2 MATLAB语句输入矩阵
3．假设已知矩阵试出相应MATLAB命令全部偶数行提取出赋矩阵命令生成矩阵述命令检验结果正确
4．数值方法求出试采循环形式求出式数值解数值方法采double形式进行计算难保证效位数字结果定精确试采运算方法求该式精确值
5．选择合适步距绘制出面图形
（1）中 （2）中
6 试绘制出二元函数三维图三视图
7 试求出极限
（1） （2） （3）
8 已知参数方程试求出
9 假设试求
10 试求出面极限
（1）
（2）
11 试求出曲线积分
（1）曲线
（2）中正半椭圆
12 试求出Vandermonde矩阵行列式简形式显示结果
13 试矩阵进行Jordan变换出变换矩阵
14 试数值方法解析方法求取面Sylvester方程验证出结果
15 假设已知矩阵试求出
第二部分数学问题求解数处理(4 学时)
问题：掌握代数方程优化问题微分方程问题数处理问题MATLAB 求解方法
1 列函数进行Laplace变换
（1）（2）（3）
2 面式进行Laplace反变换
（1）（2）
（3）
3 试求出面函数Fourier变换出结果进行Fourier反变换观察否出原函数
（1）（2）
4 请述时域序列函数进行Z变换结果进行反变换检验
（1）（2）（3）
5 数值求解函数求解述元二元方程根出结果进行检验
（1）（2）
6 试求出取极值值
7 试求解面非线性规划问题
8 求解面整数线性规划问题
9 试求出微分方程解析解通解求出满足边界条件解析解
10 试求出面微分方程通解
（1）（2）
11 考虑著名化学反应方程组选定绘制仿真结果三维相轨迹出xy面投影实际求解中建议作附加参数样方程设时绘制出状态变量二维图三维图
12 试选择状态变量面非线性微分方程组转换成阶显式微分方程组 MATLAB求解绘制出解相面相空间曲线
13考虑简单线性微分方程方程初值试Simulink搭建起系统仿真模型绘制出仿真结果曲线
14 生成组较稀疏数维数插值方法出数进行曲线拟合结果理曲线相较
第部分
第二题
（1）
>> A[1234432123413241]
A
1 2 3 4
4 3 2 1
2 3 4 1
3 2 4 1
（2）
>> B[1+4j2+3j3+2j4+1j4+1j3+2j2+3j1+4j2+3j3+2j4+1j1+4j3+2j2+3j4+1j1+4j]
B
10000 + 40000i 20000 + 30000i 30000 + 20000i 40000 + 10000i
40000 + 10000i 30000 + 20000i 20000 + 30000i 10000 + 40000i
20000 + 30000i 30000 + 20000i 40000 + 10000i 10000 + 40000i
30000 + 20000i 20000 + 30000i 40000 + 10000i 10000 + 40000i
第三题
>> Amagic(8)
>> BA(22end)
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
第四题
>> i063ssum(2^i)
s
18447e+019
第五题
（1）
>> t[100011]
>> ysin(1t)
Warning Divide by zero
>> plot(ty)
（2）
t[pi00518179900011212005121201000118181005pi]
>> ysin(tan(t))tan(sin(t))
>> plot(ty)
第六题
>> xx[201121100209080108090021112012]
>> yy[10102010020102011][xy]meshgrid(xxyy)
>> z1(sqrt((1x)^2+y^2))+1(sqrt((1+x)^2+y^2))
Warning Divide by zero
Warning Divide by zero
>> subplot(224)surf(xyz)
>> subplot(221)surf(xyz)view(090)
>> subplot(222)surf(xyz)view(900)
>> subplot(223)surf(xyz)view(00)
第七题
（1）>> syms xf(3^x+9^x)^(1x)llimit(fxinf)
l
9
（2）>> syms x yfx*y(sqrt(x*y+1)1)limit(limit(fx0)y0)
ans
2
（3）>> syms x yf(1cos(x^2+y^2))*exp(x^2+y^2)(x^2+y^2)limit(limit(fx0)y0)
ans
0
第八题
>> syms txlog(cos(t))ycos(t)t*sin(t)diff(yt)diff(xt)
ans
(2*sin(t)t*cos(t))sin(t)*cos(t)
>> fdiff(yt2)diff(xt2)subs(ftsym(pi)3)
ans
38124*pi*3^(12)
第九题
>> syms x y t
>> sint(exp(t^2)t0x*y)
>> xy*diff(fx2)2*diff(diff(fx)y)+diff(fy2)
ans
2*x^2*y^2*exp(x^2*y^2)2*exp(x^2*y^2)2*x^3*y*exp(x^2*y^2)
第十题
（1）
>> syms k nsymsum(1((2*k)^21)k1inf)
ans
12
>> limit(symsum(1((2*k)^21)k1n)ninf)
ans
12
（2）
>> limit(n*symsum(1(n^2+k*pi)k1n)ninf)
ans
1
第十题
（1）
>> syms a txa*(cos(t)+t*sin(t))ya*(sin(t)t*cos(t))
>> fx^2+y^2Iint(f*sqrt(diff(xt)^2+diff(yt)^2)t02*pi)
I
2*a^2*pi^2*(a^2)^(12)+4*a^2*pi^4*(a^2)^(12)
（2）
>> syms x y a b c txc*cos(t)ayc*sin(t)b
>> Py*x^3+exp(y)Qx*y^3+x*exp(y)2*y
>> ds[diff(xt)diff(yt)]Iint([P Q]*dst0pi)
I
215*c*(2*c^4+15*b^4)b^4a
第十二题
>> syms a b c d eAvander([a b c d e])
A
[ a^4 a^3 a^2 a 1]
[ b^4 b^3 b^2 b 1]
[ c^4 c^3 c^2 c 1]
[ d^4 d^3 d^2 d 1]
[ e^4 e^3 e^2 e 1]
>> det(A)simple(ans)
ans
a^4*b^3*c^2*da^4*b^3*c^2*ea^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*ca^4*b^3*e^2*da^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*ba^4*c^3*d^2*ea^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*ca^4*d^3*b^2*ea^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*ba^4*d^3*e^2*ca^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*ba^4*e^3*c^2*da^4*e^3*d^2*b+a^4*e^3*d^2*cb^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*cb^4*a^3*d^2*eb^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*db^4*c^3*a^2*eb^4*c^3*d^2*a+b^4*c^3*d^2*e+b^4*c^3*e^2*ab^4*c^3*e^2*db^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*ab^4*d^3*c^2*eb^4*d^3*e^2*a+b^4*d^3*e^2*c+b^4*e^3*a^2*cb^4*e^3*a^2*db^4*e^3*c^2*a+b^4*e^3*c^2*d+b^4*e^3*d^2*ab^4*e^3*d^2*c+c^4*a^3*b^2*dc^4*a^3*b^2*ec^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*bc^4*a^3*e^2*dc^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*ac^4*b^3*d^2*ec^4*b^3*e^2*a+c^4*b^3*e^2*d+c^4*d^3*a^2*bc^4*d^3*a^2*ec^4*d^3*b^2*a+c^4*d^3*b^2*e+c^4*d^3*e^2*ac^4*d^3*e^2*bc^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*ac^4*e^3*b^2*dc^4*e^3*d^2*a+c^4*e^3*d^2*bd^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*bd^4*a^3*c^2*ed^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*cd^4*b^3*a^2*ed^4*b^3*c^2*a+d^4*b^3*c^2*e+d^4*b^3*e^2*ad^4*b^3*e^2*cd^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*ad^4*c^3*b^2*ed^4*c^3*e^2*a+d^4*c^3*e^2*b+d^4*e^3*a^2*bd^4*e^3*a^2*cd^4*e^3*b^2*a+d^4*e^3*b^2*c+d^4*e^3*c^2*ad^4*e^3*c^2*b+e^4*a^3*b^2*ce^4*a^3*b^2*de^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*be^4*a^3*d^2*ce^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*ae^4*b^3*c^2*de^4*b^3*d^2*a+e^4*b^3*d^2*c+e^4*c^3*a^2*be^4*c^3*a^2*de^4*c^3*b^2*a+e^4*c^3*b^2*d+e^4*c^3*d^2*ae^4*c^3*d^2*be^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*ae^4*d^3*b^2*ce^4*d^3*c^2*a+e^4*d^3*c^2*b
simplify
a^4*b^3*c^2*da^4*b^3*c^2*ea^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*ca^4*b^3*e^2*da^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*ba^4*c^3*d^2*ea^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*ca^4*d^3*b^2*ea^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*ba^4*d^3*e^2*ca^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*ba^4*e^3*c^2*da^4*e^3*d^2*b+a^4*e^3*d^2*cb^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*cb^4*a^3*d^2*eb^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*db^4*c^3*a^2*eb^4*c^3*d^2*a+b^4*c^3*d^2*e+b^4*c^3*e^2*ab^4*c^3*e^2*db^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*ab^4*d^3*c^2*eb^4*d^3*e^2*a+b^4*d^3*e^2*c+b^4*e^3*a^2*cb^4*e^3*a^2*db^4*e^3*c^2*a+b^4*e^3*c^2*d+b^4*e^3*d^2*ab^4*e^3*d^2*c+c^4*a^3*b^2*dc^4*a^3*b^2*ec^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*bc^4*a^3*e^2*dc^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*ac^4*b^3*d^2*ec^4*b^3*e^2*a+c^4*b^3*e^2*d+c^4*d^3*a^2*bc^4*d^3*a^2*ec^4*d^3*b^2*a+c^4*d^3*b^2*e+c^4*d^3*e^2*ac^4*d^3*e^2*bc^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*ac^4*e^3*b^2*dc^4*e^3*d^2*a+c^4*e^3*d^2*bd^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*bd^4*a^3*c^2*ed^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*cd^4*b^3*a^2*ed^4*b^3*c^2*a+d^4*b^3*c^2*e+d^4*b^3*e^2*ad^4*b^3*e^2*cd^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*ad^4*c^3*b^2*ed^4*c^3*e^2*a+d^4*c^3*e^2*b+d^4*e^3*a^2*bd^4*e^3*a^2*cd^4*e^3*b^2*a+d^4*e^3*b^2*c+d^4*e^3*c^2*ad^4*e^3*c^2*b+e^4*a^3*b^2*ce^4*a^3*b^2*de^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*be^4*a^3*d^2*ce^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*ae^4*b^3*c^2*de^4*b^3*d^2*a+e^4*b^3*d^2*c+e^4*c^3*a^2*be^4*c^3*a^2*de^4*c^3*b^2*a+e^4*c^3*b^2*d+e^4*c^3*d^2*ae^4*c^3*d^2*be^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*ae^4*d^3*b^2*ce^4*d^3*c^2*a+e^4*d^3*c^2*b
radsimp
