
2. 4. 1.999999999999999 0.
3 _% r8 B) x! ]4 d4 ^6 l2 S
2. 4. 3.999999999999999 0.
& ~8 k0 n7 U1 f6 }% f& h( |- v
2.5 1.5 1.135767284302283 0.
. W7 h* K2 L4 W! x
2.5 1.5 3.301732715697717 0.
) J0 Y! @7 [3 D+ n: G4 Z& A' X
2.5 2. 1.149218940641788 0.
5 w. ~' W8 M( X( A1 e0 F
2.5 2. 4.350781059358212 0.
# t. i" p; R* k2 r6 e3 ?5 C7 k$ S
2.5 2.5 1.25 0.
- a r5 i* I( j' U" W$ S
2.5 2.5 4.999999999999998 0.
0 ~; d$ G- @; T' }
2.5 3. 1.39451558049041 0.
! L+ Q$ o8 d0 C
2.5 3. 5.378211692236864 5.684341886080802e-014
( R' N) j/ D- w2 ^- ~ C& P
2.5 3.5 1.577202478216426 0.
' m# m" w% C+ U1 [' `# A& Y/ g! w" s
2.5 3.5 5.547797521783575 0.
5 b* q' ^8 V# S1 ]9 U/ h
2.5 4. 1.804522914534426 0.
( X2 S2 \ W$ i0 a; R5 S+ `
2.5 4. 5.541630931619419 0.
8 G9 s2 G6 F1 \( M7 k. |) k, P
2.5 4.5 2.09541126457111 0.
5 {# Y, X/ u9 @8 b9 t0 ?
2.5 4.5 5.368874449714605 0.
; L5 e' A E5 r6 P# H+ L) l' B9 I0 d+ D
2.5 5. 2.5 0.
* ]" g+ h: ]9 z$ `* y+ x
2.5 5. 4.999999999999998 0.
1 T! J) k9 F8 ?, h/ ?
2.5 5.5 3.292157134434847 0.
h6 x$ W" w) Y/ k
2.5 5.5 4.176592865565161 0.
( C2 n- h3 x9 _# ?8 I* S/ D
3. 1.5 1.499999999999999 0.
! ~$ z2 y, a. \& T# p0 _4 Y
3. 1.5 3.000000000000004 0.
$ X; }7 y5 m' {, ?
3. 2. 1.347582530373997 0.
2 M! b- E/ a) R
3. 2. 4.452417469626003 0.
5 ?7 ~% H" a$ U5 e7 B% J
3. 2.5 1.39451558049041 0.
5 l4 S3 z& [6 S+ G
3. 2.5 5.378211692236861 -5.684341886080802e-014
7 _4 v O: \9 x5 h4 p# E3 ~0 l% G
3. 3. 1.5 0.
1 E5 @. D) s1 Z0 I0 s9 z
3. 3. 6.000000000000001 0.
* n$ S5 Z! ?; M2 |+ b- l8 [6 Y
3. 3.5 1.641371232518948 0.
8 z1 x) p4 C/ R- H
3. 3.5 6.397090305942587 0.
3 z+ @+ F4 f" p% {( |
3. 4. 1.814243197655509 -2.842170943040401e-014
1 h, ^4 N \+ @* M5 B( V7 u
3. 4. 6.614328230915922 0.
% l& ^; E* K) X, _9 U
3. 4.5 2.021373795560996 0.
2 U2 v5 R( W, _8 T, `1 n
3. 4.5 6.678626204439006 0.
0 s5 g, R8 a! [: E
3. 5. 2.271534568604568 0.
- y! {! w8 ~! d3 V( {5 M! R
3. 5. 6.603465431395431 0.
- l5 t/ h0 `/ |; F! l- C6 s
3. 5.5 2.583225948048685 0.
$ |+ }$ F+ z% U" O
3. 5.5 6.387362287245431 0.
" k6 z8 B7 f* Z0 Q
3. 6. 3. 0.
( }7 c2 R0 v- g. A/ X9 d* o. A9 `
3. 6. 6.000000000000004 0.
% G7 N8 X1 F2 d; `! L
3. 6.5 3.692013773129524 0.
. P+ |+ q) ]. h
3. 6.5 5.281670437396789 0.
" X6 r1 V* s# @) ]* R
3.5 2. 1.611932882193128 0.
