数学建模社区-数学中国
标题:
求方程的全部解
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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。
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参考：
http://www.forcal.net/sysm/forcal9/fchtm/fcopt.htm
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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;
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f(x)=x^6-5*x^5+3*x^4+x^3-7*x^2+7*x-20;
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fcopt::isolve[HFor("f")];
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复制代码
-1.402463030422577 3.552713678800501e-015
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4.333755446919994 -2.984279490192421e-013
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2.
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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。
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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;
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!using("fcopt");
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f(x,y)=(x^2+y^2)^3-36*(x^2-y^2)^2;
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isolve[HFor("f"),optpara,1];
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复制代码
-5.530393535267971 1. -3.637978807091713e-012
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-1.32936186218296 1. -7.105427357601002e-015
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-0.8047014256478491 1. -1.776356839400251e-015
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0.8047014256478491 1. -1.776356839400251e-015
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1.32936186218296 1. -7.105427357601002e-015
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5.530393535267971 1. -3.637978807091713e-012
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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;
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!using("fcopt");
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f(x,y)=(x^2+y^2)^3-36*(x^2-y^2)^2;
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isolve[HFor("f"), optthis,1, optpara,1.1];
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复制代码
1.1 -5.413569621185505 0.
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1.1 -1.52029233271966 0.
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1.1 -0.8671650244626143 8.881784197001252e-016
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1.1 0.8671650244626143 8.881784197001252e-016
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1.1 1.52029233271966 0.
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1.1 5.413569621185504 0.
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6.
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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;
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!using("fcopt");
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f(x,y,z)=(x+y+z)*(x*y+x*z+y*z)-10*x*y*z;
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init(:x,y,i)={
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i=0,
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x=1,while{x<=10,
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y=1,while{y<=10,
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i=i+isolve[HFor("f"), optrange,1,10, optthis,2, optpara,x,y],
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y=y+0.5
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},
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x=x+0.5
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},
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i
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};
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1. 1. 2. 0.
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1. 1.5 2.226208734813002 0.
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1. 2. 1. 0.
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1. 2. 1.999999999999999 0.
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1.5 1. 2.226208734813 0.
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1.5 1.5 3. 0.
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1.5 2. 3.30716411545796 0.
- H+ ^1 N" g6 X/ h! O3 [
1.5 2.5 1.135767284302283 0.
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1.5 2.5 3.301732715697718 0.
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1.5 3. 1.499999999999999 0.
! M/ _9 x7 Q( E! V% T! R8 c' g
1.5 3. 3.000000000000004 0.
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2. 1. 1. 0.
2 [) R2 w4 {! J: u& U
2. 1. 1.999999999999996 0.
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2. 1.5 3.30716411545796 0.
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2. 2. 1. 0.
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2. 2. 4.000000000000001 0.
5 G& [; O$ v; B$ v
2. 2.5 1.149218940641788 0.
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2. 2.5 4.350781059358212 0.
2 l% Z" m( t6 d$ [6 @' h, h
2. 3. 1.347582530373998 0.
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2. 3. 4.452417469626003 0.
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2. 3.5 1.611932882193128 0.
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2. 3.5 4.342612572352325 0.
# T4 @$ F8 j( R5 P) b. |
2. 4. 1.999999999999999 0.
2 P2 \) b- }/ A2 x% f7 }0 `
2. 4. 3.999999999999999 0.
# Y: A. l+ P$ |. q% m' r
2.5 1.5 1.135767284302283 0.
0 w6 e& @9 h& f- Y& R/ y
2.5 1.5 3.301732715697717 0.
, F1 U# J% _0 \# v4 Q
2.5 2. 1.149218940641788 0.
7 I( G" s# X: S) w2 o" l
2.5 2. 4.350781059358212 0.
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2.5 2.5 1.25 0.
M% L. t6 v# c- G0 k F2 B
2.5 2.5 4.999999999999998 0.
6 \' v4 ~* @# k% |2 A
2.5 3. 1.39451558049041 0.
