MATLAB習(xí)題及答案

1、2. 用MATLAB語句輸入矩陣和3假設(shè)已知矩陣，試給出相應(yīng)的MATLAB命令，將其全部偶數(shù)行提取出來，賦給矩陣，用命令生成矩陣，用上述命令檢驗(yàn)一下結(jié)果是不是正確。4用數(shù)值方法可以求出，試不采用循環(huán)的形式求出和式的數(shù)值解。由于數(shù)值方法是采用double形式進(jìn)行計(jì)算的，難以保證有效位數(shù)字，所以結(jié)果不一定精確。試采用運(yùn)算的方法求該和式的精確值。5選擇合適的步距繪制出下面的圖形。（1），其中； （2），其中6. 試?yán)L制出二元函數(shù)的三維圖和三視圖7. 試求出如下極限。（1）； （2）； （3）8. 已知參數(shù)方程，試求出和9. 假設(shè)，試求10. 試求出下面的極限。 （1）；（2）11. 試求出以下的曲線

2、積分。 （1），為曲線， 。 （2），其中為正向上半橢圓。12. 試求出Vandermonde矩陣的行列式，并以最簡的形式顯示結(jié)果。13. 試對矩陣進(jìn)行Jordan變換，并得出變換矩陣。14. 試用數(shù)值方法和解析方法求取下面的Sylvester方程，并驗(yàn)證得出的結(jié)果。15. 假設(shè)已知矩陣如下，試求出，。第二部分?jǐn)?shù)學(xué)問題求解與數(shù)據(jù)處理(4 學(xué)時(shí))主要問題：掌握代數(shù)方程與最優(yōu)化問題、微分方程問題、數(shù)據(jù)處理問題的MATLAB 求解方法。1. 對下列的函數(shù)進(jìn)行Laplace變換。（1）；（2）；（3）2. 對下面的式進(jìn)行Laplace反變換。（1）；（2）；（3）。3. 試求出下面函數(shù)的Fourier

3、變換，對得出的結(jié)果再進(jìn)行Fourier反變換，觀察是否能得出原來函數(shù)。（1）；（2）。4. 請將下述時(shí)域序列函數(shù)進(jìn)行Z變換，并對結(jié)果進(jìn)行反變換檢驗(yàn)。（1）；（2）；（3）5. 用數(shù)值求解函數(shù)求解下述一元和二元方程的根，并對得出的結(jié)果進(jìn)行檢驗(yàn)。（1）；（2）6. 試求出使得取得極小值的值。7. 試求解下面的非線性規(guī)劃問題。 8. 求解下面的整數(shù)線性規(guī)劃問題。9. 試求出微分方程的解析解通解，并求出滿足邊界條件的解析解。10. 試求出下面微分方程的通解。（1）；（2）11. 考慮著名的化學(xué)反應(yīng)方程組，選定，且，繪制仿真結(jié)果的三維相軌跡，并得出其在x-y平面上的投影。在實(shí)際求解中建議將作為附加參數(shù)，

4、同樣的方程若設(shè)，時(shí)，繪制出狀態(tài)變量的二維圖和三維圖。12. 試選擇狀態(tài)變量，將下面的非線性微分方程組轉(zhuǎn)換成一階顯式微分方程組，并用 MATLAB對其求解，繪制出解的相平面或相空間曲線。13.考慮簡單的線性微分方程，且方程的初值為，試用Simulink搭建起系統(tǒng)的仿真模型，并繪制出仿真結(jié)果曲線。14. 用生成一組較稀疏的數(shù)據(jù)，并用一維數(shù)據(jù)插值的方法對給出的數(shù)據(jù)進(jìn)行曲線擬合，并將結(jié)果與理論曲線相比較。第一部分 第二題（1） A=1,2,3,4;4,3,2,1;2,3,4,1;3,2,4,1A = 1 2 3 4 4 3 2 1 2 3 4 1 3 2 4 1（2） B=1+4j,2+3j,3+2j

5、,4+1j;4+1j,3+2j,2+3j,1+4j;2+3j,3+2j,4+1j,1+4j;3+2j,2+3j,4+1j,1+4jB = 1.0000 + 4.0000i 2.0000 + 3.0000i 3.0000 + 2.0000i 4.0000 + 1.0000i 4.0000 + 1.0000i 3.0000 + 2.0000i 2.0000 + 3.0000i 1.0000 + 4.0000i 2.0000 + 3.0000i 3.0000 + 2.0000i 4.0000 + 1.0000i 1.0000 + 4.0000i 3.0000 + 2.0000i 2.0000 + 3