a^4*b^3*c^2*da^4*b^3*c^2*ea^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*ca^4*b^3*e^2*da^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*ba^4*c^3*d^2*ea^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*ca^4*d^3*b^2*ea^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*ba^4*d^3*e^2*ca^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*ba^4*e^3*c^2*da^4*e^3*d^2*b+a^4*e^3*d^2*cb^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*cb^4*a^3*d^2*eb^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*db^4*c^3*a^2*eb^4*c^3*d^2*a+b^4*c^3*d^2*e+b^4*c^3*e^2*ab^4*c^3*e^2*db^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*ab^4*d^3*c^2*eb^4*d^3*e^2*a+b^4*d^3*e^2*c+b^4*e^3*a^2*cb^4*e^3*a^2*db^4*e^3*c^2*a+b^4*e^3*c^2*d+b^4*e^3*d^2*ab^4*e^3*d^2*c+c^4*a^3*b^2*dc^4*a^3*b^2*ec^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*bc^4*a^3*e^2*dc^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*ac^4*b^3*d^2*ec^4*b^3*e^2*a+c^4*b^3*e^2*d+c^4*d^3*a^2*bc^4*d^3*a^2*ec^4*d^3*b^2*a+c^4*d^3*b^2*e+c^4*d^3*e^2*ac^4*d^3*e^2*bc^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*ac^4*e^3*b^2*dc^4*e^3*d^2*a+c^4*e^3*d^2*bd^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*bd^4*a^3*c^2*ed^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*cd^4*b^3*a^2*ed^4*b^3*c^2*a+d^4*b^3*c^2*e+d^4*b^3*e^2*ad^4*b^3*e^2*cd^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*ad^4*c^3*b^2*ed^4*c^3*e^2*a+d^4*c^3*e^2*b+d^4*e^3*a^2*bd^4*e^3*a^2*cd^4*e^3*b^2*a+d^4*e^3*b^2*c+d^4*e^3*c^2*ad^4*e^3*c^2*b+e^4*a^3*b^2*ce^4*a^3*b^2*de^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*be^4*a^3*d^2*ce^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*ae^4*b^3*c^2*de^4*b^3*d^2*a+e^4*b^3*d^2*c+e^4*c^3*a^2*be^4*c^3*a^2*de^4*c^3*b^2*a+e^4*c^3*b^2*d+e^4*c^3*d^2*ae^4*c^3*d^2*be^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*ae^4*d^3*b^2*ce^4*d^3*c^2*a+e^4*d^3*c^2*b
combine(trig)
a^4*b^3*c^2*da^4*b^3*c^2*ea^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*ca^4*b^3*e^2*da^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*ba^4*c^3*d^2*ea^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*ca^4*d^3*b^2*ea^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*ba^4*d^3*e^2*ca^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*ba^4*e^3*c^2*da^4*e^3*d^2*b+a^4*e^3*d^2*cb^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*cb^4*a^3*d^2*eb^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*db^4*c^3*a^2*eb^4*c^3*d^2*a+b^4*c^3*d^2*e+b^4*c^3*e^2*ab^4*c^3*e^2*db^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*ab^4*d^3*c^2*eb^4*d^3*e^2*a+b^4*d^3*e^2*c+b^4*e^3*a^2*cb^4*e^3*a^2*db^4*e^3*c^2*a+b^4*e^3*c^2*d+b^4*e^3*d^2*ab^4*e^3*d^2*c+c^4*a^3*b^2*dc^4*a^3*b^2*ec^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*bc^4*a^3*e^2*dc^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*ac^4*b^3*d^2*ec^4*b^3*e^2*a+c^4*b^3*e^2*d+c^4*d^3*a^2*bc^4*d^3*a^2*ec^4*d^3*b^2*a+c^4*d^3*b^2*e+c^4*d^3*e^2*ac^4*d^3*e^2*bc^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*ac^4*e^3*b^2*dc^4*e^3*d^2*a+c^4*e^3*d^2*bd^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*bd^4*a^3*c^2*ed^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*cd^4*b^3*a^2*ed^4*b^3*c^2*a+d^4*b^3*c^2*e+d^4*b^3*e^2*ad^4*b^3*e^2*cd^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*ad^4*c^3*b^2*ed^4*c^3*e^2*a+d^4*c^3*e^2*b+d^4*e^3*a^2*bd^4*e^3*a^2*cd^4*e^3*b^2*a+d^4*e^3*b^2*c+d^4*e^3*c^2*ad^4*e^3*c^2*b+e^4*a^3*b^2*ce^4*a^3*b^2*de^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*be^4*a^3*d^2*ce^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*ae^4*b^3*c^2*de^4*b^3*d^2*a+e^4*b^3*d^2*c+e^4*c^3*a^2*be^4*c^3*a^2*de^4*c^3*b^2*a+e^4*c^3*b^2*d+e^4*c^3*d^2*ae^4*c^3*d^2*be^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*ae^4*d^3*b^2*ce^4*d^3*c^2*a+e^4*d^3*c^2*b
factor
(cd)*(bd)*(bc)*(ad)*(ac)*(ab)*(d+e)*(ec)*(eb)*(ea)
expand
a^4*b^3*c^2*da^4*b^3*c^2*ea^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*ca^4*b^3*e^2*da^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*ba^4*c^3*d^2*ea^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*ca^4*d^3*b^2*ea^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*ba^4*d^3*e^2*ca^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*ba^4*e^3*c^2*da^4*e^3*d^2*b+a^4*e^3*d^2*cb^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*cb^4*a^3*d^2*eb^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*db^4*c^3*a^2*eb^4*c^3*d^2*a+b^4*c^3*d^2*e+b^4*c^3*e^2*ab^4*c^3*e^2*db^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*ab^4*d^3*c^2*eb^4*d^3*e^2*a+b^4*d^3*e^2*c+b^4*e^3*a^2*cb^4*e^3*a^2*db^4*e^3*c^2*a+b^4*e^3*c^2*d+b^4*e^3*d^2*ab^4*e^3*d^2*c+c^4*a^3*b^2*dc^4*a^3*b^2*ec^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*bc^4*a^3*e^2*dc^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*ac^4*b^3*d^2*ec^4*b^3*e^2*a+c^4*b^3*e^2*d+c^4*d^3*a^2*bc^4*d^3*a^2*ec^4*d^3*b^2*a+c^4*d^3*b^2*e+c^4*d^3*e^2*ac^4*d^3*e^2*bc^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*ac^4*e^3*b^2*dc^4*e^3*d^2*a+c^4*e^3*d^2*bd^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*bd^4*a^3*c^2*ed^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*cd^4*b^3*a^2*ed^4*b^3*c^2*a+d^4*b^3*c^2*e+d^4*b^3*e^2*ad^4*b^3*e^2*cd^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*ad^4*c^3*b^2*ed^4*c^3*e^2*a+d^4*c^3*e^2*b+d^4*e^3*a^2*bd^4*e^3*a^2*cd^4*e^3*b^2*a+d^4*e^3*b^2*c+d^4*e^3*c^2*ad^4*e^3*c^2*b+e^4*a^3*b^2*ce^4*a^3*b^2*de^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*be^4*a^3*d^2*ce^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*ae^4*b^3*c^2*de^4*b^3*d^2*a+e^4*b^3*d^2*c+e^4*c^3*a^2*be^4*c^3*a^2*de^4*c^3*b^2*a+e^4*c^3*b^2*d+e^4*c^3*d^2*ae^4*c^3*d^2*be^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*ae^4*d^3*b^2*ce^4*d^3*c^2*a+e^4*d^3*c^2*b
combine
a^4*b^3*c^2*da^4*b^3*c^2*ea^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*ca^4*b^3*e^2*da^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*ba^4*c^3*d^2*ea^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*ca^4*d^3*b^2*ea^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*ba^4*d^3*e^2*ca^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*ba^4*e^3*c^2*da^4*e^3*d^2*b+a^4*e^3*d^2*cb^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*cb^4*a^3*d^2*eb^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*db^4*c^3*a^2*eb^4*c^3*d^2*a+b^4*c^3*d^2*e+b^4*c^3*e^2*ab^4*c^3*e^2*db^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*ab^4*d^3*c^2*eb^4*d^3*e^2*a+b^4*d^3*e^2*c+b^4*e^3*a^2*cb^4*e^3*a^2*db^4*e^3*c^2*a+b^4*e^3*c^2*d+b^4*e^3*d^2*ab^4*e^3*d^2*c+c^4*a^3*b^2*dc^4*a^3*b^2*ec^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*bc^4*a^3*e^2*dc^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*ac^4*b^3*d^2*ec^4*b^3*e^2*a+c^4*b^3*e^2*d+c^4*d^3*a^2*bc^4*d^3*a^2*ec^4*d^3*b^2*a+c^4*d^3*b^2*e+c^4*d^3*e^2*ac^4*d^3*e^2*bc^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*ac^4*e^3*b^2*dc^4*e^3*d^2*a+c^4*e^3*d^2*bd^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*bd^4*a^3*c^2*ed^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*cd^4*b^3*a^2*ed^4*b^3*c^2*a+d^4*b^3*c^2*e+d^4*b^3*e^2*ad^4*b^3*e^2*cd^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*ad^4*c^3*b^2*ed^4*c^3*e^2*a+d^4*c^3*e^2*b+d^4*e^3*a^2*bd^4*e^3*a^2*cd^4*e^3*b^2*a+d^4*e^3*b^2*c+d^4*e^3*c^2*ad^4*e^3*c^2*b+e^4*a^3*b^2*ce^4*a^3*b^2*de^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*be^4*a^3*d^2*ce^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*ae^4*b^3*c^2*de^4*b^3*d^2*a+e^4*b^3*d^2*c+e^4*c^3*a^2*be^4*c^3*a^2*de^4*c^3*b^2*a+e^4*c^3*b^2*d+e^4*c^3*d^2*ae^4*c^3*d^2*be^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*ae^4*d^3*b^2*ce^4*d^3*c^2*a+e^4*d^3*c^2*b
convert(exp)