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2.5 3. 5.378211692236864 5.684341886080802e-014
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2.5 3.5 1.577202478216426 0.
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2.5 3.5 5.547797521783575 0.
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2.5 4. 1.804522914534426 0.
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2.5 4. 5.541630931619419 0.
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2.5 4.5 2.09541126457111 0.
2 r' s+ |1 d5 n# P* g
2.5 4.5 5.368874449714605 0.
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2.5 5. 2.5 0.
! M& F5 J: {/ E0 N% u- v% u" k
2.5 5. 4.999999999999998 0.
' t" ]$ g: Q7 C/ | {8 l
2.5 5.5 3.292157134434847 0.
j* [% a, ?1 l6 V8 h* N: {4 H
2.5 5.5 4.176592865565161 0.
2 c( {& f1 E H: _* Y, @
3. 1.5 1.499999999999999 0.
: x3 T/ Q. C7 w& V4 A( e
3. 1.5 3.000000000000004 0.
3 h* r! ?7 @/ u! j( y
3. 2. 1.347582530373997 0.
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3. 2. 4.452417469626003 0.
! ]# Y2 e. q ~2 k, Y7 [
3. 2.5 1.39451558049041 0.
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3. 2.5 5.378211692236861 -5.684341886080802e-014
9 {2 h6 R- C& \+ Z, k! z" D: g+ P
3. 3. 1.5 0.
2 U. a, R7 B R* A* f8 j3 p
3. 3. 6.000000000000001 0.
0 G7 @. L4 x4 K& F/ V, T/ c
3. 3.5 1.641371232518948 0.
8 `( y) Y% |) j k
3. 3.5 6.397090305942587 0.
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3. 4. 1.814243197655509 -2.842170943040401e-014
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3. 4. 6.614328230915922 0.
" \# Z; b8 G9 t+ V. |, t- X4 v" y
3. 4.5 2.021373795560996 0.
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3. 4.5 6.678626204439006 0.
7 e) `7 D5 L' y6 D: I
3. 5. 2.271534568604568 0.
# Z$ r- |1 F; e7 s$ R; u7 C: u
3. 5. 6.603465431395431 0.
+ j: I4 R" n- m2 m
3. 5.5 2.583225948048685 0.
0 e- C) c, d! S
3. 5.5 6.387362287245431 0.
; {) V" U" r3 @# C' J- ]5 D$ m
3. 6. 3. 0.
0 ^+ N- e2 J6 t+ t! ^# f3 @
3. 6. 6.000000000000004 0.
9 W! G( ?5 s4 M4 U+ e4 ~2 b. E$ Z
3. 6.5 3.692013773129524 0.
2 `- Q9 J e2 N% m& D+ _
3. 6.5 5.281670437396789 0.
" Q m5 }& r2 I/ g! z( i
3.5 2. 1.611932882193128 0.
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3.5 2. 4.342612572352325 0.
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3.5 2.5 1.577202478216427 0.
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3.5 2.5 5.547797521783575 0.
' G3 o) W9 }$ f8 \3 B" {
3.5 3. 1.641371232518947 0.
% \! Z2 b2 O5 |4 I7 }: T9 o+ i
3.5 3. 6.397090305942591 0.
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3.5 3.5 1.75 0.
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3.5 3.5 7. 0.
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3.5 4. 1.889112461544294 0.
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3.5 4. 7.410887538455708 0.
& l1 l, r; V' Z1 b2 z9 a
3.5 4.5 2.055177184113076 0.
2 @6 a& q" |4 r
3.5 4.5 7.663572815886926 0.
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3.5 5. 2.249335186315033 0.
& n& X2 U! w) g5 c" q
3.5 5. 7.78007657839085 0.
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3.5 5.5 2.476297487447864 0.
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3.5 5.5 7.773702512552139 0.
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3.5 6. 2.745300211529267 0.
4 b% H: Z# V7 ~$ C: X
3.5 6. 7.649436630576002 0.
! G5 X6 f. ~9 p M2 o* D6 t
3.5 6.5 3.073844239487252 0.