6、.0000i 4.0000 + 1.0000i 1.0000 + 4.0000i第三題 A=magic(8); B=A(2:2:end,:)B = 9 55 54 12 13 51 50 16 40 26 27 37 36 30 31 33 41 23 22 44 45 19 18 48 8 58 59 5 4 62 63 1第四題 i=0:63;s=sum(2.i)s = 1.8447e+019第五題（1） t=-1:0.001:1; y=sin(1./t);Warning: Divide by zero. plot(t,y)（2）t=-pi:0.05:-1.8,-1.799:0.001:-

7、1.2,-1.2:0.05:1.2,1.201:0.001:1.8,1.81:0.05:pi; y=sin(tan(t)-tan(sin(t); plot(t,y)第六題 xx=-2:0.1:-1.2,-1.1:0.02:-0.9,-0.8:0.1:0.8,0.9:0.02:1.1,1.2:0.1:2; yy=-1:0.1:-0.2,-0.1:0.02:0.1,0.2:0.1:1;x,y=meshgrid(xx,yy); z=1./(sqrt(1-x).2+y.2)+1./(sqrt(1+x).2+y.2);Warning: Divide by zero.Warning: Divide by

8、zero. subplot(224),surf(x,y,z) subplot(221),surf(x,y,z),view(0,90) subplot(222),surf(x,y,z),view(90,0) subplot(223),surf(x,y,z),view(0,0)第七題（1） syms x;f=(3x+9x)(1/x);l=limit(f,x,inf) l = 9（2） syms x y;f=x*y/(sqrt(x*y+1)-1);limit(limit(f,x,0),y,0) ans = 2（3） syms x y;f=(1-cos(x2+y2)*exp(x2+y2)/(x2+y2

9、);limit(limit(f,x,0),y,0) ans = 0第八題 syms t;x=log(cos(t);y=cos(t)-t*sin(t);diff(y,t)/diff(x,t) ans = -(-2*sin(t)-t*cos(t)/sin(t)*cos(t) f=diff(y,t,2)/diff(x,t,2);subs(f,t,sym(pi)/3) ans = 3/8-1/24*pi*3(1/2)第九題 syms x y t s=int(exp(-t2),t,0,x*y); x/y*diff(f,x,2)-2*diff(diff(f,x),y)+diff(f,y,2) ans =

10、2*x2*y2*exp(-x2*y2)-2*exp(-x2*y2)-2*x3*y*exp(-x2*y2) 第十題（1） syms k n;symsum(1/(2*k)2-1),k,1,inf) ans = 1/2 limit(symsum(1/(2*k)2-1),k,1,n),n,inf) ans = 1/2（2） limit(n*symsum(1/(n2+k*pi),k,1,n),n,inf) ans = 1第十一題（1） syms a t;x=a*(cos(t)+t*sin(t);y=a*(sin(t)-t*cos(t); f=x2+y2;I=int(f*sqrt(diff(x,t)2+d

11、iff(y,t)2),t,0,2*pi) I = 2*a2*pi2*(a2)(1/2)+4*a2*pi4*(a2)(1/2)（2） syms x y a b c t;x=c*cos(t)/a;y=c*sin(t)/b; P=y*x3+exp(y);Q=x*y3+x*exp(y)-2*y; ds=diff(x,t);diff(y,t);I=int(P Q*ds,t,0,pi) I = -2/15*c*(-2*c4+15*b4)/b4/a第十二題 syms a b c d e;A=vander(a b c d e) A = a4, a3, a2, a, 1 b4, b3, b2, b, 1 c4,

12、 c3, c2, c, 1 d4, d3, d2, d, 1 e4, e3, e2, e, 1 det(A),simple(ans) ans = a4*b3*c2*d-a4*b3*c2*e-a4*b3*d2*c+a4*b3*d2*e+a4*b3*e2*c-a4*b3*e2*d-a4*c3*b2*d+a4*c3*b2*e+a4*c3*d2*b-a4*c3*d2*e-a4*c3*e2*b+a4*c3*e2*d+a4*d3*b2*c-a4*d3*b2*e-a4*d3*c2*b+a4*d3*c2*e+a4*d3*e2*b-a4*d3*e2*c-a4*e3*b2*c+a4*e3*b2*d+a4*e3*c