1 B# S2 q ~9 o1 M
3.5 2. 4.342612572352325 0.
4 ?9 Z6 u% B, I- X* s, I" l, ]2 t" k7 t
3.5 2.5 1.577202478216427 0.
5 l2 C6 @! H6 X, g( a: y
3.5 2.5 5.547797521783575 0.
7 I4 `1 y+ V& C0 L
3.5 3. 1.641371232518947 0.
7 `9 h" Z# U; {* l4 h# a
3.5 3. 6.397090305942591 0.
: c& X1 C. z$ `" y1 x$ B
3.5 3.5 1.75 0.
8 G1 n' J Q5 z# z5 i }
3.5 3.5 7. 0.
) q+ b1 M& ?3 E# {) k
3.5 4. 1.889112461544294 0.
3 Q) f. Z L" q: `* z
3.5 4. 7.410887538455708 0.
( o7 [ e5 m1 w- q- w( o g! W8 Q
3.5 4.5 2.055177184113076 0.
; S8 z: v. b$ _1 P5 U
3.5 4.5 7.663572815886926 0.
' I. V, @+ d' f8 }* t: f
3.5 5. 2.249335186315033 0.
5 T C, t" X4 l0 ^. t6 S4 ?# G
3.5 5. 7.78007657839085 0.
1 E. P6 w2 g( _
3.5 5.5 2.476297487447864 0.
$ ^" d- ]) u7 A$ f$ N2 h
3.5 5.5 7.773702512552139 0.
$ C/ I- g8 d7 [& j. `7 Y
3.5 6. 2.745300211529267 0.
2 t! R, U+ w X, P; h
3.5 6. 7.649436630576002 0.
' _# r& p* `+ t7 E: Q* E6 Z
3.5 6.5 3.073844239487252 0.
5 ?- l6 Z0 E V5 Z3 y# _7 R
3.5 6.5 7.401155760512754 0.
$ S5 `7 _/ @( h q3 y9 n7 u0 k# F
3.5 7. 3.5 0.
5 h' ], A$ w, w8 e9 a
3.5 7. 7. 0.
# S3 B0 F% } K N
3.5 7.5 4.146248634662254 0.
l# B8 c9 V. ^- A
3.5 7.5 6.331024092610477 0.
' V: A# W) ?- P7 o. A' |* B6 ]
4. 2. 2.000000000000001 0.
$ N1 p7 Z; E% H" U4 r# R9 |2 d( y) l }
4. 2. 3.999999999999997 0.
9 P8 p: _1 T' t
4. 2.5 1.804522914534426 0.
' ^4 o, x2 B( a( T, \1 N7 L
4. 2.5 5.541630931619421 0.
" C& V3 z3 X. q% ~
4. 3. 1.814243197655509 0.
+ W& [0 \# x/ ^$ p5 [
4. 3. 6.614328230915922 0.
+ ^, a0 l8 c+ Z& R) n; L
4. 3.5 1.889112461544296 0.
& ?) G ~& z: L0 M9 y$ s/ w7 a
4. 3.5 7.410887538455708 0.
. d5 o9 s' p# B
4. 4. 2. 0.
; m d! f. J$ b) X0 z
4. 4. 8. 0.
) R0 O0 _ l+ c! ^
4. 4.5 2.137407852977751 0.
- N& t) S! }, u. _3 [
4. 4.5 8.421415676434013 0.
2 y6 I- O; q4 j3 ^/ U
4. 5. 2.298437881283576 0.
$ A/ c' D9 q: s1 X% j5 |
4. 5. 8.701562118716424 0.
; K% K& ~" @7 \! x
4. 5.5 2.483445700017514 0.
1 g; L* B$ p% s' `0 Z8 W
4. 5.5 8.858659563140384 0.
+ P- k- z9 \) j" ^+ e( g2 ?1 p
4. 6. 2.695165060747996 0.
$ i" H* `! T- o( H& ]
4. 6. 8.904834939252009 0.
, G) |$ m) x" O5 ?* O* N
4. 6.5 2.938916502606828 0.
3 i, A* n0 a+ P3 |6 P
4. 6.5 8.846797783107462 0.
+ G$ m( {( H- a
4. 7. 3.223865764386256 0.