a^4*b^3*c^2*da^4*b^3*c^2*ea^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*ca^4*b^3*e^2*da^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*ba^4*c^3*d^2*ea^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*ca^4*d^3*b^2*ea^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*ba^4*d^3*e^2*ca^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*ba^4*e^3*c^2*da^4*e^3*d^2*b+a^4*e^3*d^2*cb^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*cb^4*a^3*d^2*eb^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*db^4*c^3*a^2*eb^4*c^3*d^2*a+b^4*c^3*d^2*e+b^4*c^3*e^2*ab^4*c^3*e^2*db^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*ab^4*d^3*c^2*eb^4*d^3*e^2*a+b^4*d^3*e^2*c+b^4*e^3*a^2*cb^4*e^3*a^2*db^4*e^3*c^2*a+b^4*e^3*c^2*d+b^4*e^3*d^2*ab^4*e^3*d^2*c+c^4*a^3*b^2*dc^4*a^3*b^2*ec^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*bc^4*a^3*e^2*dc^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*ac^4*b^3*d^2*ec^4*b^3*e^2*a+c^4*b^3*e^2*d+c^4*d^3*a^2*bc^4*d^3*a^2*ec^4*d^3*b^2*a+c^4*d^3*b^2*e+c^4*d^3*e^2*ac^4*d^3*e^2*bc^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*ac^4*e^3*b^2*dc^4*e^3*d^2*a+c^4*e^3*d^2*bd^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*bd^4*a^3*c^2*ed^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*cd^4*b^3*a^2*ed^4*b^3*c^2*a+d^4*b^3*c^2*e+d^4*b^3*e^2*ad^4*b^3*e^2*cd^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*ad^4*c^3*b^2*ed^4*c^3*e^2*a+d^4*c^3*e^2*b+d^4*e^3*a^2*bd^4*e^3*a^2*cd^4*e^3*b^2*a+d^4*e^3*b^2*c+d^4*e^3*c^2*ad^4*e^3*c^2*b+e^4*a^3*b^2*ce^4*a^3*b^2*de^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*be^4*a^3*d^2*ce^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*ae^4*b^3*c^2*de^4*b^3*d^2*a+e^4*b^3*d^2*c+e^4*c^3*a^2*be^4*c^3*a^2*de^4*c^3*b^2*a+e^4*c^3*b^2*d+e^4*c^3*d^2*ae^4*c^3*d^2*be^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*ae^4*d^3*b^2*ce^4*d^3*c^2*a+e^4*d^3*c^2*b
convert(sincos)
a^4*b^3*c^2*da^4*b^3*c^2*ea^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*ca^4*b^3*e^2*da^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*ba^4*c^3*d^2*ea^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*ca^4*d^3*b^2*ea^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*ba^4*d^3*e^2*ca^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*ba^4*e^3*c^2*da^4*e^3*d^2*b+a^4*e^3*d^2*cb^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*cb^4*a^3*d^2*eb^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*db^4*c^3*a^2*eb^4*c^3*d^2*a+b^4*c^3*d^2*e+b^4*c^3*e^2*ab^4*c^3*e^2*db^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*ab^4*d^3*c^2*eb^4*d^3*e^2*a+b^4*d^3*e^2*c+b^4*e^3*a^2*cb^4*e^3*a^2*db^4*e^3*c^2*a+b^4*e^3*c^2*d+b^4*e^3*d^2*ab^4*e^3*d^2*c+c^4*a^3*b^2*dc^4*a^3*b^2*ec^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*bc^4*a^3*e^2*dc^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*ac^4*b^3*d^2*ec^4*b^3*e^2*a+c^4*b^3*e^2*d+c^4*d^3*a^2*bc^4*d^3*a^2*ec^4*d^3*b^2*a+c^4*d^3*b^2*e+c^4*d^3*e^2*ac^4*d^3*e^2*bc^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*ac^4*e^3*b^2*dc^4*e^3*d^2*a+c^4*e^3*d^2*bd^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*bd^4*a^3*c^2*ed^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*cd^4*b^3*a^2*ed^4*b^3*c^2*a+d^4*b^3*c^2*e+d^4*b^3*e^2*ad^4*b^3*e^2*cd^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*ad^4*c^3*b^2*ed^4*c^3*e^2*a+d^4*c^3*e^2*b+d^4*e^3*a^2*bd^4*e^3*a^2*cd^4*e^3*b^2*a+d^4*e^3*b^2*c+d^4*e^3*c^2*ad^4*e^3*c^2*b+e^4*a^3*b^2*ce^4*a^3*b^2*de^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*be^4*a^3*d^2*ce^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*ae^4*b^3*c^2*de^4*b^3*d^2*a+e^4*b^3*d^2*c+e^4*c^3*a^2*be^4*c^3*a^2*de^4*c^3*b^2*a+e^4*c^3*b^2*d+e^4*c^3*d^2*ae^4*c^3*d^2*be^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*ae^4*d^3*b^2*ce^4*d^3*c^2*a+e^4*d^3*c^2*b
convert(tan)
a^4*b^3*c^2*da^4*b^3*c^2*ea^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*ca^4*b^3*e^2*da^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*ba^4*c^3*d^2*ea^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*ca^4*d^3*b^2*ea^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*ba^4*d^3*e^2*ca^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*ba^4*e^3*c^2*da^4*e^3*d^2*b+a^4*e^3*d^2*cb^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*cb^4*a^3*d^2*eb^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*db^4*c^3*a^2*eb^4*c^3*d^2*a+b^4*c^3*d^2*e+b^4*c^3*e^2*ab^4*c^3*e^2*db^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*ab^4*d^3*c^2*eb^4*d^3*e^2*a+b^4*d^3*e^2*c+b^4*e^3*a^2*cb^4*e^3*a^2*db^4*e^3*c^2*a+b^4*e^3*c^2*d+b^4*e^3*d^2*ab^4*e^3*d^2*c+c^4*a^3*b^2*dc^4*a^3*b^2*ec^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*bc^4*a^3*e^2*dc^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*ac^4*b^3*d^2*ec^4*b^3*e^2*a+c^4*b^3*e^2*d+c^4*d^3*a^2*bc^4*d^3*a^2*ec^4*d^3*b^2*a+c^4*d^3*b^2*e+c^4*d^3*e^2*ac^4*d^3*e^2*bc^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*ac^4*e^3*b^2*dc^4*e^3*d^2*a+c^4*e^3*d^2*bd^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*bd^4*a^3*c^2*ed^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*cd^4*b^3*a^2*ed^4*b^3*c^2*a+d^4*b^3*c^2*e+d^4*b^3*e^2*ad^4*b^3*e^2*cd^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*ad^4*c^3*b^2*ed^4*c^3*e^2*a+d^4*c^3*e^2*b+d^4*e^3*a^2*bd^4*e^3*a^2*cd^4*e^3*b^2*a+d^4*e^3*b^2*c+d^4*e^3*c^2*ad^4*e^3*c^2*b+e^4*a^3*b^2*ce^4*a^3*b^2*de^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*be^4*a^3*d^2*ce^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*ae^4*b^3*c^2*de^4*b^3*d^2*a+e^4*b^3*d^2*c+e^4*c^3*a^2*be^4*c^3*a^2*de^4*c^3*b^2*a+e^4*c^3*b^2*d+e^4*c^3*d^2*ae^4*c^3*d^2*be^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*ae^4*d^3*b^2*ce^4*d^3*c^2*a+e^4*d^3*c^2*b
collect(e)
a^4*b^3*c^2*da^4*b^3*d^2*ca^4*c^3*b^2*d+a^4*c^3*d^2*b+a^4*d^3*b^2*ca^4*d^3*c^2*bb^4*a^3*c^2*d+b^4*a^3*d^2*c+b^4*c^3*a^2*db^4*c^3*d^2*ab^4*d^3*a^2*c+b^4*d^3*c^2*a+c^4*a^3*b^2*dc^4*a^3*d^2*bc^4*b^3*a^2*d+c^4*b^3*d^2*a+c^4*d^3*a^2*bc^4*d^3*b^2*ad^4*a^3*b^2*c+d^4*a^3*c^2*b+d^4*b^3*a^2*cd^4*b^3*c^2*ad^4*c^3*a^2*b+d^4*c^3*b^2*a+(a^3*b^2*ca^3*b^2*da^3*c^2*b+a^3*c^2*d+a^3*d^2*ba^3*d^2*cb^3*a^2*c+b^3*a^2*d+b^3*c^2*ab^3*c^2*db^3*d^2*a+b^3*d^2*c+c^3*a^2*bc^3*a^2*dc^3*b^2*a+c^3*b^2*d+c^3*d^2*ac^3*d^2*bd^3*a^2*b+d^3*a^2*c+d^3*b^2*ad^3*b^2*cd^3*c^2*a+d^3*c^2*b)*e^4+(a^4*b^2*cc^4*d*b^2c^4*d^2*a+c^4*d^2*b+a^4*b^2*d+a^4*c^2*ba^4*c^2*dc^4*a^2*b+c^4*a^2*d+c^4*b^2*a+b^4*a^2*cb^4*a^2*db^4*c^2*a+c^2*d*b^4+b^4*d^2*ad^2*c*b^4a^4*d^2*b+a^4*d^2*c+d^4*a^2*bd^4*a^2*cd^4*b^2*a+c*d^4*b^2+d^4*c^2*ac^2*d^4*b)*e^3+(b^4*a^3*dc^4*b^3*aa^4*c^3*bc*d^4*b^3+c^4*d*b^3a^4*b^3*db^4*a^3*c+a^4*c^3*d+a^4*b^3*ca^4*d^3*cc^3*d*b^4+d^4*b^3*a+a^4*d^3*b+b^4*c^3*ac^4*a^3*dd^4*a^3*b+c^4*d^3*a+c^4*a^3*bc^4*d^3*bb^4*d^3*a+c*d^3*b^4+d^4*a^3*cd^4*c^3*a+c^3*d^4*b)*e^2+(a^4*b^3*d^2+c^4*a^3*d^2b^4*c^3*a^2a^4*b^3*c^2+a^4*d^3*c^2+d^4*c^3*a^2c^4*d^2*b^3a^4*c^3*d^2+c^4*d^3*b^2+c^4*b^3*a^2c^4*d^3*a^2a^4*d^3*b^2b^4*a^3*d^2+b^4*d^3*a^2+b^4*a^3*c^2c^3*d^4*b^2d^4*a^3*c^2+c^2*d^4*b^3+a^4*c^3*b^2+c^3*d^2*b^4c^2*d^3*b^4c^4*a^3*b^2+d^4*a^3*b^2d^4*b^3*a^2)*e
mwcos2sin