1 X$ M. \- {, a( C2 K' b5 P
3.5 6.5 7.401155760512754 0.
1 f+ H' U8 @( t, j0 o7 U
3.5 7. 3.5 0.
1 _8 l5 E( {9 ~2 ?( F0 E; c( b0 {
3.5 7. 7. 0.
, \/ o' @: Z. f& v
3.5 7.5 4.146248634662254 0.
0 A+ f) t' A5 {( C3 K( i
3.5 7.5 6.331024092610477 0.
+ D/ A7 l2 a* `$ z4 F! ^, w( |
4. 2. 2.000000000000001 0.
! O( p: f! C7 g# N& b6 C G+ v
4. 2. 3.999999999999997 0.
2 D' \) O+ g/ V! v" {
4. 2.5 1.804522914534426 0.
. L5 Z3 t1 Z. x* w
4. 2.5 5.541630931619421 0.
+ u6 ~# y2 `, D; u# T, p
4. 3. 1.814243197655509 0.
- _9 c/ F5 f3 S7 G( I! q
4. 3. 6.614328230915922 0.
* k4 b p3 w, l3 h V
4. 3.5 1.889112461544296 0.
* f- f# e, X$ e1 M! R
4. 3.5 7.410887538455708 0.
m: J1 t- M/ Q% ~+ j3 p! V; s
4. 4. 2. 0.
6 [) n$ u, h2 z6 \. S2 U& R
4. 4. 8. 0.
/ U1 Z& g6 |) f/ N4 H, ~2 p
4. 4.5 2.137407852977751 0.
; P+ P( u' @* r* ?2 h3 B, X% f
4. 4.5 8.421415676434013 0.
! ?4 m9 b9 y! ^: ?/ G( r- v
4. 5. 2.298437881283576 0.
3 P; e7 `8 K( h
4. 5. 8.701562118716424 0.
+ u' g z: s( ]0 h+ o, i
4. 5.5 2.483445700017514 0.
* g: N' w3 k, |5 V* D( ?6 A" n
4. 5.5 8.858659563140384 0.
; g: q/ U. D0 K0 T! h) w! P+ x: O
4. 6. 2.695165060747996 0.
% Y& b! {: C* F! p' t% H z
4. 6. 8.904834939252009 0.
3 p8 C: t+ u, }# @: l8 A7 D
4. 6.5 2.938916502606828 0.
: E' ^1 ^8 N+ s8 B; J$ @8 L$ h
4. 6.5 8.846797783107462 0.
: l6 F/ `$ K2 n( t
4. 7. 3.223865764386256 0.
+ j" z, g0 ?4 ?* ~. G
4. 7. 8.685225144704656 0.
# c: V0 G% U/ e9 m3 a- @
4. 7.5 3.566387492405245 0.
& @) {# \7 }( d9 J8 N
4. 7.5 8.411873377159974 0.
& k6 H0 E0 F) v- ~' L( j; C4 s& | [
4. 8. 4.000000000000002 0.
- |; S: d E: k0 y- b% S! _
4. 8. 7.999999999999995 0.
7 q0 [( F/ _5 H
4. 8.5 4.618832614156824 0.
! r, ?0 A h! E! F$ r
4. 8.5 7.361167385843178 0.
, q( X! j6 e5 q% V
4.5 2.5 2.095411264571111 0.
% k* X/ w3 p. t) g' Z" l$ z
4.5 2.5 5.368874449714603 0.
# H8 `4 D5 Q; u5 T+ y
4.5 3. 2.021373795560996 0.
$ ~; s! W1 B" Q
4.5 3. 6.678626204439004 0.
! m' K# m5 y4 I5 E- v6 h0 w; g( ?
4.5 3.5 2.055177184113076 0.
4 x- `2 c% i& v5 G$ Z+ [$ A5 Y
4.5 3.5 7.663572815886925 0.
% b' K4 A! h& h* v* g, t/ i6 z
4.5 4. 2.137407852977751 0.
! o/ y& s7 p% x5 m* I; ~( t
4.5 4. 8.421415676434013 0.