9 K8 A- T9 w$ N7 q/ b# H$ D
4. 7. 8.685225144704656 0.
$ N# X% j/ x0 f8 g7 R2 ~
4. 7.5 3.566387492405245 0.
M! W6 J6 l( U% c e; [4 }% Z# W) `
4. 7.5 8.411873377159974 0.
4 l: ?- b- i$ m' |, m1 B2 E, C
4. 8. 4.000000000000002 0.
/ R" p; @/ K- O( d- ^8 p& J9 M
4. 8. 7.999999999999995 0.
5 c% P% v6 D- L( p/ E! d! t4 y
4. 8.5 4.618832614156824 0.
# p9 l+ l) {; X( N/ y
4. 8.5 7.361167385843178 0.
7 A- ^+ O8 Z* Y9 F- j
4.5 2.5 2.095411264571111 0.
* X3 U' H4 V9 t, {
4.5 2.5 5.368874449714603 0.
9 s- z9 z1 F7 Z# n- d" o* s
4.5 3. 2.021373795560996 0.
3 N' i3 e" E8 X/ L1 j& N& f
4.5 3. 6.678626204439004 0.
3 L( Z N4 C2 J: Q/ W
4.5 3.5 2.055177184113076 0.
6 I" E) k: W! u# b4 E& _" u
4.5 3.5 7.663572815886925 0.
+ B/ F* L2 k( d+ ^3 k
4.5 4. 2.137407852977751 0.
" J# R- P! l; u- w" d% n# T
4.5 4. 8.421415676434013 0.
' _; \5 r- u* d# X" Q4 K6 U1 ?* i
4.5 4.5 2.25 0.
' c8 s* c! V: _/ h+ ]
4.5 4.5 9. 0.
2 U: R% I9 J9 Y3 \( H6 |) e
4.5 5. 2.386074153449669 0.
. X5 b; d" l3 Z$ d" I
4.5 5. 9.429715320234545 0.
# |* \, O, Z/ J; a' U$ W
4.5 5.5 2.543211996792689 0.
% a s+ Q: P) T8 g& _, O R
4.5 5.5 9.731788003207315 0.
+ H7 d1 K' W) C1 ]0 a
4.5 6. 2.721364796483262 0.
; }; t1 U) N; |% [! `- b9 _
4.5 6. 9.92149234637388 0.
5 o$ J- N* i/ i& j/ d
4.5 6.5 2.922185008548723 0.
+ K: `) |! G/ y( r9 C& ]
4.5 7. 3.149000780229209 0.
5 O- G# q& [% |( A2 C
4.5 7.5 3.407301852906852 0.
0 U: Z- _; v2 [: B( E
4.5 7.5 9.905198147093154 0.
$ D, C5 q8 c4 c/ B8 f! X+ o
4.5 8. 3.705986018674346 0.
) e( K' `: t% B" y. M
4.5 8. 9.714013981325651 0.
+ c9 N* N: ?8 e4 ^' z4 Z$ j0 C
4.5 8.5 4.060312832145664 0.
) q: I! @+ ?1 c0 r W
4.5 8.5 9.420456398623564 0.
7 i$ _/ A; l$ o
4.5 9. 4.5 0.
& Q# Z) J( v" `
4.5 9. 9.000000000000005 0.
5 {8 S: T" R5 Z+ G
4.5 9.5 5.100326474258905 0.
; U- v$ `% ], a* U, z
4.5 9.5 8.381816382883958 0.
: r% C9 @# @* @ G) e3 G! Y* G& g
4.5 10. 6.402193416458818 0.
+ L+ D k' W; w+ G" h( n( [
4.5 10. 7.028841066299776 4.547473508864641e-013
. U9 [4 m3 L% K6 z/ U
5. 2.5 2.499999999999997 0.
0 S% s" U' g- W8 m
5. 2.5 4.999999999999998 0.
) r- Q2 Q* W- C# K
5. 3. 2.271534568604568 0.
% ?' i9 Z9 d6 }8 O
5. 3. 6.603465431395431 0.
3 K/ G/ S6 t( n- F6 b8 f
5. 3.5 2.249335186315031 0.
9 [- _$ M$ J$ z# Y3 V* }
5. 3.5 7.78007657839085 0.
) i) E# k* K' u) }8 _& Z# M
5. 4. 2.298437881283576 0.