13、2*b-a4*e3*c2*d-a4*e3*d2*b+a4*e3*d2*c-b4*a3*c2*d+b4*a3*c2*e+b4*a3*d2*c-b4*a3*d2*e-b4*a3*e2*c+b4*a3*e2*d+b4*c3*a2*d-b4*c3*a2*e-b4*c3*d2*a+b4*c3*d2*e+b4*c3*e2*a-b4*c3*e2*d-b4*d3*a2*c+b4*d3*a2*e+b4*d3*c2*a-b4*d3*c2*e-b4*d3*e2*a+b4*d3*e2*c+b4*e3*a2*c-b4*e3*a2*d-b4*e3*c2*a+b4*e3*c2*d+b4*e3*d2*a-b4*e3*d2*c

14、+c4*a3*b2*d-c4*a3*b2*e-c4*a3*d2*b+c4*a3*d2*e+c4*a3*e2*b-c4*a3*e2*d-c4*b3*a2*d+c4*b3*a2*e+c4*b3*d2*a-c4*b3*d2*e-c4*b3*e2*a+c4*b3*e2*d+c4*d3*a2*b-c4*d3*a2*e-c4*d3*b2*a+c4*d3*b2*e+c4*d3*e2*a-c4*d3*e2*b-c4*e3*a2*b+c4*e3*a2*d+c4*e3*b2*a-c4*e3*b2*d-c4*e3*d2*a+c4*e3*d2*b-d4*a3*b2*c+d4*a3*b2*e+d4*a3*c2*b-d4

15、*a3*c2*e-d4*a3*e2*b+d4*a3*e2*c+d4*b3*a2*c-d4*b3*a2*e-d4*b3*c2*a+d4*b3*c2*e+d4*b3*e2*a-d4*b3*e2*c-d4*c3*a2*b+d4*c3*a2*e+d4*c3*b2*a-d4*c3*b2*e-d4*c3*e2*a+d4*c3*e2*b+d4*e3*a2*b-d4*e3*a2*c-d4*e3*b2*a+d4*e3*b2*c+d4*e3*c2*a-d4*e3*c2*b+e4*a3*b2*c-e4*a3*b2*d-e4*a3*c2*b+e4*a3*c2*d+e4*a3*d2*b-e4*a3*d2*c-e4*b3

16、*a2*c+e4*b3*a2*d+e4*b3*c2*a-e4*b3*c2*d-e4*b3*d2*a+e4*b3*d2*c+e4*c3*a2*b-e4*c3*a2*d-e4*c3*b2*a+e4*c3*b2*d+e4*c3*d2*a-e4*c3*d2*b-e4*d3*a2*b+e4*d3*a2*c+e4*d3*b2*a-e4*d3*b2*c-e4*d3*c2*a+e4*d3*c2*b simplify: a4*b3*c2*d-a4*b3*c2*e-a4*b3*d2*c+a4*b3*d2*e+a4*b3*e2*c-a4*b3*e2*d-a4*c3*b2*d+a4*c3*b2*e+a4*c3*d2*

17、b-a4*c3*d2*e-a4*c3*e2*b+a4*c3*e2*d+a4*d3*b2*c-a4*d3*b2*e-a4*d3*c2*b+a4*d3*c2*e+a4*d3*e2*b-a4*d3*e2*c-a4*e3*b2*c+a4*e3*b2*d+a4*e3*c2*b-a4*e3*c2*d-a4*e3*d2*b+a4*e3*d2*c-b4*a3*c2*d+b4*a3*c2*e+b4*a3*d2*c-b4*a3*d2*e-b4*a3*e2*c+b4*a3*e2*d+b4*c3*a2*d-b4*c3*a2*e-b4*c3*d2*a+b4*c3*d2*e+b4*c3*e2*a-b4*c3*e2*d-b

18、4*d3*a2*c+b4*d3*a2*e+b4*d3*c2*a-b4*d3*c2*e-b4*d3*e2*a+b4*d3*e2*c+b4*e3*a2*c-b4*e3*a2*d-b4*e3*c2*a+b4*e3*c2*d+b4*e3*d2*a-b4*e3*d2*c+c4*a3*b2*d-c4*a3*b2*e-c4*a3*d2*b+c4*a3*d2*e+c4*a3*e2*b-c4*a3*e2*d-c4*b3*a2*d+c4*b3*a2*e+c4*b3*d2*a-c4*b3*d2*e-c4*b3*e2*a+c4*b3*e2*d+c4*d3*a2*b-c4*d3*a2*e-c4*d3*b2*a+c4*d