0 q% E8 v3 l$ U7 f' [; |
4.5 4.5 2.25 0.
& [ [) e+ _$ \) X) ?) P
4.5 4.5 9. 0.
- I% }1 S& L- ^+ y1 z
4.5 5. 2.386074153449669 0.
# A/ @% h' n. ~% g
4.5 5. 9.429715320234545 0.
% [: q7 W. V p* D
4.5 5.5 2.543211996792689 0.
! X' U6 }& o1 a2 @- W! W& i- Q
4.5 5.5 9.731788003207315 0.
4 x D- q! V9 N
4.5 6. 2.721364796483262 0.
9 I% w1 Q* ]3 s& S/ u" V) z' f9 g {
4.5 6. 9.92149234637388 0.
5 {' h0 P6 @9 o8 C) A8 f; ?
4.5 6.5 2.922185008548723 0.
: z7 _ s' g0 t* T5 ]# k
4.5 7. 3.149000780229209 0.
/ T' k2 [) n2 e2 {; q- x, J6 U
4.5 7.5 3.407301852906852 0.
6 [1 m; K! y V4 x4 _
4.5 7.5 9.905198147093154 0.
! x F% U5 W9 t* Y
4.5 8. 3.705986018674346 0.
, X0 S3 N2 H) S8 T1 [7 P: [0 D0 s
4.5 8. 9.714013981325651 0.
0 W+ }4 _: J$ h! V+ `
4.5 8.5 4.060312832145664 0.
* T/ H! A$ B% l1 |
4.5 8.5 9.420456398623564 0.
1 x2 j+ ?8 U" E Q g
4.5 9. 4.5 0.
9 a6 n$ W' y6 k5 ]5 x" I
4.5 9. 9.000000000000005 0.
" q7 @7 }) ~+ w V8 j
4.5 9.5 5.100326474258905 0.
& H0 q2 b5 u4 p, g& S% N: s
4.5 9.5 8.381816382883958 0.
g5 F7 ?/ C, p$ i7 m8 w
4.5 10. 6.402193416458818 0.
/ |+ E0 _% I. u* n% s
4.5 10. 7.028841066299776 4.547473508864641e-013
" [, D9 D* ~( v8 b: H N6 k
5. 2.5 2.499999999999997 0.
9 x2 Y( O& \/ j q- t1 Q
5. 2.5 4.999999999999998 0.
* Q$ F' s% B- B& w! z" c7 h. c
5. 3. 2.271534568604568 0.
% [$ j7 h% z7 {, J% T
5. 3. 6.603465431395431 0.
# q( L1 i, _5 \2 H/ m
5. 3.5 2.249335186315031 0.
' ?% p i3 a1 y; t: n4 c7 B
5. 3.5 7.78007657839085 0.
' \4 {. _( S ?3 i
5. 4. 2.298437881283576 0.
* C8 _# A( ~8 [# I Q/ }. S3 j
5. 4. 8.701562118716424 0.
; g) S x/ z9 S2 I
5. 4.5 2.386074153449668 0.
) A% W( c* n2 j6 `& L
5. 4.5 9.429715320234545 0.
' h: P; n) d. `' m6 k
5. 5. 2.5 0.
+ n" Y/ s7 e9 w$ J5 z
5. 5. 9.999999999999993 0.
0 b: s& c- I( f2 K
5. 5.5 2.635001373375082 0.
) _' T: S, A& a Z4 a9 u8 Z- d+ ]
5. 6. 2.789031160980821 0.
; M" O$ }, ]! Z; G, t: G; G# U
5. 6.5 2.961827475384206 0.
" A. O' ?- u% {. s, V0 G8 n3 E
5. 7. 3.154404956432853 0.
# B9 Y* {. ], r Q6 e
5. 7.5 3.368956325934996 0.
# Z; K- ^1 q `9 c Q$ G# c7 |4 y
5. 8. 3.609045829068848 0.
# `9 s9 [& a9 L
5. 8.5 3.880150804346176 0.
5 a/ \ P0 B* s6 X: X: ] O- Y% f
5. 9. 4.190822529142221 0.