a^4*b^3*c^2*da^4*b^3*c^2*ea^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*ca^4*b^3*e^2*da^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*ba^4*c^3*d^2*ea^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*ca^4*d^3*b^2*ea^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*ba^4*d^3*e^2*ca^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*ba^4*e^3*c^2*da^4*e^3*d^2*b+a^4*e^3*d^2*cb^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*cb^4*a^3*d^2*eb^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*db^4*c^3*a^2*eb^4*c^3*d^2*a+b^4*c^3*d^2*e+b^4*c^3*e^2*ab^4*c^3*e^2*db^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*ab^4*d^3*c^2*eb^4*d^3*e^2*a+b^4*d^3*e^2*c+b^4*e^3*a^2*cb^4*e^3*a^2*db^4*e^3*c^2*a+b^4*e^3*c^2*d+b^4*e^3*d^2*ab^4*e^3*d^2*c+c^4*a^3*b^2*dc^4*a^3*b^2*ec^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*bc^4*a^3*e^2*dc^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*ac^4*b^3*d^2*ec^4*b^3*e^2*a+c^4*b^3*e^2*d+c^4*d^3*a^2*bc^4*d^3*a^2*ec^4*d^3*b^2*a+c^4*d^3*b^2*e+c^4*d^3*e^2*ac^4*d^3*e^2*bc^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*ac^4*e^3*b^2*dc^4*e^3*d^2*a+c^4*e^3*d^2*bd^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*bd^4*a^3*c^2*ed^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*cd^4*b^3*a^2*ed^4*b^3*c^2*a+d^4*b^3*c^2*e+d^4*b^3*e^2*ad^4*b^3*e^2*cd^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*ad^4*c^3*b^2*ed^4*c^3*e^2*a+d^4*c^3*e^2*b+d^4*e^3*a^2*bd^4*e^3*a^2*cd^4*e^3*b^2*a+d^4*e^3*b^2*c+d^4*e^3*c^2*ad^4*e^3*c^2*b+e^4*a^3*b^2*ce^4*a^3*b^2*de^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*be^4*a^3*d^2*ce^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*ae^4*b^3*c^2*de^4*b^3*d^2*a+e^4*b^3*d^2*c+e^4*c^3*a^2*be^4*c^3*a^2*de^4*c^3*b^2*a+e^4*c^3*b^2*d+e^4*c^3*d^2*ae^4*c^3*d^2*be^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*ae^4*d^3*b^2*ce^4*d^3*c^2*a+e^4*d^3*c^2*b
ans
(cd)*(bd)*(bc)*(ad)*(ac)*(ab)*(d+e)*(ec)*(eb)*(ea)
>>
第十三题
>> A[2050505015050520545052122][V J]jordan(sym(A))
V
[ 0 12 12 14]
[ 0 0 12 1]
[ 14 12 12 14]
[ 14 12 1 14]
J
[ 4 0 0 0]
[ 0 2 1 0]
[ 0 0 2 1]
[ 0 0 0 2]
第十四题
数值方法
>> A[3640514224636731310011004034]
>> B[321292219]
>> C[211412561644663]
>> Xlyap(ABC)
X
23192 04678 01505
36284 01579 00629
54246 10516 05090
05718 25848 03649
30417 06265 01580
>> norm(A*X+X*B+C)
ans
38830e014
解析方法
>> edit
function Xlyap(ABC)
if nargin2CBBA＇end
[nrnc]size(C)A0kron(Aeye(nc))+kron(eye(nr)B＇)
try
C1C＇x0inv(A0)*C1()Xreshape(x0ncnr)＇
catcherror(＇singular matrix found＇)end
>> A[3640514224636731310011004034]
>> B[321292219]
>> C[211412561644663]Xlyap(sym(A)BC)
X
[ 434641749950107136516451 4664546747350321409549353 503105815912321409549353]
[ 3809507498107136516451 8059112319373321409549353 880921527508321409549353]
[ 1016580400173107136516451 8334897743767321409549353 1419901706449321409549353]
[ 288938859984107136516451 6956912657222321409549353 927293592476321409549353]
[ 827401644798107136516451 10256166034813321409549353 1209595497577321409549353]
>> A*X+X*B+C
ans
[ 0 0 0]
[ 0 0 0]
[ 0 0 0]
[ 0 0 0]
[ 0 0 0]
第十五题
（1）
>> A[4500515054050515125150113]
>> Asym(A)syms t
>> expm(A*t)
ans
[ 12*exp(3*t)12*t*exp(3*t)+12*exp(5*t)+12*t^2*exp(3*t) 12*exp(5*t)12*exp(3*t)+t*exp(3*t) 12*t*exp(3*t)+12*t^2*exp(3*t) 12*exp(5*t)12*exp(3*t)12*t*exp(3*t)+12*t^2*exp(3*t)]
[ 12*t*exp(3*t)+12*exp(5*t)12*exp(3*t) 12*exp(3*t)+12*exp(5*t) 12*t*exp(3*t) 12*t*exp(3*t)+12*exp(5*t)12*exp(3*t)]
[ 12*t*exp(3*t)12*exp(5*t)+12*exp(3*t) 12*exp(5*t)+12*exp(3*t) exp(3*t)+12*t*exp(3*t) 12*t*exp(3*t)12*exp(5*t)+12*exp(3*t)]
[ 12*t^2*exp(3*t) t*exp(3*t) 12*t^2*exp(3*t)t*exp(3*t) exp(3*t)12*t^2*exp(3*t)]
(2)
>> A[4500515054050515125150113]
>> Asym(A)syms t
>> sin(A*t)
ans
[ sin(92*t) 0 sin(12*t) sin(32*t)]
[ sin(12*t) sin(4*t) sin(12*t) sin(12*t)]
[ sin(32*t) sin(t) sin(52*t) sin(32*t)]
[ 0 sin(t) sin(t) sin(3*t)]
(3)
第二部分
第题
（1）
>> syms a tfsin(a*t)tlaplace(f)
ans
atan(as)
（2）
>> syms t aft^5*sin(a*t)laplace(f)
ans
60*i*(1(si*a)^6+1(s+i*a)^6)
（3）
>> syms t aft^8*cos(a*t)laplace(f)
ans
20160(si*a)^9+20160(s+i*a)^9
第二题
（1）
>> syms s a bF1(s^2*(s^2a^2)*(a+b))ilaplace(F)
ans
1(a+b)*(1a^2*t+1a^3*sinh(a*t))
（2）
>> syms s a bFsqrt(sa)sqrt(sb)ilaplace(F)
ans
12t^(32)pi^(12)*(exp(b*t)exp(a*t))
（3）
>> syms s a bFlog((sa)(sb))ilaplace(F)
ans
1t*(exp(b*t)exp(a*t))
第三题
（1）
>> syms xfx^2*(3*sym(pi)2*abs(x))Ffourier(f)
F
6*(4+pi^2*dirac(2w)*w^4)w^4
>> ifourier(F)
ans
x^2*(4*x*heaviside(x)+3*pi+2*x)
（2）
>> syms tft^2*(t2*sym(pi))^2Ffourier(f)
F
2*pi*(4*pi^2*dirac(2w)+4*i*pi*dirac(3w)+dirac(4w))
>> ifourier(F)
ans
x^2*(2*pi+x)^2
第四题
（1）
>> syms k a Tfcos(k*a*T)Fztrans(f)
F
(zcos(a*T))*z(z^22*z*cos(a*T)+1)
>> f1iztrans(F)
f1
cos(a*T*n)
（2）
>> syms k T af(k*T)^2*exp(a*k*T)Fztrans(f)
F
T^2*z*exp(a*T)*(z+exp(a*T))(zexp(a*T))^3
>> f1iztrans(F)
f1
T^2*(1exp(a*T))^n*n^2
（3）
>> syms a k Tf(a*k*T1+exp(a*k*T))aFztrans(f)
F
1a*(a*T*z(z1)^2z(z1)+zexp(a*T)(zexp(a*T)1))
>> iztrans(F)
ans
((1exp(a*T))^n+a*T*n1)a
第五题
（1）
>> syms xx1solve(＇exp((x+1)^2+pi2)*sin(5*x+2)＇)
x1
25
>> subs(＇exp((x+1)^2+pi2)*sin(5*x+2)＇xx1)
ans
0
>> finline(＇exp((x+1)^2+pi2)*sin(5*x+2)＇＇x＇)
>> x2fsolve(f0)
Optimization terminated firstorder optimality is less than optionsTolFun
x2
02283
>> subs(＇exp((x+1)^2+pi2)*sin(5*x+2)＇xx2)
ans
47509e008
（2）
>> syms xy1solve(＇(x^2+y^2+x*y)*exp(x^2y^2x*y)0＇＇y＇)
y1
(12+12*i*3^(12))*x
(1212*i*3^(12))*x
>> y2simple(subs(＇(x^2+y^2+x*y)*exp(x^2y*2x*y)＇＇y＇y1))
y2
0
0
第六题
>> syms x cyint((exp(x)c*x)^2x01)
y
12*exp(1)^2+13*c^2122*c
>> edit
function yf(c)
y12*exp(1)^2+13*c122*c
>> xfminsearch(＇f＇0)
x
31691e+026
>> ezplot(y[05])
第七题
>> edit
function yf1(x)
yexp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+1)
function [cce]f2(x)
ce[]
c[x(1)+x(2)x(1)*x(2)x(1)x(2)+1510x(1)*x(2)]
>> edit
>> A[]B[]Aeq[]Beq[]xm[1010]xM[1010]
>> x0(xm+xM)2
>> ffoptimsetffTolX1e10ffTolFun1e20
>> xfmincon(＇f1＇x0ABAeqBeqxmxM＇f2＇ff)
Maximum number of function evaluations exceeded
increase OPTIONSMaxFunEvals
x
04195
04195
>> i1xx0
>> while (1)
[xab]fmincon(＇f1＇xABAeqBeqxmxM＇f2＇ff)
if b>0breakend
ii+1
end
>> xi
x
11825
17398
i
5
第八题
function yf3 (x)
y(592*x(1)+381*x(2)+273*x(3)+55*x(4)+48*x(5)+37*x(6)+23*x(7))
function [cceq]f4(x)
c[]ceq[]
>> A[353423561767589528451304]B119567
intlistones(71)Aeq[]Beq[]
xmzeros(71)xMinf*ones(71)x0zeros(71)
ffoptimsetffTolFun1e6ffTolX1e6ffTolCon1e20
ffMaxSQPIter1000settings[0]
ix(intlist1)xm(ix)ceil(xm(ix))xM(ix)floor(xM(ix))
[errmsgfx]bnb20(＇f3＇x0intlistxmxMABAeqBeqf4 settingsff)
if length(errmsg)0xround(x)end
x
32
2
1
0
0
0
0
第九题
>> syms x
>> ydsolve(＇D2y(21x)*Dy+(11x)*yx^2*exp(5*x)＇＇x＇)
y
exp(x)*C2+exp(x)*log(x)*C1+1216*Ei(16*x)*exp(x)+111296*exp(5*x)+5216*exp(5*x)*x+136*x^2*exp(5*x)
>> syms x
>> ydsolve(＇D2y(21x)*Dy+(11x)*yx^2*exp(5*x)＇＇y(1)sym(pi)＇＇y(sym(pi))1＇＇x＇)
y
11296*exp(x)*(1296*sym(pi)*exp(5)+6*exp(6)*Ei(16)+77)exp(1)exp(5)11296*exp(x)*log(x)*(1296*exp(1)*exp(5)+1296*exp(sym(pi))*sym(pi)*exp(5)6*exp(sym(pi))*exp(6)*Ei(16)77*exp(sym(pi))+6*exp(5*sym(pi))*exp(6*sym(pi))*Ei(16*sym(pi))*exp(1)*exp(5)+11*exp(5*sym(pi))*exp(1)*exp(5)+30*exp(5*sym(pi))*sym(pi)*exp(1)*exp(5)+36*exp(5*sym(pi))*sym(pi)^2*exp(1)*exp(5))exp(sym(pi))log(sym(pi))exp(1)exp(5)+11296*(6*exp(6*x)*Ei(16*x)+11+30*x+36*x^2)*exp(5*x)
第十题
>> syms t
>> xdsolve(＇D2x+2*t*Dx+t^2*xt+1＇)
x
exp(t12*t^2)*C2+exp(t12*t^2)*C112*i*pi^(12)*2^(12)*erf(12*i*2^(12)*(1+t))*exp(12+t12*t^2)
>> syms x
>> ydsolve(＇Dy+2*x*yx*exp(x^2)＇＇x＇)
y
12*(x^2+2*C1)*exp(x^2)
第十题
>> finline(＇[x(2)x(3)x(1)+a*x(2)b+(x(1)c)*x(3)]＇＇t＇＇x＇＇flag＇＇a＇＇b＇＇c＇)
>> [tx]ode45(f[0100][000][]020257)
>> plot3(x(1)x(2)x(3))grid
>> [tx]ode45(f[0100][000][]020510)
>> plot3(x(1)x(2)x(3))grid
第十二题
>> finline([＇[x(2)x(1)x(3)(3*x(2))^2+(x(4))^3+6*x(5)+2*t＇＇x(4)x(5)x(5)x(2)exp(x(1))t]＇]＇t＇＇x＇)
>> [t1x1]ode45(f[10][24276]＇)
>> [t2x2]ode45(f[12][24276]＇)
>> t[t1(end11)t2]x[x1(end11)x2]
>> plot(tx)
>> figureplot(x(1)x(3))
第十三题
>> [txy]sim(＇yws＇[010])plot(tx)
>> figureplot(ty)
第十四题
>> t0022
>> yt^2*exp(5*t)*sin(t)plot(ty＇o＇)
>> ezplot(＇t^2*exp(5*t)*sin(t)＇[02])hold on
>> x100012y1interp1(tyx1＇spline＇)