19、3*b2*e+c4*d3*e2*a-c4*d3*e2*b-c4*e3*a2*b+c4*e3*a2*d+c4*e3*b2*a-c4*e3*b2*d-c4*e3*d2*a+c4*e3*d2*b-d4*a3*b2*c+d4*a3*b2*e+d4*a3*c2*b-d4*a3*c2*e-d4*a3*e2*b+d4*a3*e2*c+d4*b3*a2*c-d4*b3*a2*e-d4*b3*c2*a+d4*b3*c2*e+d4*b3*e2*a-d4*b3*e2*c-d4*c3*a2*b+d4*c3*a2*e+d4*c3*b2*a-d4*c3*b2*e-d4*c3*e2*a+d4*c3*e2*b+d4*e3*a

20、2*b-d4*e3*a2*c-d4*e3*b2*a+d4*e3*b2*c+d4*e3*c2*a-d4*e3*c2*b+e4*a3*b2*c-e4*a3*b2*d-e4*a3*c2*b+e4*a3*c2*d+e4*a3*d2*b-e4*a3*d2*c-e4*b3*a2*c+e4*b3*a2*d+e4*b3*c2*a-e4*b3*c2*d-e4*b3*d2*a+e4*b3*d2*c+e4*c3*a2*b-e4*c3*a2*d-e4*c3*b2*a+e4*c3*b2*d+e4*c3*d2*a-e4*c3*d2*b-e4*d3*a2*b+e4*d3*a2*c+e4*d3*b2*a-e4*d3*b2*c

21、-e4*d3*c2*a+e4*d3*c2*b radsimp: a4*b3*c2*d-a4*b3*c2*e-a4*b3*d2*c+a4*b3*d2*e+a4*b3*e2*c-a4*b3*e2*d-a4*c3*b2*d+a4*c3*b2*e+a4*c3*d2*b-a4*c3*d2*e-a4*c3*e2*b+a4*c3*e2*d+a4*d3*b2*c-a4*d3*b2*e-a4*d3*c2*b+a4*d3*c2*e+a4*d3*e2*b-a4*d3*e2*c-a4*e3*b2*c+a4*e3*b2*d+a4*e3*c2*b-a4*e3*c2*d-a4*e3*d2*b+a4*e3*d2*c-b4*a

22、3*c2*d+b4*a3*c2*e+b4*a3*d2*c-b4*a3*d2*e-b4*a3*e2*c+b4*a3*e2*d+b4*c3*a2*d-b4*c3*a2*e-b4*c3*d2*a+b4*c3*d2*e+b4*c3*e2*a-b4*c3*e2*d-b4*d3*a2*c+b4*d3*a2*e+b4*d3*c2*a-b4*d3*c2*e-b4*d3*e2*a+b4*d3*e2*c+b4*e3*a2*c-b4*e3*a2*d-b4*e3*c2*a+b4*e3*c2*d+b4*e3*d2*a-b4*e3*d2*c+c4*a3*b2*d-c4*a3*b2*e-c4*a3*d2*b+c4*a3*d

23、2*e+c4*a3*e2*b-c4*a3*e2*d-c4*b3*a2*d+c4*b3*a2*e+c4*b3*d2*a-c4*b3*d2*e-c4*b3*e2*a+c4*b3*e2*d+c4*d3*a2*b-c4*d3*a2*e-c4*d3*b2*a+c4*d3*b2*e+c4*d3*e2*a-c4*d3*e2*b-c4*e3*a2*b+c4*e3*a2*d+c4*e3*b2*a-c4*e3*b2*d-c4*e3*d2*a+c4*e3*d2*b-d4*a3*b2*c+d4*a3*b2*e+d4*a3*c2*b-d4*a3*c2*e-d4*a3*e2*b+d4*a3*e2*c+d4*b3*a2*c

24、-d4*b3*a2*e-d4*b3*c2*a+d4*b3*c2*e+d4*b3*e2*a-d4*b3*e2*c-d4*c3*a2*b+d4*c3*a2*e+d4*c3*b2*a-d4*c3*b2*e-d4*c3*e2*a+d4*c3*e2*b+d4*e3*a2*b-d4*e3*a2*c-d4*e3*b2*a+d4*e3*b2*c+d4*e3*c2*a-d4*e3*c2*b+e4*a3*b2*c-e4*a3*b2*d-e4*a3*c2*b+e4*a3*c2*d+e4*a3*d2*b-e4*a3*d2*c-e4*b3*a2*c+e4*b3*a2*d+e4*b3*c2*a-e4*b3*c2*d-e4