1 p1 k' B( z+ F' N
5. 4. 8.701562118716424 0.
, j2 Y9 k8 @% h/ U+ R
5. 4.5 2.386074153449668 0.
; ?5 f- @3 C" D* N
5. 4.5 9.429715320234545 0.
" Y9 G" t8 h, o5 z' K
5. 5. 2.5 0.
4 j% h/ ?; @6 H9 v
5. 5. 9.999999999999993 0.
0 [$ |7 x7 V3 d. O
5. 5.5 2.635001373375082 0.
( ?* S4 m8 d& ^+ x! h1 X
5. 6. 2.789031160980821 0.
; U8 h- ]) _) Z& d! s$ b
5. 6.5 2.961827475384206 0.
6 C$ M3 L# F- Q9 s* u" u: X: y
5. 7. 3.154404956432853 0.
2 R2 f0 ~1 T# Y
5. 7.5 3.368956325934996 0.
" M1 E3 T& _. r
5. 8. 3.609045829068848 0.
/ Z3 ?8 |: a8 r- H) P M
5. 8.5 3.880150804346176 0.
6 u" k* ?/ |* A
5. 9. 4.190822529142221 0.
* l/ w# B5 @* ]" ], i
5. 9.5 4.555265557190405 0.
) M& i' s% U1 Y. f
5. 10. 4.999999999999997 0.
H) P3 p9 E2 |
5. 10. 10. 0.
9 I7 e: S/ b$ ~" k) u9 e: @
5.5 2.5 3.292157134434847 0.
" A& |3 v! }8 y4 s# j. [% y
5.5 2.5 4.176592865565167 0.
% E2 j% i6 f/ s! i- D' q
5.5 3. 2.583225948048685 0.
2 L8 ~; Y" y/ _0 K: n% e- G1 u
5.5 3. 6.387362287245431 0.
8 p6 p* G8 P% [
5.5 3.5 2.476297487447864 0.
2 ?! R6 R- [, ~. w( i
5.5 3.5 7.773702512552133 0.
# s% a" B' f4 x
5.5 4. 2.483445700017513 0.
! Q9 a: L. \" ?1 w. L7 e' M. a O
5.5 4. 8.858659563140384 0.
9 c0 H4 K+ n: \( J- \
5.5 4.5 2.543211996792689 0.
- P+ }: {+ o4 A7 }. E
5.5 4.5 9.731788003207313 0.
( y& u* Z% n. }' G! r/ {6 X
5.5 5. 2.635001373375081 0.
$ E' V0 w9 i. K! X' v
5.5 5.5 2.749999999999999 0.
& }6 V+ X' p3 g2 `, G
5.5 6. 2.884119329429114 0.
# K( s& c1 d" `( N5 m4 l
5.5 6.5 3.035604845963815 0.
G, P' Z' b6 @4 b
5.5 7. 3.204083523261024 0.
g" g$ u" n! P+ ]! N! \; c
5.5 7.5 3.390173520212255 0.
/ ~: g' ?3 ]3 j$ a: G- }
5.5 8. 3.595369279178611 0.
3 d- G7 E1 I. N/ V8 J: g' ?
5.5 8.5 3.822111065390602 0.
5 t% D! m. R- O
5.5 9. 4.074041860443781 0.
6 N8 I0 A! w- D5 u u+ D
5.5 9.5 4.356541541407054 0.
) q/ L+ E8 Q# c
5.5 10. 4.677786777828594 0.
6 [- @7 i6 v. T% P
6. 3. 3. 0.
; E: L3 @1 L2 f" Q9 B. r
6. 3. 5.999999999999999 0.
- ^$ x) M& |9 B, w# G( _% F
6. 3.5 2.745300211529266 0.
& s. O/ V% S/ \* {
6. 3.5 7.649436630575996 0.
% e6 T& @$ z( D
6. 4. 2.695165060747994 0.
9 s1 t2 i# q7 X, \
6. 4. 8.904834939252005 0.
0 L! z* S1 w9 `( i* {9 w1 ?
6. 4.5 2.721364796483262 0.
3 S& E: b0 c4 e2 ^, | l
6. 4.5 9.92149234637388 0.
3 j: T7 {; U7 m- b, T4 t
6. 5. 2.78903116098082 0.