>> plot(x1y1)
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3．假设已知矩阵试出相应MATLAB命令全部偶数行提取出赋矩阵命令生成矩阵述命令检验结果正确
4．数值方法求出试采循环形式求出式数值解数值方法采double形式进行计算难保证效位数字结果定精确试采运算方法求该式精确值
5．选择合适步距绘制出面图形
（1）中 （2）中
6 试绘制出二元函数三维图三视图
7 试求出极限
（1） （2） （3）
8 已知参数方程试求出
9 假设试求
10 试求出面极限
（1）
（2）
11 试求出曲线积分
（1）曲线
（2）中正半椭圆
12 试求出Vandermonde矩阵行列式简形式显示结果
13 试矩阵进行Jordan变换出变换矩阵
14 试数值方法解析方法求取面Sylvester方程验证出结果
15 假设已知矩阵试求出
第二部分数学问题求解数处理(4 学时)
问题：掌握代数方程优化问题微分方程问题数处理问题MATLAB 求解方法
1 列函数进行Laplace变换
（1）（2）（3）
2 面式进行Laplace反变换
（1）（2）
（3）
3 试求出面函数Fourier变换出结果进行Fourier反变换观察否出原函数
（1）（2）
4 请述时域序列函数进行Z变换结果进行反变换检验
（1）（2）（3）
5 数值求解函数求解述元二元方程根出结果进行检验
（1）（2）
6 试求出取极值值
7 试求解面非线性规划问题
8 求解面整数线性规划问题
9 试求出微分方程解析解通解求出满足边界条件解析解
10 试求出面微分方程通解
（1）（2）
11 考虑著名化学反应方程组选定绘制仿真结果三维相轨迹出xy面投影实际求解中建议作附加参数样方程设时绘制出状态变量二维图三维图
12 试选择状态变量面非线性微分方程组转换成阶显式微分方程组 MATLAB求解绘制出解相面相空间曲线
13考虑简单线性微分方程方程初值试Simulink搭建起系统仿真模型绘制出仿真结果曲线
14 生成组较稀疏数维数插值方法出数进行曲线拟合结果理曲线相较
第部分
第二题
（1）
>> A[1234432123413241]
A
1 2 3 4
4 3 2 1
2 3 4 1
3 2 4 1
（2）
>> B[1+4j2+3j3+2j4+1j4+1j3+2j2+3j1+4j2+3j3+2j4+1j1+4j3+2j2+3j4+1j1+4j]
B
10000 + 40000i 20000 + 30000i 30000 + 20000i 40000 + 10000i
40000 + 10000i 30000 + 20000i 20000 + 30000i 10000 + 40000i
20000 + 30000i 30000 + 20000i 40000 + 10000i 10000 + 40000i
30000 + 20000i 20000 + 30000i 40000 + 10000i 10000 + 40000i
第三题
>> Amagic(8)
>> BA(22end)
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
第四题
>> i063ssum(2^i)
s
18447e+019
第五题
（1）
>> t[100011]
>> ysin(1t)
Warning Divide by zero
>> plot(ty)
（2）
t[pi00518179900011212005121201000118181005pi]
>> ysin(tan(t))tan(sin(t))
>> plot(ty)
第六题
>> xx[201121100209080108090021112012]
>> yy[10102010020102011][xy]meshgrid(xxyy)
>> z1(sqrt((1x)^2+y^2))+1(sqrt((1+x)^2+y^2))
Warning Divide by zero
Warning Divide by zero
>> subplot(224)surf(xyz)
>> subplot(221)surf(xyz)view(090)
>> subplot(222)surf(xyz)view(900)
>> subplot(223)surf(xyz)view(00)
第七题
（1）>> syms xf(3^x+9^x)^(1x)llimit(fxinf)
l
9
（2）>> syms x yfx*y(sqrt(x*y+1)1)limit(limit(fx0)y0)
ans
2
（3）>> syms x yf(1cos(x^2+y^2))*exp(x^2+y^2)(x^2+y^2)limit(limit(fx0)y0)
ans
0
第八题
>> syms txlog(cos(t))ycos(t)t*sin(t)diff(yt)diff(xt)
ans
(2*sin(t)t*cos(t))sin(t)*cos(t)
>> fdiff(yt2)diff(xt2)subs(ftsym(pi)3)
ans
38124*pi*3^(12)
第九题
>> syms x y t
>> sint(exp(t^2)t0x*y)
>> xy*diff(fx2)2*diff(diff(fx)y)+diff(fy2)
ans
2*x^2*y^2*exp(x^2*y^2)2*exp(x^2*y^2)2*x^3*y*exp(x^2*y^2)
第十题
（1）
>> syms k nsymsum(1((2*k)^21)k1inf)
ans
12
>> limit(symsum(1((2*k)^21)k1n)ninf)
ans
12
（2）
>> limit(n*symsum(1(n^2+k*pi)k1n)ninf)
ans
1
第十题
（1）
>> syms a txa*(cos(t)+t*sin(t))ya*(sin(t)t*cos(t))
>> fx^2+y^2Iint(f*sqrt(diff(xt)^2+diff(yt)^2)t02*pi)
I
2*a^2*pi^2*(a^2)^(12)+4*a^2*pi^4*(a^2)^(12)
（2）
>> syms x y a b c txc*cos(t)ayc*sin(t)b
>> Py*x^3+exp(y)Qx*y^3+x*exp(y)2*y
>> ds[diff(xt)diff(yt)]Iint([P Q]*dst0pi)
I
215*c*(2*c^4+15*b^4)b^4a
第十二题
>> syms a b c d eAvander([a b c d e])
A
[ a^4 a^3 a^2 a 1]
[ b^4 b^3 b^2 b 1]
[ c^4 c^3 c^2 c 1]
[ d^4 d^3 d^2 d 1]
[ e^4 e^3 e^2 e 1]
>> det(A)simple(ans)
ans
a^4*b^3*c^2*da^4*b^3*c^2*ea^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*ca^4*b^3*e^2*da^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*ba^4*c^3*d^2*ea^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*ca^4*d^3*b^2*ea^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*ba^4*d^3*e^2*ca^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*ba^4*e^3*c^2*da^4*e^3*d^2*b+a^4*e^3*d^2*cb^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*cb^4*a^3*d^2*eb^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*db^4*c^3*a^2*eb^4*c^3*d^2*a+b^4*c^3*d^2*e+b^4*c^3*e^2*ab^4*c^3*e^2*db^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*ab^4*d^3*c^2*eb^4*d^3*e^2*a+b^4*d^3*e^2*c+b^4*e^3*a^2*cb^4*e^3*a^2*db^4*e^3*c^2*a+b^4*e^3*c^2*d+b^4*e^3*d^2*ab^4*e^3*d^2*c+c^4*a^3*b^2*dc^4*a^3*b^2*ec^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*bc^4*a^3*e^2*dc^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*ac^4*b^3*d^2*ec^4*b^3*e^2*a+c^4*b^3*e^2*d+c^4*d^3*a^2*bc^4*d^3*a^2*ec^4*d^3*b^2*a+c^4*d^3*b^2*e+c^4*d^3*e^2*ac^4*d^3*e^2*bc^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*ac^4*e^3*b^2*dc^4*e^3*d^2*a+c^4*e^3*d^2*bd^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*bd^4*a^3*c^2*ed^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*cd^4*b^3*a^2*ed^4*b^3*c^2*a+d^4*b^3*c^2*e+d^4*b^3*e^2*ad^4*b^3*e^2*cd^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*ad^4*c^3*b^2*ed^4*c^3*e^2*a+d^4*c^3*e^2*b+d^4*e^3*a^2*bd^4*e^3*a^2*cd^4*e^3*b^2*a+d^4*e^3*b^2*c+d^4*e^3*c^2*ad^4*e^3*c^2*b+e^4*a^3*b^2*ce^4*a^3*b^2*de^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*be^4*a^3*d^2*ce^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*ae^4*b^3*c^2*de^4*b^3*d^2*a+e^4*b^3*d^2*c+e^4*c^3*a^2*be^4*c^3*a^2*de^4*c^3*b^2*a+e^4*c^3*b^2*d+e^4*c^3*d^2*ae^4*c^3*d^2*be^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*ae^4*d^3*b^2*ce^4*d^3*c^2*a+e^4*d^3*c^2*b
simplify
a^4*b^3*c^2*da^4*b^3*c^2*ea^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*ca^4*b^3*e^2*da^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*ba^4*c^3*d^2*ea^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*ca^4*d^3*b^2*ea^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*ba^4*d^3*e^2*ca^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*ba^4*e^3*c^2*da^4*e^3*d^2*b+a^4*e^3*d^2*cb^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*cb^4*a^3*d^2*eb^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*db^4*c^3*a^2*eb^4*c^3*d^2*a+b^4*c^3*d^2*e+b^4*c^3*e^2*ab^4*c^3*e^2*db^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*ab^4*d^3*c^2*eb^4*d^3*e^2*a+b^4*d^3*e^2*c+b^4*e^3*a^2*cb^4*e^3*a^2*db^4*e^3*c^2*a+b^4*e^3*c^2*d+b^4*e^3*d^2*ab^4*e^3*d^2*c+c^4*a^3*b^2*dc^4*a^3*b^2*ec^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*bc^4*a^3*e^2*dc^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*ac^4*b^3*d^2*ec^4*b^3*e^2*a+c^4*b^3*e^2*d+c^4*d^3*a^2*bc^4*d^3*a^2*ec^4*d^3*b^2*a+c^4*d^3*b^2*e+c^4*d^3*e^2*ac^4*d^3*e^2*bc^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*ac^4*e^3*b^2*dc^4*e^3*d^2*a+c^4*e^3*d^2*bd^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*bd^4*a^3*c^2*ed^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*cd^4*b^3*a^2*ed^4*b^3*c^2*a+d^4*b^3*c^2*e+d^4*b^3*e^2*ad^4*b^3*e^2*cd^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*ad^4*c^3*b^2*ed^4*c^3*e^2*a+d^4*c^3*e^2*b+d^4*e^3*a^2*bd^4*e^3*a^2*cd^4*e^3*b^2*a+d^4*e^3*b^2*c+d^4*e^3*c^2*ad^4*e^3*c^2*b+e^4*a^3*b^2*ce^4*a^3*b^2*de^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*be^4*a^3*d^2*ce^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*ae^4*b^3*c^2*de^4*b^3*d^2*a+e^4*b^3*d^2*c+e^4*c^3*a^2*be^4*c^3*a^2*de^4*c^3*b^2*a+e^4*c^3*b^2*d+e^4*c^3*d^2*ae^4*c^3*d^2*be^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*ae^4*d^3*b^2*ce^4*d^3*c^2*a+e^4*d^3*c^2*b
radsimp