25、*b3*d2*a+e4*b3*d2*c+e4*c3*a2*b-e4*c3*a2*d-e4*c3*b2*a+e4*c3*b2*d+e4*c3*d2*a-e4*c3*d2*b-e4*d3*a2*b+e4*d3*a2*c+e4*d3*b2*a-e4*d3*b2*c-e4*d3*c2*a+e4*d3*c2*b combine(trig): a4*b3*c2*d-a4*b3*c2*e-a4*b3*d2*c+a4*b3*d2*e+a4*b3*e2*c-a4*b3*e2*d-a4*c3*b2*d+a4*c3*b2*e+a4*c3*d2*b-a4*c3*d2*e-a4*c3*e2*b+a4*c3*e2*d+a

26、4*d3*b2*c-a4*d3*b2*e-a4*d3*c2*b+a4*d3*c2*e+a4*d3*e2*b-a4*d3*e2*c-a4*e3*b2*c+a4*e3*b2*d+a4*e3*c2*b-a4*e3*c2*d-a4*e3*d2*b+a4*e3*d2*c-b4*a3*c2*d+b4*a3*c2*e+b4*a3*d2*c-b4*a3*d2*e-b4*a3*e2*c+b4*a3*e2*d+b4*c3*a2*d-b4*c3*a2*e-b4*c3*d2*a+b4*c3*d2*e+b4*c3*e2*a-b4*c3*e2*d-b4*d3*a2*c+b4*d3*a2*e+b4*d3*c2*a-b4*d

27、3*c2*e-b4*d3*e2*a+b4*d3*e2*c+b4*e3*a2*c-b4*e3*a2*d-b4*e3*c2*a+b4*e3*c2*d+b4*e3*d2*a-b4*e3*d2*c+c4*a3*b2*d-c4*a3*b2*e-c4*a3*d2*b+c4*a3*d2*e+c4*a3*e2*b-c4*a3*e2*d-c4*b3*a2*d+c4*b3*a2*e+c4*b3*d2*a-c4*b3*d2*e-c4*b3*e2*a+c4*b3*e2*d+c4*d3*a2*b-c4*d3*a2*e-c4*d3*b2*a+c4*d3*b2*e+c4*d3*e2*a-c4*d3*e2*b-c4*e3*a

28、2*b+c4*e3*a2*d+c4*e3*b2*a-c4*e3*b2*d-c4*e3*d2*a+c4*e3*d2*b-d4*a3*b2*c+d4*a3*b2*e+d4*a3*c2*b-d4*a3*c2*e-d4*a3*e2*b+d4*a3*e2*c+d4*b3*a2*c-d4*b3*a2*e-d4*b3*c2*a+d4*b3*c2*e+d4*b3*e2*a-d4*b3*e2*c-d4*c3*a2*b+d4*c3*a2*e+d4*c3*b2*a-d4*c3*b2*e-d4*c3*e2*a+d4*c3*e2*b+d4*e3*a2*b-d4*e3*a2*c-d4*e3*b2*a+d4*e3*b2*c

29、+d4*e3*c2*a-d4*e3*c2*b+e4*a3*b2*c-e4*a3*b2*d-e4*a3*c2*b+e4*a3*c2*d+e4*a3*d2*b-e4*a3*d2*c-e4*b3*a2*c+e4*b3*a2*d+e4*b3*c2*a-e4*b3*c2*d-e4*b3*d2*a+e4*b3*d2*c+e4*c3*a2*b-e4*c3*a2*d-e4*c3*b2*a+e4*c3*b2*d+e4*c3*d2*a-e4*c3*d2*b-e4*d3*a2*b+e4*d3*a2*c+e4*d3*b2*a-e4*d3*b2*c-e4*d3*c2*a+e4*d3*c2*b factor: (c-d)

30、*(b-d)*(b-c)*(a-d)*(a-c)*(a-b)*(-d+e)*(e-c)*(e-b)*(e-a) expand: a4*b3*c2*d-a4*b3*c2*e-a4*b3*d2*c+a4*b3*d2*e+a4*b3*e2*c-a4*b3*e2*d-a4*c3*b2*d+a4*c3*b2*e+a4*c3*d2*b-a4*c3*d2*e-a4*c3*e2*b+a4*c3*e2*d+a4*d3*b2*c-a4*d3*b2*e-a4*d3*c2*b+a4*d3*c2*e+a4*d3*e2*b-a4*d3*e2*c-a4*e3*b2*c+a4*e3*b2*d+a4*e3*c2*b-a4*e3