2 f& a: \" r: d1 o& V. _
5. 9.5 4.555265557190405 0.
% L# ~+ h! N! Y6 D, n/ d
5. 10. 4.999999999999997 0.
7 P; x! L+ o/ Q: ~8 o
5. 10. 10. 0.
3 {( D9 [( Y0 N8 ^) x
5.5 2.5 3.292157134434847 0.
5 w: C$ w1 Y# l# p& o( D
5.5 2.5 4.176592865565167 0.
+ `9 q# E) [, E. B
5.5 3. 2.583225948048685 0.
) j2 V1 t" V9 Z( |0 d5 m
5.5 3. 6.387362287245431 0.
* \* p/ z; _9 ?+ R; O
5.5 3.5 2.476297487447864 0.
& n) X- `' p+ N
5.5 3.5 7.773702512552133 0.
% _0 ~7 W1 o0 M) a0 P5 u P
5.5 4. 2.483445700017513 0.
- m( H. }" d8 u: \$ o7 N
5.5 4. 8.858659563140384 0.
% [5 n5 ^3 a4 d) }0 {) Y0 c" t0 F$ y5 s
5.5 4.5 2.543211996792689 0.
8 m: g" |! R; W
5.5 4.5 9.731788003207313 0.
) |7 a( Z: k' D* T* w) j; Y
5.5 5. 2.635001373375081 0.
' l* s$ n. p5 L4 m$ G3 b
5.5 5.5 2.749999999999999 0.
0 h* Z) l0 [! |5 r3 _% C- J6 Q
5.5 6. 2.884119329429114 0.
4 f9 a7 y0 w9 D
5.5 6.5 3.035604845963815 0.
6 b* m8 _: o/ ^
5.5 7. 3.204083523261024 0.
/ T1 \( g" Y" t& w7 M% |+ X9 Y
5.5 7.5 3.390173520212255 0.
# Q4 N2 J0 ^$ N7 E
5.5 8. 3.595369279178611 0.
; Z8 O! c7 S) Y0 s5 B
5.5 8.5 3.822111065390602 0.
5 o6 |+ `$ ]; N; k6 e
5.5 9. 4.074041860443781 0.
( q' I+ g4 h R9 ]; E2 B8 Q
5.5 9.5 4.356541541407054 0.
& I: P* z- L, d, p, F
5.5 10. 4.677786777828594 0.
8 S" E! W/ i& a1 J; J# t8 x+ v
6. 3. 3. 0.
; i0 ]. g3 o+ }3 B' x' \# S& {
6. 3. 5.999999999999999 0.
1 M) B0 d( G' D' N5 E
6. 3.5 2.745300211529266 0.
2 U: x& |$ e9 \* D7 L% j# g+ N
6. 3.5 7.649436630575996 0.
, x2 ]' o5 V E2 v2 w/ |
6. 4. 2.695165060747994 0.
# p; f: r! j: @" I, Q: I8 I) ^ d
6. 4. 8.904834939252005 0.
& f$ h( X+ \# F& u7 X7 C
6. 4.5 2.721364796483262 0.
3 {" B" P) e9 u5 y% k+ j
6. 4.5 9.92149234637388 0.
* A) M! V& K9 g8 C
6. 5. 2.78903116098082 0.
% R; T& D3 U# p5 r
6. 5.5 2.884119329429112 0.
% |5 ^4 m# @5 o2 H
6. 6. 3. 0.
' \. q1 p( N- x% Y& [" D
6. 6.5 3.133381054885423 0.
/ P9 |: I6 W* i0 I" C
6. 7. 3.282742465037893 0.
$ E( h( R, n( m% T' h
6. 7.5 3.447656821925362 2.273736754432321e-013
7 ?% O$ b# g+ G! K) Z4 f( o7 P
6. 8. 3.628486395311015 0.
/ D5 [! {7 l/ y0 o W9 Q
6. 8.5 3.826272163735232 0.
" R0 U6 D( g8 ^ o/ p& }) m
6. 9. 4.042747591121993 0.