& m) ~8 F4 y/ k5 Y/ \
6. 5.5 2.884119329429112 0.
* f9 V4 v+ r, [4 z, W
6. 6. 3. 0.
, e* X/ y) K" M1 H
6. 6.5 3.133381054885423 0.
6 Z! L, Y6 I: s5 A$ l' A. ]
6. 7. 3.282742465037893 0.
) P3 q0 V$ i) a! p
6. 7.5 3.447656821925362 2.273736754432321e-013
( b- u* x# L% j) J7 v% |
6. 8. 3.628486395311015 0.
) f1 ]4 m n# E& j7 T6 ^& V- b
6. 8.5 3.826272163735232 0.
/ i3 c# b/ z9 h
6. 9. 4.042747591121993 0.
* P, r3 K; v ^
6. 9.5 4.280465505524228 0.
9 {* I, u, L( j( j0 b+ [
6. 10. 4.543069137209136 0.
9 P# r: T: J0 R7 W# Q
6.5 3. 3.692013773129525 0.
4 k& N; g# f+ X$ T5 R; K3 ^
6.5 3. 5.281670437396786 0.
: P1 u' l' y" c: R$ Y
6.5 3.5 3.073844239487251 0.
, G) F8 l8 g: r9 @* m: V5 _; s5 d
6.5 3.5 7.401155760512746 0.
" v$ K- a+ T2 }+ c4 q
6.5 4. 2.938916502606827 0.
/ {' `8 l! R- u$ n
6.5 4. 8.846797783107464 0.
! h3 D& _$ |. \6 o( }. o* K% s
6.5 4.5 2.922185008548724 0.
n) k2 v# ^; z" s+ ^5 ]
6.5 5. 2.961827475384206 0.
2 B" V y$ l: x4 \
6.5 5.5 3.035604845963813 0.
- e3 z: k r5 ?
6.5 6. 3.133381054885422 0.
_- e/ v/ y3 k5 B: U
6.5 6.5 3.25 0.
: j9 a0 X* K( J) }
6.5 7. 3.382753896487015 0.
) L! [0 K- r7 S e7 A
6.5 7.5 3.530313399868478 0.
2 U) O3 N# n0 |9 D, u1 U
6.5 8. 3.692229149874506 0.
0 Z+ |; P( o5 d, r) r
6.5 8.5 3.868693727795107 0.
, g: T$ Y# ~1 S3 c0 V2 q
6.5 9. 4.060441442861232 0.
3 X( B* J8 ^7 K7 I) N3 O& }
6.5 9.5 4.268736592110795 0.
2 U) t, Z' \; q7 X$ [" G; _5 M
6.5 10. 4.495435882583067 0.
5 c3 \" O' z$ c, j# P
7. 3.5 3.500000000000001 0.
$ ~" [2 d/ _& i' U2 s
7. 3.5 7. 0.
; j# S* n z% d$ p* X Y
7. 4. 3.223865764386255 0.
0 x" N7 E$ S3 F" P8 \$ D
7. 4. 8.685225144704656 0.
* y: V( C6 l7 `; U- c% r- y8 i1 |
7. 4.5 3.14900078022921 0.
; p/ w3 R2 u$ v. e
7. 5. 3.154404956432853 0.
$ S" A8 z9 z( c8 A/ d) H- W) c
7. 5.5 3.204083523261021 0.
5 Z6 w* j0 ^3 }6 E
7. 6. 3.282742465037893 0.
4 F% W. y. M( F. C# z, }: Y6 ]; |
7. 6.5 3.382753896487015 0.
) a' p ~, q. N
7. 7. 3.5 0.
" O+ {0 a4 S1 a* _
7. 7.5 3.632214429249618 0.
; N: a7 o* N% f* n% n- T
7. 8. 3.778224923088592 0.
0 R2 d8 U3 c2 A, F# I
7. 8.5 3.93757894317775 0.
# h: k- j7 K! P- Y7 c' o
7. 9. 4.110354368226149 0.
* e( s! q: j$ N! U1 E" Y* w7 ?
7. 9.5 4.297071556823225 0.
6 p' t% g! z3 m H
7. 10. 4.498670372630065 0.
$ e; i, t( W) v$ u; {7 t6 H& U& [3 N
7.5 3.5 4.146248634662252 0.