a^4*b^3*c^2*da^4*b^3*c^2*ea^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*ca^4*b^3*e^2*da^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*ba^4*c^3*d^2*ea^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*ca^4*d^3*b^2*ea^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*ba^4*d^3*e^2*ca^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*ba^4*e^3*c^2*da^4*e^3*d^2*b+a^4*e^3*d^2*cb^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*cb^4*a^3*d^2*eb^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*db^4*c^3*a^2*eb^4*c^3*d^2*a+b^4*c^3*d^2*e+b^4*c^3*e^2*ab^4*c^3*e^2*db^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*ab^4*d^3*c^2*eb^4*d^3*e^2*a+b^4*d^3*e^2*c+b^4*e^3*a^2*cb^4*e^3*a^2*db^4*e^3*c^2*a+b^4*e^3*c^2*d+b^4*e^3*d^2*ab^4*e^3*d^2*c+c^4*a^3*b^2*dc^4*a^3*b^2*ec^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*bc^4*a^3*e^2*dc^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*ac^4*b^3*d^2*ec^4*b^3*e^2*a+c^4*b^3*e^2*d+c^4*d^3*a^2*bc^4*d^3*a^2*ec^4*d^3*b^2*a+c^4*d^3*b^2*e+c^4*d^3*e^2*ac^4*d^3*e^2*bc^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*ac^4*e^3*b^2*dc^4*e^3*d^2*a+c^4*e^3*d^2*bd^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*bd^4*a^3*c^2*ed^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*cd^4*b^3*a^2*ed^4*b^3*c^2*a+d^4*b^3*c^2*e+d^4*b^3*e^2*ad^4*b^3*e^2*cd^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*ad^4*c^3*b^2*ed^4*c^3*e^2*a+d^4*c^3*e^2*b+d^4*e^3*a^2*bd^4*e^3*a^2*cd^4*e^3*b^2*a+d^4*e^3*b^2*c+d^4*e^3*c^2*ad^4*e^3*c^2*b+e^4*a^3*b^2*ce^4*a^3*b^2*de^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*be^4*a^3*d^2*ce^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*ae^4*b^3*c^2*de^4*b^3*d^2*a+e^4*b^3*d^2*c+e^4*c^3*a^2*be^4*c^3*a^2*de^4*c^3*b^2*a+e^4*c^3*b^2*d+e^4*c^3*d^2*ae^4*c^3*d^2*be^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*ae^4*d^3*b^2*ce^4*d^3*c^2*a+e^4*d^3*c^2*b
combine(trig)
a^4*b^3*c^2*da^4*b^3*c^2*ea^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*ca^4*b^3*e^2*da^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*ba^4*c^3*d^2*ea^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*ca^4*d^3*b^2*ea^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*ba^4*d^3*e^2*ca^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*ba^4*e^3*c^2*da^4*e^3*d^2*b+a^4*e^3*d^2*cb^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*cb^4*a^3*d^2*eb^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*db^4*c^3*a^2*eb^4*c^3*d^2*a+b^4*c^3*d^2*e+b^4*c^3*e^2*ab^4*c^3*e^2*db^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*ab^4*d^3*c^2*eb^4*d^3*e^2*a+b^4*d^3*e^2*c+b^4*e^3*a^2*cb^4*e^3*a^2*db^4*e^3*c^2*a+b^4*e^3*c^2*d+b^4*e^3*d^2*ab^4*e^3*d^2*c+c^4*a^3*b^2*dc^4*a^3*b^2*ec^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*bc^4*a^3*e^2*dc^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*ac^4*b^3*d^2*ec^4*b^3*e^2*a+c^4*b^3*e^2*d+c^4*d^3*a^2*bc^4*d^3*a^2*ec^4*d^3*b^2*a+c^4*d^3*b^2*e+c^4*d^3*e^2*ac^4*d^3*e^2*bc^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*ac^4*e^3*b^2*dc^4*e^3*d^2*a+c^4*e^3*d^2*bd^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*bd^4*a^3*c^2*ed^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*cd^4*b^3*a^2*ed^4*b^3*c^2*a+d^4*b^3*c^2*e+d^4*b^3*e^2*ad^4*b^3*e^2*cd^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*ad^4*c^3*b^2*ed^4*c^3*e^2*a+d^4*c^3*e^2*b+d^4*e^3*a^2*bd^4*e^3*a^2*cd^4*e^3*b^2*a+d^4*e^3*b^2*c+d^4*e^3*c^2*ad^4*e^3*c^2*b+e^4*a^3*b^2*ce^4*a^3*b^2*de^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*be^4*a^3*d^2*ce^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*ae^4*b^3*c^2*de^4*b^3*d^2*a+e^4*b^3*d^2*c+e^4*c^3*a^2*be^4*c^3*a^2*de^4*c^3*b^2*a+e^4*c^3*b^2*d+e^4*c^3*d^2*ae^4*c^3*d^2*be^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*ae^4*d^3*b^2*ce^4*d^3*c^2*a+e^4*d^3*c^2*b
factor
(cd)*(bd)*(bc)*(ad)*(ac)*(ab)*(d+e)*(ec)*(eb)*(ea)
expand
a^4*b^3*c^2*da^4*b^3*c^2*ea^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*ca^4*b^3*e^2*da^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*ba^4*c^3*d^2*ea^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*ca^4*d^3*b^2*ea^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*ba^4*d^3*e^2*ca^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*ba^4*e^3*c^2*da^4*e^3*d^2*b+a^4*e^3*d^2*cb^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*cb^4*a^3*d^2*eb^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*db^4*c^3*a^2*eb^4*c^3*d^2*a+b^4*c^3*d^2*e+b^4*c^3*e^2*ab^4*c^3*e^2*db^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*ab^4*d^3*c^2*eb^4*d^3*e^2*a+b^4*d^3*e^2*c+b^4*e^3*a^2*cb^4*e^3*a^2*db^4*e^3*c^2*a+b^4*e^3*c^2*d+b^4*e^3*d^2*ab^4*e^3*d^2*c+c^4*a^3*b^2*dc^4*a^3*b^2*ec^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*bc^4*a^3*e^2*dc^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*ac^4*b^3*d^2*ec^4*b^3*e^2*a+c^4*b^3*e^2*d+c^4*d^3*a^2*bc^4*d^3*a^2*ec^4*d^3*b^2*a+c^4*d^3*b^2*e+c^4*d^3*e^2*ac^4*d^3*e^2*bc^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*ac^4*e^3*b^2*dc^4*e^3*d^2*a+c^4*e^3*d^2*bd^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*bd^4*a^3*c^2*ed^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*cd^4*b^3*a^2*ed^4*b^3*c^2*a+d^4*b^3*c^2*e+d^4*b^3*e^2*ad^4*b^3*e^2*cd^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*ad^4*c^3*b^2*ed^4*c^3*e^2*a+d^4*c^3*e^2*b+d^4*e^3*a^2*bd^4*e^3*a^2*cd^4*e^3*b^2*a+d^4*e^3*b^2*c+d^4*e^3*c^2*ad^4*e^3*c^2*b+e^4*a^3*b^2*ce^4*a^3*b^2*de^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*be^4*a^3*d^2*ce^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*ae^4*b^3*c^2*de^4*b^3*d^2*a+e^4*b^3*d^2*c+e^4*c^3*a^2*be^4*c^3*a^2*de^4*c^3*b^2*a+e^4*c^3*b^2*d+e^4*c^3*d^2*ae^4*c^3*d^2*be^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*ae^4*d^3*b^2*ce^4*d^3*c^2*a+e^4*d^3*c^2*b
combine
a^4*b^3*c^2*da^4*b^3*c^2*ea^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*ca^4*b^3*e^2*da^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*ba^4*c^3*d^2*ea^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*ca^4*d^3*b^2*ea^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*ba^4*d^3*e^2*ca^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*ba^4*e^3*c^2*da^4*e^3*d^2*b+a^4*e^3*d^2*cb^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*cb^4*a^3*d^2*eb^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*db^4*c^3*a^2*eb^4*c^3*d^2*a+b^4*c^3*d^2*e+b^4*c^3*e^2*ab^4*c^3*e^2*db^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*ab^4*d^3*c^2*eb^4*d^3*e^2*a+b^4*d^3*e^2*c+b^4*e^3*a^2*cb^4*e^3*a^2*db^4*e^3*c^2*a+b^4*e^3*c^2*d+b^4*e^3*d^2*ab^4*e^3*d^2*c+c^4*a^3*b^2*dc^4*a^3*b^2*ec^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*bc^4*a^3*e^2*dc^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*ac^4*b^3*d^2*ec^4*b^3*e^2*a+c^4*b^3*e^2*d+c^4*d^3*a^2*bc^4*d^3*a^2*ec^4*d^3*b^2*a+c^4*d^3*b^2*e+c^4*d^3*e^2*ac^4*d^3*e^2*bc^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*ac^4*e^3*b^2*dc^4*e^3*d^2*a+c^4*e^3*d^2*bd^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*bd^4*a^3*c^2*ed^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*cd^4*b^3*a^2*ed^4*b^3*c^2*a+d^4*b^3*c^2*e+d^4*b^3*e^2*ad^4*b^3*e^2*cd^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*ad^4*c^3*b^2*ed^4*c^3*e^2*a+d^4*c^3*e^2*b+d^4*e^3*a^2*bd^4*e^3*a^2*cd^4*e^3*b^2*a+d^4*e^3*b^2*c+d^4*e^3*c^2*ad^4*e^3*c^2*b+e^4*a^3*b^2*ce^4*a^3*b^2*de^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*be^4*a^3*d^2*ce^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*ae^4*b^3*c^2*de^4*b^3*d^2*a+e^4*b^3*d^2*c+e^4*c^3*a^2*be^4*c^3*a^2*de^4*c^3*b^2*a+e^4*c^3*b^2*d+e^4*c^3*d^2*ae^4*c^3*d^2*be^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*ae^4*d^3*b^2*ce^4*d^3*c^2*a+e^4*d^3*c^2*b
convert(exp)