5 s5 l2 V9 y- U' G3 l0 A4 ]$ z
6. 9.5 4.280465505524228 0.
7 K9 R' k* _ y2 y& ]4 b
6. 10. 4.543069137209136 0.
4 k t7 l/ E9 {" k9 g$ ^% R
6.5 3. 3.692013773129525 0.
" N' x: l% f( I$ i+ ^% e
6.5 3. 5.281670437396786 0.
9 t$ p6 n! H" l; _
6.5 3.5 3.073844239487251 0.
* K. L t; Q& g' [9 [0 d
6.5 3.5 7.401155760512746 0.
/ T+ c3 g$ r! m' {7 t2 l* V0 x; I
6.5 4. 2.938916502606827 0.
2 ?5 r5 I- M/ ^
6.5 4. 8.846797783107464 0.
, i& K2 m9 t9 k4 l q3 J! c
6.5 4.5 2.922185008548724 0.
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6.5 5. 2.961827475384206 0.
6 x, \$ P, L- H) u
6.5 5.5 3.035604845963813 0.
& x2 I5 v8 R X$ h3 X1 R1 v F- G0 O
6.5 6. 3.133381054885422 0.
$ @2 x% ?4 u* |7 P! G" C
6.5 6.5 3.25 0.
, C H3 d, n, l4 D" L2 Z
6.5 7. 3.382753896487015 0.
$ Q" W5 Z1 o9 Z
6.5 7.5 3.530313399868478 0.
. w$ Q# S5 e9 h4 m$ y$ e. H$ b
6.5 8. 3.692229149874506 0.
7 Q/ Q" S1 \3 r# N$ u
6.5 8.5 3.868693727795107 0.
) E M% A/ K4 x9 ~& x/ o
6.5 9. 4.060441442861232 0.
# [: U1 ~8 w' \7 r% {' {
6.5 9.5 4.268736592110795 0.
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6.5 10. 4.495435882583067 0.
4 C* D7 T* x! [0 _
7. 3.5 3.500000000000001 0.
9 `6 Y6 g' u, U: r6 }- Y) G
7. 3.5 7. 0.
j" K J9 j& U
7. 4. 3.223865764386255 0.
" h- k" e$ n8 _$ J+ O- K
7. 4. 8.685225144704656 0.
3 a/ H% m0 @8 x8 J" K2 i. E
7. 4.5 3.14900078022921 0.
p8 ^( J) S, |. u8 W0 \
7. 5. 3.154404956432853 0.
# x3 P5 M( H6 ?% g5 {5 |. W
7. 5.5 3.204083523261021 0.
/ |9 J/ i7 i. U
7. 6. 3.282742465037893 0.
7 \ S2 r/ W3 K8 E: ^: E* |
7. 6.5 3.382753896487015 0.
. B* U6 x. S/ I7 A+ z) c* Z
7. 7. 3.5 0.
8 f/ M9 v9 ? B% a `' S% I' J
7. 7.5 3.632214429249618 0.
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7. 8. 3.778224923088592 0.
# {$ o- F4 P0 |% w# A/ `: p6 T3 s
7. 8.5 3.93757894317775 0.
7 V: b) Y% K+ h% I" Z6 x/ T# o O
7. 9. 4.110354368226149 0.
1 B. `7 n" E2 Z1 E, ]
7. 9.5 4.297071556823225 0.
6 ~2 Y4 ]" R8 M* g
7. 10. 4.498670372630065 0.
, E" r3 v* \( G2 O: C9 L5 n
7.5 3.5 4.146248634662252 0.
6 S( e! N1 m: x& |
7.5 3.5 6.331024092610478 0.
- w( i; a. M2 d! R- B1 ~* U
7.5 4. 3.566387492405242 0.
( l0 r2 q3 j( p6 O# H% {
7.5 4. 8.411873377159969 0.
) s0 n0 H% G. e
7.5 4.5 3.407301852906851 0.
0 x. z0 Y5 @$ d6 e1 J
7.5 4.5 9.905198147093145 0.