( m2 r% B, v6 e3 h( L8 V) i6 g
7.5 3.5 6.331024092610478 0.
' G. i$ M! w) ^
7.5 4. 3.566387492405242 0.
% T2 c @ J3 W3 p$ z
7.5 4. 8.411873377159969 0.
" ?' R" }, H6 _& K% H* L
7.5 4.5 3.407301852906851 0.
% z' Y* O+ s. E4 R U! j
7.5 4.5 9.905198147093145 0.
( R. n* w; V- y! |. n
7.5 5. 3.368956325934993 0.
* E. T8 a* K2 h+ z
7.5 5.5 3.390173520212255 0.
$ d3 k7 P# e3 c. d" u
7.5 6. 3.447656821925362 0.
/ I8 ~+ w% ?1 x U- y
7.5 6.5 3.530313399868477 0.
. M! G" o* G8 h% q- f/ m
7.5 7. 3.632214429249618 0.
5 `1 P& [) y/ V4 G+ ^* ]6 L
7.5 7.5 3.750000000000003 0.
& z8 O5 W, I1 [' l+ q5 i
7.5 8. 3.881745401569135 0.
, |- D Z6 X# Z
7.5 8.5 4.026409271112575 0.
3 S; V+ L: F: p
7.5 9. 4.183546741471229 0.
, S0 K$ {; F$ B8 E7 \0 s: M8 e, d9 M
7.5 9.5 4.353157178625922 0.
2 Z# ` V% B! q1 }' \
7.5 10. 4.535607994138771 0.
8 h7 }: r6 J0 n g
8. 4. 4.000000000000002 0.
7 f. w& b( q" w+ i1 u" _ b$ T! q& _5 ]
8. 4. 8. 0.
3 F0 f9 Z7 h4 c4 J) I/ Q# G W
8. 4.5 3.705986018674347 0.
* q- J- c7 m6 _3 V6 Z& |
8. 4.5 9.714013981325657 0.
# J0 p5 U3 M8 k8 x' G1 d' m: c
8. 5. 3.609045829068849 0.
/ {- ?* y" a; @% e w# |: s' G
8. 5.5 3.595369279178607 0.
* h& {9 G+ {" R: I# [/ {) N
8. 6. 3.628486395311016 0.
; o7 j3 Z% X) T) d9 S; d/ L3 d
8. 6.5 3.692229149874504 0.
( B: r0 k8 H) ~2 Q. D
8. 7. 3.77822492308859 0.
* Q) L. y7 ~' s6 z2 j* f
8. 7.5 3.881745401569135 0.
9 z4 x0 }" O& G. x. ^ X( j
8. 8. 4.000000000000003 0.
/ P' E, a- [3 }/ m5 f x
8. 8.5 4.131333821659408 0.
Z3 j' {) ^* k0 }/ c
8. 9. 4.274815705955503 0.
. W8 ^$ g. T g, I, V/ }! N
8. 9.5 4.430014593640446 0.
2 V+ m7 j8 i4 ]0 e# o
8. 10. 4.596875762567152 0.
4 Y9 f9 E) k9 v( K
8.5 4. 4.618832614156823 0.
$ ]3 E- O% g3 T( m- n# a
8.5 4. 7.361167385843172 0.
: \8 ]( ?$ j5 Q r, C0 J
8.5 4.5 4.060312832145666 0.
8 u; Q. N. h7 \, {
8.5 4.5 9.420456398623564 0.
, g! X& R9 \6 w+ y# k) \
8.5 5. 3.880150804346178 0.
: G0 [+ O8 m4 X" M5 N: T
8.5 5.5 3.822111065390603 0.
3 P4 _& s, f; o$ G2 q9 @
8.5 6. 3.826272163735231 0.
( }7 w8 B; F1 q) w: e- k) p6 e; f8 o
8.5 6.5 3.868693727795108 0.
: C! D9 h" f7 M
8.5 7. 3.937578943177748 0.
+ {/ X8 g8 m7 _8 m1 Z
8.5 7.5 4.026409271112575 0.
+ t, v. _- [# B' Y8 `0 P2 s* ^6 Z+ T
8.5 8. 4.13133382165941 0.
$ j a( B3 I/ z0 G9 e
8.5 8.5 4.25 0.