a^4*b^3*c^2*da^4*b^3*c^2*ea^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*ca^4*b^3*e^2*da^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*ba^4*c^3*d^2*ea^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*ca^4*d^3*b^2*ea^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*ba^4*d^3*e^2*ca^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*ba^4*e^3*c^2*da^4*e^3*d^2*b+a^4*e^3*d^2*cb^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*cb^4*a^3*d^2*eb^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*db^4*c^3*a^2*eb^4*c^3*d^2*a+b^4*c^3*d^2*e+b^4*c^3*e^2*ab^4*c^3*e^2*db^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*ab^4*d^3*c^2*eb^4*d^3*e^2*a+b^4*d^3*e^2*c+b^4*e^3*a^2*cb^4*e^3*a^2*db^4*e^3*c^2*a+b^4*e^3*c^2*d+b^4*e^3*d^2*ab^4*e^3*d^2*c+c^4*a^3*b^2*dc^4*a^3*b^2*ec^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*bc^4*a^3*e^2*dc^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*ac^4*b^3*d^2*ec^4*b^3*e^2*a+c^4*b^3*e^2*d+c^4*d^3*a^2*bc^4*d^3*a^2*ec^4*d^3*b^2*a+c^4*d^3*b^2*e+c^4*d^3*e^2*ac^4*d^3*e^2*bc^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*ac^4*e^3*b^2*dc^4*e^3*d^2*a+c^4*e^3*d^2*bd^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*bd^4*a^3*c^2*ed^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*cd^4*b^3*a^2*ed^4*b^3*c^2*a+d^4*b^3*c^2*e+d^4*b^3*e^2*ad^4*b^3*e^2*cd^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*ad^4*c^3*b^2*ed^4*c^3*e^2*a+d^4*c^3*e^2*b+d^4*e^3*a^2*bd^4*e^3*a^2*cd^4*e^3*b^2*a+d^4*e^3*b^2*c+d^4*e^3*c^2*ad^4*e^3*c^2*b+e^4*a^3*b^2*ce^4*a^3*b^2*de^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*be^4*a^3*d^2*ce^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*ae^4*b^3*c^2*de^4*b^3*d^2*a+e^4*b^3*d^2*c+e^4*c^3*a^2*be^4*c^3*a^2*de^4*c^3*b^2*a+e^4*c^3*b^2*d+e^4*c^3*d^2*ae^4*c^3*d^2*be^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*ae^4*d^3*b^2*ce^4*d^3*c^2*a+e^4*d^3*c^2*b
convert(sincos)
a^4*b^3*c^2*da^4*b^3*c^2*ea^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*ca^4*b^3*e^2*da^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*ba^4*c^3*d^2*ea^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*ca^4*d^3*b^2*ea^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*ba^4*d^3*e^2*ca^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*ba^4*e^3*c^2*da^4*e^3*d^2*b+a^4*e^3*d^2*cb^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*cb^4*a^3*d^2*eb^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*db^4*c^3*a^2*eb^4*c^3*d^2*a+b^4*c^3*d^2*e+b^4*c^3*e^2*ab^4*c^3*e^2*db^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*ab^4*d^3*c^2*eb^4*d^3*e^2*a+b^4*d^3*e^2*c+b^4*e^3*a^2*cb^4*e^3*a^2*db^4*e^3*c^2*a+b^4*e^3*c^2*d+b^4*e^3*d^2*ab^4*e^3*d^2*c+c^4*a^3*b^2*dc^4*a^3*b^2*ec^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*bc^4*a^3*e^2*dc^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*ac^4*b^3*d^2*ec^4*b^3*e^2*a+c^4*b^3*e^2*d+c^4*d^3*a^2*bc^4*d^3*a^2*ec^4*d^3*b^2*a+c^4*d^3*b^2*e+c^4*d^3*e^2*ac^4*d^3*e^2*bc^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*ac^4*e^3*b^2*dc^4*e^3*d^2*a+c^4*e^3*d^2*bd^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*bd^4*a^3*c^2*ed^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*cd^4*b^3*a^2*ed^4*b^3*c^2*a+d^4*b^3*c^2*e+d^4*b^3*e^2*ad^4*b^3*e^2*cd^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*ad^4*c^3*b^2*ed^4*c^3*e^2*a+d^4*c^3*e^2*b+d^4*e^3*a^2*bd^4*e^3*a^2*cd^4*e^3*b^2*a+d^4*e^3*b^2*c+d^4*e^3*c^2*ad^4*e^3*c^2*b+e^4*a^3*b^2*ce^4*a^3*b^2*de^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*be^4*a^3*d^2*ce^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*ae^4*b^3*c^2*de^4*b^3*d^2*a+e^4*b^3*d^2*c+e^4*c^3*a^2*be^4*c^3*a^2*de^4*c^3*b^2*a+e^4*c^3*b^2*d+e^4*c^3*d^2*ae^4*c^3*d^2*be^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*ae^4*d^3*b^2*ce^4*d^3*c^2*a+e^4*d^3*c^2*b
convert(tan)
a^4*b^3*c^2*da^4*b^3*c^2*ea^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*ca^4*b^3*e^2*da^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*ba^4*c^3*d^2*ea^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*ca^4*d^3*b^2*ea^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*ba^4*d^3*e^2*ca^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*ba^4*e^3*c^2*da^4*e^3*d^2*b+a^4*e^3*d^2*cb^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*cb^4*a^3*d^2*eb^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*db^4*c^3*a^2*eb^4*c^3*d^2*a+b^4*c^3*d^2*e+b^4*c^3*e^2*ab^4*c^3*e^2*db^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*ab^4*d^3*c^2*eb^4*d^3*e^2*a+b^4*d^3*e^2*c+b^4*e^3*a^2*cb^4*e^3*a^2*db^4*e^3*c^2*a+b^4*e^3*c^2*d+b^4*e^3*d^2*ab^4*e^3*d^2*c+c^4*a^3*b^2*dc^4*a^3*b^2*ec^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*bc^4*a^3*e^2*dc^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*ac^4*b^3*d^2*ec^4*b^3*e^2*a+c^4*b^3*e^2*d+c^4*d^3*a^2*bc^4*d^3*a^2*ec^4*d^3*b^2*a+c^4*d^3*b^2*e+c^4*d^3*e^2*ac^4*d^3*e^2*bc^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*ac^4*e^3*b^2*dc^4*e^3*d^2*a+c^4*e^3*d^2*bd^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*bd^4*a^3*c^2*ed^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*cd^4*b^3*a^2*ed^4*b^3*c^2*a+d^4*b^3*c^2*e+d^4*b^3*e^2*ad^4*b^3*e^2*cd^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*ad^4*c^3*b^2*ed^4*c^3*e^2*a+d^4*c^3*e^2*b+d^4*e^3*a^2*bd^4*e^3*a^2*cd^4*e^3*b^2*a+d^4*e^3*b^2*c+d^4*e^3*c^2*ad^4*e^3*c^2*b+e^4*a^3*b^2*ce^4*a^3*b^2*de^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*be^4*a^3*d^2*ce^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*ae^4*b^3*c^2*de^4*b^3*d^2*a+e^4*b^3*d^2*c+e^4*c^3*a^2*be^4*c^3*a^2*de^4*c^3*b^2*a+e^4*c^3*b^2*d+e^4*c^3*d^2*ae^4*c^3*d^2*be^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*ae^4*d^3*b^2*ce^4*d^3*c^2*a+e^4*d^3*c^2*b
collect(e)
a^4*b^3*c^2*da^4*b^3*d^2*ca^4*c^3*b^2*d+a^4*c^3*d^2*b+a^4*d^3*b^2*ca^4*d^3*c^2*bb^4*a^3*c^2*d+b^4*a^3*d^2*c+b^4*c^3*a^2*db^4*c^3*d^2*ab^4*d^3*a^2*c+b^4*d^3*c^2*a+c^4*a^3*b^2*dc^4*a^3*d^2*bc^4*b^3*a^2*d+c^4*b^3*d^2*a+c^4*d^3*a^2*bc^4*d^3*b^2*ad^4*a^3*b^2*c+d^4*a^3*c^2*b+d^4*b^3*a^2*cd^4*b^3*c^2*ad^4*c^3*a^2*b+d^4*c^3*b^2*a+(a^3*b^2*ca^3*b^2*da^3*c^2*b+a^3*c^2*d+a^3*d^2*ba^3*d^2*cb^3*a^2*c+b^3*a^2*d+b^3*c^2*ab^3*c^2*db^3*d^2*a+b^3*d^2*c+c^3*a^2*bc^3*a^2*dc^3*b^2*a+c^3*b^2*d+c^3*d^2*ac^3*d^2*bd^3*a^2*b+d^3*a^2*c+d^3*b^2*ad^3*b^2*cd^3*c^2*a+d^3*c^2*b)*e^4+(a^4*b^2*cc^4*d*b^2c^4*d^2*a+c^4*d^2*b+a^4*b^2*d+a^4*c^2*ba^4*c^2*dc^4*a^2*b+c^4*a^2*d+c^4*b^2*a+b^4*a^2*cb^4*a^2*db^4*c^2*a+c^2*d*b^4+b^4*d^2*ad^2*c*b^4a^4*d^2*b+a^4*d^2*c+d^4*a^2*bd^4*a^2*cd^4*b^2*a+c*d^4*b^2+d^4*c^2*ac^2*d^4*b)*e^3+(b^4*a^3*dc^4*b^3*aa^4*c^3*bc*d^4*b^3+c^4*d*b^3a^4*b^3*db^4*a^3*c+a^4*c^3*d+a^4*b^3*ca^4*d^3*cc^3*d*b^4+d^4*b^3*a+a^4*d^3*b+b^4*c^3*ac^4*a^3*dd^4*a^3*b+c^4*d^3*a+c^4*a^3*bc^4*d^3*bb^4*d^3*a+c*d^3*b^4+d^4*a^3*cd^4*c^3*a+c^3*d^4*b)*e^2+(a^4*b^3*d^2+c^4*a^3*d^2b^4*c^3*a^2a^4*b^3*c^2+a^4*d^3*c^2+d^4*c^3*a^2c^4*d^2*b^3a^4*c^3*d^2+c^4*d^3*b^2+c^4*b^3*a^2c^4*d^3*a^2a^4*d^3*b^2b^4*a^3*d^2+b^4*d^3*a^2+b^4*a^3*c^2c^3*d^4*b^2d^4*a^3*c^2+c^2*d^4*b^3+a^4*c^3*b^2+c^3*d^2*b^4c^2*d^3*b^4c^4*a^3*b^2+d^4*a^3*b^2d^4*b^3*a^2)*e
mwcos2sin