. j( r8 T) s& I: G v' a5 \; o
7.5 5. 3.368956325934993 0.
9 x8 o4 P1 t4 m0 h9 ~0 W1 S
7.5 5.5 3.390173520212255 0.
. N" j V3 N% P' @; h- d& _' @
7.5 6. 3.447656821925362 0.
: S; p+ A4 a& H7 T2 V; ?! E" c
7.5 6.5 3.530313399868477 0.
/ v7 z+ t4 p6 }, [2 W5 }
7.5 7. 3.632214429249618 0.
* F" B2 y, U# F8 d P4 c- c+ @
7.5 7.5 3.750000000000003 0.
; X# d& [& ]0 C0 g
7.5 8. 3.881745401569135 0.
; P- H. @* y' E3 O
7.5 8.5 4.026409271112575 0.
( L9 l7 r( r4 D7 N, E
7.5 9. 4.183546741471229 0.
8 j: {' v( m# U- S( M/ ?' w7 M
7.5 9.5 4.353157178625922 0.
; H. O, u: \* ]% y! R
7.5 10. 4.535607994138771 0.
9 m3 h. I# |* N; w( z' j
8. 4. 4.000000000000002 0.
& |4 ?! C0 v0 G, M9 G3 ^" P
8. 4. 8. 0.
. C; u( o( K# S h. F0 C' [
8. 4.5 3.705986018674347 0.
) U6 D7 W7 e/ R4 X) k! E0 ^
8. 4.5 9.714013981325657 0.
: D. d; P1 _3 B' v( `5 X8 [
8. 5. 3.609045829068849 0.
3 t9 _$ Z W G! E( b
8. 5.5 3.595369279178607 0.
" E% i" {! K: y
8. 6. 3.628486395311016 0.
( V, ?; C% ^- ]# A$ N
8. 6.5 3.692229149874504 0.
1 Y- }, S2 X- [
8. 7. 3.77822492308859 0.
, ]; a' j7 o( j9 n# r0 c& b" J
8. 7.5 3.881745401569135 0.
: \. R! z9 s& V; b* o
8. 8. 4.000000000000003 0.
8 _- }: B- W! C
8. 8.5 4.131333821659408 0.
5 S/ {- i( J+ k* ?
8. 9. 4.274815705955503 0.
9 R$ O7 Z4 H1 }) A6 i2 ~. c; X
8. 9.5 4.430014593640446 0.
' G' t0 c( N% [: W& p2 O R
8. 10. 4.596875762567152 0.
/ U% W( t8 o- i% d0 L i, M
8.5 4. 4.618832614156823 0.
4 ^- Y1 @- g" \
8.5 4. 7.361167385843172 0.
9 @+ ]5 j" n+ s( O7 S$ z$ |: o
8.5 4.5 4.060312832145666 0.
- D. h! o, u; c- `+ g; Q7 ^
8.5 4.5 9.420456398623564 0.
5 c" M4 F) k: g$ }& l# t0 S
8.5 5. 3.880150804346178 0.
4 L8 E4 y& ?9 Y* w% k; b% r
8.5 5.5 3.822111065390603 0.
0 S8 c+ Z; U4 ^
8.5 6. 3.826272163735231 0.
' w5 m% Q3 k1 A+ y4 U
8.5 6.5 3.868693727795108 0.
1 ~0 e7 @1 d, F5 R6 K) U. ^6 r; l
8.5 7. 3.937578943177748 0.
+ K" |' Q; ^" F; W2 ^; r& ]/ u( X
8.5 7.5 4.026409271112575 0.
& D3 w/ n: X+ y( Y
8.5 8. 4.13133382165941 0.
& z/ Q7 g% _4 I7 g/ I0 m
8.5 8.5 4.25 0.
) m0 y( H$ V1 k% z D. N
8.5 9. 4.380969715903502 0.
; L6 L6 r4 z6 O3 [
8.5 9.5 4.523405444098199 0.
n% A# Q% H) W& R. Q
8.5 10. 4.676893219133843 0.