31、*c2*d-a4*e3*d2*b+a4*e3*d2*c-b4*a3*c2*d+b4*a3*c2*e+b4*a3*d2*c-b4*a3*d2*e-b4*a3*e2*c+b4*a3*e2*d+b4*c3*a2*d-b4*c3*a2*e-b4*c3*d2*a+b4*c3*d2*e+b4*c3*e2*a-b4*c3*e2*d-b4*d3*a2*c+b4*d3*a2*e+b4*d3*c2*a-b4*d3*c2*e-b4*d3*e2*a+b4*d3*e2*c+b4*e3*a2*c-b4*e3*a2*d-b4*e3*c2*a+b4*e3*c2*d+b4*e3*d2*a-b4*e3*d2*c+c4*a3*b2

32、*d-c4*a3*b2*e-c4*a3*d2*b+c4*a3*d2*e+c4*a3*e2*b-c4*a3*e2*d-c4*b3*a2*d+c4*b3*a2*e+c4*b3*d2*a-c4*b3*d2*e-c4*b3*e2*a+c4*b3*e2*d+c4*d3*a2*b-c4*d3*a2*e-c4*d3*b2*a+c4*d3*b2*e+c4*d3*e2*a-c4*d3*e2*b-c4*e3*a2*b+c4*e3*a2*d+c4*e3*b2*a-c4*e3*b2*d-c4*e3*d2*a+c4*e3*d2*b-d4*a3*b2*c+d4*a3*b2*e+d4*a3*c2*b-d4*a3*c2*e-

33、d4*a3*e2*b+d4*a3*e2*c+d4*b3*a2*c-d4*b3*a2*e-d4*b3*c2*a+d4*b3*c2*e+d4*b3*e2*a-d4*b3*e2*c-d4*c3*a2*b+d4*c3*a2*e+d4*c3*b2*a-d4*c3*b2*e-d4*c3*e2*a+d4*c3*e2*b+d4*e3*a2*b-d4*e3*a2*c-d4*e3*b2*a+d4*e3*b2*c+d4*e3*c2*a-d4*e3*c2*b+e4*a3*b2*c-e4*a3*b2*d-e4*a3*c2*b+e4*a3*c2*d+e4*a3*d2*b-e4*a3*d2*c-e4*b3*a2*c+e4*

34、b3*a2*d+e4*b3*c2*a-e4*b3*c2*d-e4*b3*d2*a+e4*b3*d2*c+e4*c3*a2*b-e4*c3*a2*d-e4*c3*b2*a+e4*c3*b2*d+e4*c3*d2*a-e4*c3*d2*b-e4*d3*a2*b+e4*d3*a2*c+e4*d3*b2*a-e4*d3*b2*c-e4*d3*c2*a+e4*d3*c2*b combine: a4*b3*c2*d-a4*b3*c2*e-a4*b3*d2*c+a4*b3*d2*e+a4*b3*e2*c-a4*b3*e2*d-a4*c3*b2*d+a4*c3*b2*e+a4*c3*d2*b-a4*c3*d2

35、*e-a4*c3*e2*b+a4*c3*e2*d+a4*d3*b2*c-a4*d3*b2*e-a4*d3*c2*b+a4*d3*c2*e+a4*d3*e2*b-a4*d3*e2*c-a4*e3*b2*c+a4*e3*b2*d+a4*e3*c2*b-a4*e3*c2*d-a4*e3*d2*b+a4*e3*d2*c-b4*a3*c2*d+b4*a3*c2*e+b4*a3*d2*c-b4*a3*d2*e-b4*a3*e2*c+b4*a3*e2*d+b4*c3*a2*d-b4*c3*a2*e-b4*c3*d2*a+b4*c3*d2*e+b4*c3*e2*a-b4*c3*e2*d-b4*d3*a2*c+