8 D2 F- k6 \. y) K$ O0 x
8.5 9. 4.380969715903502 0.
; J- P4 G3 K8 j! g. R
8.5 9.5 4.523405444098199 0.
* Q' l: j9 Z; ?2 i$ Y* r
8.5 10. 4.676893219133843 0.
j; F0 `3 H1 ` o! r
9. 4.5 4.499999999999997 0.
$ q' j1 N3 V# ^% S. O
9. 4.5 9.000000000000009 0.
$ d# U5 l b/ Y/ y8 ~
9. 5. 4.190822529142222 0.
* Z, V* ]5 @: t3 H9 Q
9. 5.5 4.074041860443781 0.
3 @% ^7 Z! v6 i- e! r! \# A4 ]
9. 6. 4.042747591121993 0.
6 w# t, ~ D% Q8 [- u* e1 Y" Q
9. 6.5 4.060441442861232 -4.547473508864641e-013
6 V1 a. Q ^3 g& g0 f# C
9. 7. 4.110354368226151 0.
0 K- U3 n% B* i: Z) h
9. 7.5 4.183546741471229 0.
8 @0 v$ N5 x" u) w9 m0 X. R
9. 8. 4.274815705955503 0.
# @# S& b2 ~7 P4 ]( C+ Q
9. 8.5 4.380969715903502 0.
o Q7 J9 Z3 b* h( Y# r7 V- [
9. 9. 4.5 0.
3 {! e/ z4 n0 G! d/ r
9. 9.5 4.630645298521483 0.
! h z) F, p+ P3 \
9. 10. 4.772148306899336 0.
' W( @. E' q) b
9.5 4.5 5.100326474258897 0.
9 |. v! E \+ [4 Z9 {; X9 F! x& X3 B
9.5 4.5 8.381816382883978 0.
1 C+ g% c, _7 r
9.5 5. 4.555265557190406 0.
+ ^' v! @4 ]& u [9 z1 X
9.5 5.5 4.356541541407055 0.
( S( z) c" V) A! E; y
9.5 6. 4.280465505524228 0.
% E" d# V, o. L, X" d
9.5 6.5 4.268736592110795 0.
. N+ g5 c& b6 I5 e
9.5 7. 4.297071556823221 0.
- F! f0 q( q* H; G$ C, ^ F$ J
9.5 7.5 4.353157178625922 0.
" g, e( O! }, H' V/ u: K
9.5 8. 4.430014593640445 0.
4 B9 q' u6 \/ d; K9 ^
9.5 8.5 4.523405444098199 0.
3 X" i+ Q8 F+ e3 _- t) C
9.5 9. 4.630645298521484 0.
- d& s" x: A" Q
9.5 9.5 4.75 0.
8 b5 D+ B U: S( K! i
9.5 10. 4.880354401607461 0.
+ @6 k" G6 ?0 h3 f! M! X# [
10. 4.5 6.402193416458861 0.
: H* |9 x0 x: I
10. 4.5 7.028841066299777 4.547473508864641e-013
$ M+ _4 J" u5 ?; b4 V- K9 `- g+ q
10. 5. 4.999999999999997 0.
- c3 G- j, O3 G3 C1 H% ^
10. 5. 10. 0.
; u' w& u' D( M3 P( d `- S
10. 5.5 4.67778677782859 0.
. r' I7 V# r! S
10. 6. 4.543069137209136 0.
, U& I: t3 E4 }9 Y1 K% k
10. 6.5 4.495435882583067 0.
8 h: |0 K: k( _; E- _
10. 7. 4.498670372630065 0.
' Q9 B3 J3 N+ c0 m
10. 7.5 4.535607994138771 0.
% e+ A, v8 k+ A& x! @
10. 8. 4.596875762567152 0.
$ e0 z% l8 T& h. U. W7 I& x
10. 8.5 4.676893219133843 0.
$ d r5 z& i* W" O
10. 9. 4.772148306899336 0.
- ]0 W4 t/ S- F9 _& j% {
10. 9.5 4.880354401607461 0.
/ k8 M1 x! A. S, ]
10. 10. 5. 0.
\: J# j/ a; i% W
330.
/ M, k3 Y. j' Q( W( i7 s" ^
- [; B9 D+ V: X# g6 T: ]
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