3 V( Z* W7 Y, y$ Z2 i7 H$ O- r
9. 4.5 4.499999999999997 0.
) ?# h$ F C. R8 N
9. 4.5 9.000000000000009 0.
0 S% N: c! b6 j+ ?" H. g
9. 5. 4.190822529142222 0.
4 ~+ }& { B Z7 X
9. 5.5 4.074041860443781 0.
/ k( v+ |# x$ E% h# L
9. 6. 4.042747591121993 0.
# R( W0 g' s& ]7 ?
9. 6.5 4.060441442861232 -4.547473508864641e-013
: C8 b! @. ~" }9 H( K
9. 7. 4.110354368226151 0.
3 p4 z0 w& e: A' J
9. 7.5 4.183546741471229 0.
' H9 W K/ ?( j- o
9. 8. 4.274815705955503 0.
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9. 8.5 4.380969715903502 0.
# E( R: Q3 r5 l
9. 9. 4.5 0.
3 n: Q S$ D8 y! H
9. 9.5 4.630645298521483 0.
) z( f* d: s. d/ {; Y; a( R
9. 10. 4.772148306899336 0.
7 b% `" X- Q* p2 o J" D
9.5 4.5 5.100326474258897 0.
q8 v" W' n7 a7 c
9.5 4.5 8.381816382883978 0.
. d" \. L& j( r: C8 {/ o' U
9.5 5. 4.555265557190406 0.
) L' X$ j3 L* B* N5 `8 P
9.5 5.5 4.356541541407055 0.
$ q& F+ S4 ^! q$ s, W* U9 N
9.5 6. 4.280465505524228 0.
, h G; C4 K' X k; K& P7 f: ~; s& ?, k
9.5 6.5 4.268736592110795 0.
; I+ U7 z4 e0 @( r+ D7 t
9.5 7. 4.297071556823221 0.
% {2 e! f6 s4 y0 q5 `5 s7 y7 E2 D
9.5 7.5 4.353157178625922 0.
( V% k. P! t7 j/ f) g5 c6 Y2 J
9.5 8. 4.430014593640445 0.
. f9 `0 r! X1 @9 E3 \, a* g7 Z7 s; o
9.5 8.5 4.523405444098199 0.
) L# o0 I: U, M7 N
9.5 9. 4.630645298521484 0.
$ q# h/ A, K$ u4 K) V8 W' t, O& Y! ~
9.5 9.5 4.75 0.
; @% {2 ` `. q: @; L
9.5 10. 4.880354401607461 0.
0 V# @; k: w! u. v( X/ w1 p+ X
10. 4.5 6.402193416458861 0.
5 B. C. s5 U: Z Z8 X$ ~+ q0 E s( k
10. 4.5 7.028841066299777 4.547473508864641e-013
4 u9 P6 W. @2 K+ U
10. 5. 4.999999999999997 0.
" W$ e8 c! F/ Q
10. 5. 10. 0.
- i( ~1 M' V) n# |9 x
10. 5.5 4.67778677782859 0.
/ c3 }" P9 X- v2 N% W$ O# t- P
10. 6. 4.543069137209136 0.
) k0 ?# V, y! g- y) f
10. 6.5 4.495435882583067 0.
$ z6 l8 \% ?5 V% f$ b
10. 7. 4.498670372630065 0.
0 Q- u$ T, r2 X% c
10. 7.5 4.535607994138771 0.
& o( ~5 g1 ?4 b h" p2 ?
10. 8. 4.596875762567152 0.
$ X q V6 `! D0 k1 A& _4 L
10. 8.5 4.676893219133843 0.
f1 m9 L; A2 {$ _+ w5 C
10. 9. 4.772148306899336 0.
: c$ B ?* Y/ c& P( ~6 |+ i6 J
10. 9.5 4.880354401607461 0.
3 Q1 {1 x3 w+ E8 K" K6 g! i
10. 10. 5. 0.
6 H f T- M! o
330.
3 h6 Z( Y( F& w: b4 I7 G' c) I
+ N8 b% x/ N1 U" {( N$ M0 ~- S
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！
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