36、b4*d3*a2*e+b4*d3*c2*a-b4*d3*c2*e-b4*d3*e2*a+b4*d3*e2*c+b4*e3*a2*c-b4*e3*a2*d-b4*e3*c2*a+b4*e3*c2*d+b4*e3*d2*a-b4*e3*d2*c+c4*a3*b2*d-c4*a3*b2*e-c4*a3*d2*b+c4*a3*d2*e+c4*a3*e2*b-c4*a3*e2*d-c4*b3*a2*d+c4*b3*a2*e+c4*b3*d2*a-c4*b3*d2*e-c4*b3*e2*a+c4*b3*e2*d+c4*d3*a2*b-c4*d3*a2*e-c4*d3*b2*a+c4*d3*b2*e+c4*

37、d3*e2*a-c4*d3*e2*b-c4*e3*a2*b+c4*e3*a2*d+c4*e3*b2*a-c4*e3*b2*d-c4*e3*d2*a+c4*e3*d2*b-d4*a3*b2*c+d4*a3*b2*e+d4*a3*c2*b-d4*a3*c2*e-d4*a3*e2*b+d4*a3*e2*c+d4*b3*a2*c-d4*b3*a2*e-d4*b3*c2*a+d4*b3*c2*e+d4*b3*e2*a-d4*b3*e2*c-d4*c3*a2*b+d4*c3*a2*e+d4*c3*b2*a-d4*c3*b2*e-d4*c3*e2*a+d4*c3*e2*b+d4*e3*a2*b-d4*e3*

38、a2*c-d4*e3*b2*a+d4*e3*b2*c+d4*e3*c2*a-d4*e3*c2*b+e4*a3*b2*c-e4*a3*b2*d-e4*a3*c2*b+e4*a3*c2*d+e4*a3*d2*b-e4*a3*d2*c-e4*b3*a2*c+e4*b3*a2*d+e4*b3*c2*a-e4*b3*c2*d-e4*b3*d2*a+e4*b3*d2*c+e4*c3*a2*b-e4*c3*a2*d-e4*c3*b2*a+e4*c3*b2*d+e4*c3*d2*a-e4*c3*d2*b-e4*d3*a2*b+e4*d3*a2*c+e4*d3*b2*a-e4*d3*b2*c-e4*d3*c2*

39、a+e4*d3*c2*b convert(exp): a4*b3*c2*d-a4*b3*c2*e-a4*b3*d2*c+a4*b3*d2*e+a4*b3*e2*c-a4*b3*e2*d-a4*c3*b2*d+a4*c3*b2*e+a4*c3*d2*b-a4*c3*d2*e-a4*c3*e2*b+a4*c3*e2*d+a4*d3*b2*c-a4*d3*b2*e-a4*d3*c2*b+a4*d3*c2*e+a4*d3*e2*b-a4*d3*e2*c-a4*e3*b2*c+a4*e3*b2*d+a4*e3*c2*b-a4*e3*c2*d-a4*e3*d2*b+a4*e3*d2*c-b4*a3*c2*

40、d+b4*a3*c2*e+b4*a3*d2*c-b4*a3*d2*e-b4*a3*e2*c+b4*a3*e2*d+b4*c3*a2*d-b4*c3*a2*e-b4*c3*d2*a+b4*c3*d2*e+b4*c3*e2*a-b4*c3*e2*d-b4*d3*a2*c+b4*d3*a2*e+b4*d3*c2*a-b4*d3*c2*e-b4*d3*e2*a+b4*d3*e2*c+b4*e3*a2*c-b4*e3*a2*d-b4*e3*c2*a+b4*e3*c2*d+b4*e3*d2*a-b4*e3*d2*c+c4*a3*b2*d-c4*a3*b2*e-c4*a3*d2*b+c4*a3*d2*e+c

41、4*a3*e2*b-c4*a3*e2*d-c4*b3*a2*d+c4*b3*a2*e+c4*b3*d2*a-c4*b3*d2*e-c4*b3*e2*a+c4*b3*e2*d+c4*d3*a2*b-c4*d3*a2*e-c4*d3*b2*a+c4*d3*b2*e+c4*d3*e2*a-c4*d3*e2*b-c4*e3*a2*b+c4*e3*a2*d+c4*e3*b2*a-c4*e3*b2*d-c4*e3*d2*a+c4*e3*d2*b-d4*a3*b2*c+d4*a3*b2*e+d4*a3*c2*b-d4*a3*c2*e-d4*a3*e2*b+d4*a3*e2*c+d4*b3*a2*c-d4*b

42、3*a2*e-d4*b3*c2*a+d4*b3*c2*e+d4*b3*e2*a-d4*b3*e2*c-d4*c3*a2*b+d4*c3*a2*e+d4*c3*b2*a-d4*c3*b2*e-d4*c3*e2*a+d4*c3*e2*b+d4*e3*a2*b-d4*e3*a2*c-d4*e3*b2*a+d4*e3*b2*c+d4*e3*c2*a-d4*e3*c2*b+e4*a3*b2*c-e4*a3*b2*d-e4*a3*c2*b+e4*a3*c2*d+e4*a3*d2*b-e4*a3*d2*c-e4*b3*a2*c+e4*b3*a2*d+e4*b3*c2*a-e4*b3*c2*d-e4*b3*d

43、2*a+e4*b3*d2*c+e4*c3*a2*b-e4*c3*a2*d-e4*c3*b2*a+e4*c3*b2*d+e4*c3*d2*a-e4*c3*d2*b-e4*d3*a2*b+e4*d3*a2*c+e4*d3*b2*a-e4*d3*b2*c-e4*d3*c2*a+e4*d3*c2*b convert(sincos): a4*b3*c2*d-a4*b3*c2*e-a4*b3*d2*c+a4*b3*d2*e+a4*b3*e2*c-a4*b3*e2*d-a4*c3*b2*d+a4*c3*b2*e+a4*c3*d2*b-a4*c3*d2*e-a4*c3*e2*b+a4*c3*e2*d+a4*d

44、3*b2*c-a4*d3*b2*e-a4*d3*c2*b+a4*d3*c2*e+a4*d3*e2*b-a4*d3*e2*c-a4*e3*b2*c+a4*e3*b2*d+a4*e3*c2*b-a4*e3*c2*d-a4*e3*d2*b+a4*e3*d2*c-b4*a3*c2*d+b4*a3*c2*e+b4*a3*d2*c-b4*a3*d2*e-b4*a3*e2*c+b4*a3*e2*d+b4*c3*a2*d-b4*c3*a2*e-b4*c3*d2*a+b4*c3*d2*e+b4*c3*e2*a-b4*c3*e2*d-b4*d3*a2*c+b4*d3*a2*e+b4*d3*c2*a-b4*d3*c

45、2*e-b4*d3*e2*a+b4*d3*e2*c+b4*e3*a2*c-b4*e3*a2*d-b4*e3*c2*a+b4*e3*c2*d+b4*e3*d2*a-b4*e3*d2*c+c4*a3*b2*d-c4*a3*b2*e-c4*a3*d2*b+c4*a3*d2*e+c4*a3*e2*b-c4*a3*e2*d-c4*b3*a2*d+c4*b3*a2*e+c4*b3*d2*a-c4*b3*d2*e-c4*b3*e2*a+c4*b3*e2*d+c4*d3*a2*b-c4*d3*a2*e-c4*d3*b2*a+c4*d3*b2*e+c4*d3*e2*a-c4*d3*e2*b-c4*e3*a2*b

46、+c4*e3*a2*d+c4*e3*b2*a-c4*e3*b2*d-c4*e3*d2*a+c4*e3*d2*b-d4*a3*b2*c+d4*a3*b2*e+d4*a3*c2*b-d4*a3*c2*e-d4*a3*e2*b+d4*a3*e2*c+d4*b3*a2*c-d4*b3*a2*e-d4*b3*c2*a+d4*b3*c2*e+d4*b3*e2*a-d4*b3*e2*c-d4*c3*a2*b+d4*c3*a2*e+d4*c3*b2*a-d4*c3*b2*e-d4*c3*e2*a+d4*c3*e2*b+d4*e3*a2*b-d4*e3*a2*c-d4*e3*b2*a+d4*e3*b2*c+d4

47、*e3*c2*a-d4*e3*c2*b+e4*a3*b2*c-e4*a3*b2*d-e4*a3*c2*b+e4*a3*c2*d+e4*a3*d2*b-e4*a3*d2*c-e4*b3*a2*c+e4*b3*a2*d+e4*b3*c2*a-e4*b3*c2*d-e4*b3*d2*a+e4*b3*d2*c+e4*c3*a2*b-e4*c3*a2*d-e4*c3*b2*a+e4*c3*b2*d+e4*c3*d2*a-e4*c3*d2*b-e4*d3*a2*b+e4*d3*a2*c+e4*d3*b2*a-e4*d3*b2*c-e4*d3*c2*a+e4*d3*c2*b convert(tan): a4*b3*c2*d-a4*b3*c2*e-a4*b3*d2*c+a4*b3*d2*e+a4*b3*e2*c-a4*b3*e2*d-a4*