a^4*b^3*c^2*da^4*b^3*c^2*ea^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*ca^4*b^3*e^2*da^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*ba^4*c^3*d^2*ea^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*ca^4*d^3*b^2*ea^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*ba^4*d^3*e^2*ca^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*ba^4*e^3*c^2*da^4*e^3*d^2*b+a^4*e^3*d^2*cb^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*cb^4*a^3*d^2*eb^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*db^4*c^3*a^2*eb^4*c^3*d^2*a+b^4*c^3*d^2*e+b^4*c^3*e^2*ab^4*c^3*e^2*db^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*ab^4*d^3*c^2*eb^4*d^3*e^2*a+b^4*d^3*e^2*c+b^4*e^3*a^2*cb^4*e^3*a^2*db^4*e^3*c^2*a+b^4*e^3*c^2*d+b^4*e^3*d^2*ab^4*e^3*d^2*c+c^4*a^3*b^2*dc^4*a^3*b^2*ec^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*bc^4*a^3*e^2*dc^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*ac^4*b^3*d^2*ec^4*b^3*e^2*a+c^4*b^3*e^2*d+c^4*d^3*a^2*bc^4*d^3*a^2*ec^4*d^3*b^2*a+c^4*d^3*b^2*e+c^4*d^3*e^2*ac^4*d^3*e^2*bc^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*ac^4*e^3*b^2*dc^4*e^3*d^2*a+c^4*e^3*d^2*bd^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*bd^4*a^3*c^2*ed^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*cd^4*b^3*a^2*ed^4*b^3*c^2*a+d^4*b^3*c^2*e+d^4*b^3*e^2*ad^4*b^3*e^2*cd^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*ad^4*c^3*b^2*ed^4*c^3*e^2*a+d^4*c^3*e^2*b+d^4*e^3*a^2*bd^4*e^3*a^2*cd^4*e^3*b^2*a+d^4*e^3*b^2*c+d^4*e^3*c^2*ad^4*e^3*c^2*b+e^4*a^3*b^2*ce^4*a^3*b^2*de^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*be^4*a^3*d^2*ce^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*ae^4*b^3*c^2*de^4*b^3*d^2*a+e^4*b^3*d^2*c+e^4*c^3*a^2*be^4*c^3*a^2*de^4*c^3*b^2*a+e^4*c^3*b^2*d+e^4*c^3*d^2*ae^4*c^3*d^2*be^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*ae^4*d^3*b^2*ce^4*d^3*c^2*a+e^4*d^3*c^2*b
ans
(cd)*(bd)*(bc)*(ad)*(ac)*(ab)*(d+e)*(ec)*(eb)*(ea)
>>
第十三题
>> A[2050505015050520545052122][V J]jordan(sym(A))
V
[ 0 12 12 14]
[ 0 0 12 1]
[ 14 12 12 14]
[ 14 12 1 14]
J
[ 4 0 0 0]
[ 0 2 1 0]
[ 0 0 2 1]
[ 0 0 0 2]
第十四题
数值方法
>> A[3640514224636731310011004034]
>> B[321292219]
>> C[211412561644663]
>> Xlyap(ABC)
X
23192 04678 01505
36284 01579 00629
54246 10516 05090
05718 25848 03649
30417 06265 01580
>> norm(A*X+X*B+C)
ans
38830e014
解析方法
>> edit
function Xlyap(ABC)
if nargin2CBBA＇end
[nrnc]size(C)A0kron(Aeye(nc))+kron(eye(nr)B＇)
try
C1C＇x0inv(A0)*C1()Xreshape(x0ncnr)＇
catcherror(＇singular matrix found＇)end
>> A[3640514224636731310011004034]
>> B[321292219]
>> C[211412561644663]Xlyap(sym(A)BC)
X
[ 434641749950107136516451 4664546747350321409549353 503105815912321409549353]
[ 3809507498107136516451 8059112319373321409549353 880921527508321409549353]
[ 1016580400173107136516451 8334897743767321409549353 1419901706449321409549353]
[ 288938859984107136516451 6956912657222321409549353 927293592476321409549353]
[ 827401644798107136516451 10256166034813321409549353 1209595497577321409549353]
>> A*X+X*B+C
ans
[ 0 0 0]
[ 0 0 0]
[ 0 0 0]
[ 0 0 0]
[ 0 0 0]
第十五题
（1）
>> A[4500515054050515125150113]
>> Asym(A)syms t
>> expm(A*t)
ans
[ 12*exp(3*t)12*t*exp(3*t)+12*exp(5*t)+12*t^2*exp(3*t) 12*exp(5*t)12*exp(3*t)+t*exp(3*t) 12*t*exp(3*t)+12*t^2*exp(3*t) 12*exp(5*t)12*exp(3*t)12*t*exp(3*t)+12*t^2*exp(3*t)]
[ 12*t*exp(3*t)+12*exp(5*t)12*exp(3*t) 12*exp(3*t)+12*exp(5*t) 12*t*exp(3*t) 12*t*exp(3*t)+12*exp(5*t)12*exp(3*t)]
[ 12*t*exp(3*t)12*exp(5*t)+12*exp(3*t) 12*exp(5*t)+12*exp(3*t) exp(3*t)+12*t*exp(3*t) 12*t*exp(3*t)12*exp(5*t)+12*exp(3*t)]
[ 12*t^2*exp(3*t) t*exp(3*t) 12*t^2*exp(3*t)t*exp(3*t) exp(3*t)12*t^2*exp(3*t)]
(2)
>> A[4500515054050515125150113]
>> Asym(A)syms t
>> sin(A*t)
ans
[ sin(92*t) 0 sin(12*t) sin(32*t)]
[ sin(12*t) sin(4*t) sin(12*t) sin(12*t)]
[ sin(32*t) sin(t) sin(52*t) sin(32*t)]
[ 0 sin(t) sin(t) sin(3*t)]
(3)
第二部分
第题
（1）
>> syms a tfsin(a*t)tlaplace(f)
ans
atan(as)
（2）
>> syms t aft^5*sin(a*t)laplace(f)
ans
60*i*(1(si*a)^6+1(s+i*a)^6)
（3）
>> syms t aft^8*cos(a*t)laplace(f)
ans
20160(si*a)^9+20160(s+i*a)^9
第二题
（1）
>> syms s a bF1(s^2*(s^2a^2)*(a+b))ilaplace(F)
ans
1(a+b)*(1a^2*t+1a^3*sinh(a*t))
（2）
>> syms s a bFsqrt(sa)sqrt(sb)ilaplace(F)
ans
12t^(32)pi^(12)*(exp(b*t)exp(a*t))
（3）
>> syms s a bFlog((sa)(sb))ilaplace(F)
ans
1t*(exp(b*t)exp(a*t))
第三题
（1）
>> syms xfx^2*(3*sym(pi)2*abs(x))Ffourier(f)
F
6*(4+pi^2*dirac(2w)*w^4)w^4
>> ifourier(F)
ans
x^2*(4*x*heaviside(x)+3*pi+2*x)
（2）
>> syms tft^2*(t2*sym(pi))^2Ffourier(f)
F
2*pi*(4*pi^2*dirac(2w)+4*i*pi*dirac(3w)+dirac(4w))
>> ifourier(F)
ans
x^2*(2*pi+x)^2
第四题
（1）
>> syms k a Tfcos(k*a*T)Fztrans(f)
F
(zcos(a*T))*z(z^22*z*cos(a*T)+1)
>> f1iztrans(F)
f1
cos(a*T*n)
（2）
>> syms k T af(k*T)^2*exp(a*k*T)Fztrans(f)
F
T^2*z*exp(a*T)*(z+exp(a*T))(zexp(a*T))^3
>> f1iztrans(F)
f1
T^2*(1exp(a*T))^n*n^2
（3）
>> syms a k Tf(a*k*T1+exp(a*k*T))aFztrans(f)
F
1a*(a*T*z(z1)^2z(z1)+zexp(a*T)(zexp(a*T)1))
>> iztrans(F)
ans
((1exp(a*T))^n+a*T*n1)a
第五题
（1）
>> syms xx1solve(＇exp((x+1)^2+pi2)*sin(5*x+2)＇)
x1
25
>> subs(＇exp((x+1)^2+pi2)*sin(5*x+2)＇xx1)
ans
0
>> finline(＇exp((x+1)^2+pi2)*sin(5*x+2)＇＇x＇)
>> x2fsolve(f0)
Optimization terminated firstorder optimality is less than optionsTolFun
x2
02283
>> subs(＇exp((x+1)^2+pi2)*sin(5*x+2)＇xx2)
ans
47509e008
（2）
>> syms xy1solve(＇(x^2+y^2+x*y)*exp(x^2y^2x*y)0＇＇y＇)
y1
(12+12*i*3^(12))*x
(1212*i*3^(12))*x
>> y2simple(subs(＇(x^2+y^2+x*y)*exp(x^2y*2x*y)＇＇y＇y1))
y2
0
0
第六题
>> syms x cyint((exp(x)c*x)^2x01)
y
12*exp(1)^2+13*c^2122*c
>> edit
function yf(c)
y12*exp(1)^2+13*c122*c
>> xfminsearch(＇f＇0)
x
31691e+026
>> ezplot(y[05])
第七题
>> edit
function yf1(x)
yexp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+1)
function [cce]f2(x)
ce[]
c[x(1)+x(2)x(1)*x(2)x(1)x(2)+1510x(1)*x(2)]
>> edit
>> A[]B[]Aeq[]Beq[]xm[1010]xM[1010]
>> x0(xm+xM)2
>> ffoptimsetffTolX1e10ffTolFun1e20
>> xfmincon(＇f1＇x0ABAeqBeqxmxM＇f2＇ff)
Maximum number of function evaluations exceeded
increase OPTIONSMaxFunEvals
x
04195
04195
>> i1xx0
>> while (1)
[xab]fmincon(＇f1＇xABAeqBeqxmxM＇f2＇ff)
if b>0breakend
ii+1
end
>> xi
x
11825
17398
i
5
第八题
function yf3 (x)
y(592*x(1)+381*x(2)+273*x(3)+55*x(4)+48*x(5)+37*x(6)+23*x(7))
function [cceq]f4(x)
c[]ceq[]
>> A[353423561767589528451304]B119567
intlistones(71)Aeq[]Beq[]
xmzeros(71)xMinf*ones(71)x0zeros(71)
ffoptimsetffTolFun1e6ffTolX1e6ffTolCon1e20
ffMaxSQPIter1000settings[0]
ix(intlist1)xm(ix)ceil(xm(ix))xM(ix)floor(xM(ix))
[errmsgfx]bnb20(＇f3＇x0intlistxmxMABAeqBeqf4 settingsff)
if length(errmsg)0xround(x)end
x
32
2
1
0
0
0
0
第九题
>> syms x
>> ydsolve(＇D2y(21x)*Dy+(11x)*yx^2*exp(5*x)＇＇x＇)
y
exp(x)*C2+exp(x)*log(x)*C1+1216*Ei(16*x)*exp(x)+111296*exp(5*x)+5216*exp(5*x)*x+136*x^2*exp(5*x)
>> syms x
>> ydsolve(＇D2y(21x)*Dy+(11x)*yx^2*exp(5*x)＇＇y(1)sym(pi)＇＇y(sym(pi))1＇＇x＇)
y
11296*exp(x)*(1296*sym(pi)*exp(5)+6*exp(6)*Ei(16)+77)exp(1)exp(5)11296*exp(x)*log(x)*(1296*exp(1)*exp(5)+1296*exp(sym(pi))*sym(pi)*exp(5)6*exp(sym(pi))*exp(6)*Ei(16)77*exp(sym(pi))+6*exp(5*sym(pi))*exp(6*sym(pi))*Ei(16*sym(pi))*exp(1)*exp(5)+11*exp(5*sym(pi))*exp(1)*exp(5)+30*exp(5*sym(pi))*sym(pi)*exp(1)*exp(5)+36*exp(5*sym(pi))*sym(pi)^2*exp(1)*exp(5))exp(sym(pi))log(sym(pi))exp(1)exp(5)+11296*(6*exp(6*x)*Ei(16*x)+11+30*x+36*x^2)*exp(5*x)
第十题
>> syms t
>> xdsolve(＇D2x+2*t*Dx+t^2*xt+1＇)
x
exp(t12*t^2)*C2+exp(t12*t^2)*C112*i*pi^(12)*2^(12)*erf(12*i*2^(12)*(1+t))*exp(12+t12*t^2)
>> syms x
>> ydsolve(＇Dy+2*x*yx*exp(x^2)＇＇x＇)
y
12*(x^2+2*C1)*exp(x^2)
第十题
>> finline(＇[x(2)x(3)x(1)+a*x(2)b+(x(1)c)*x(3)]＇＇t＇＇x＇＇flag＇＇a＇＇b＇＇c＇)
>> [tx]ode45(f[0100][000][]020257)
>> plot3(x(1)x(2)x(3))grid
>> [tx]ode45(f[0100][000][]020510)
>> plot3(x(1)x(2)x(3))grid
第十二题
>> finline([＇[x(2)x(1)x(3)(3*x(2))^2+(x(4))^3+6*x(5)+2*t＇＇x(4)x(5)x(5)x(2)exp(x(1))t]＇]＇t＇＇x＇)
>> [t1x1]ode45(f[10][24276]＇)
>> [t2x2]ode45(f[12][24276]＇)
>> t[t1(end11)t2]x[x1(end11)x2]
>> plot(tx)
>> figureplot(x(1)x(3))
第十三题
>> [txy]sim(＇yws＇[010])plot(tx)
>> figureplot(ty)
第十四题
>> t0022
>> yt^2*exp(5*t)*sin(t)plot(ty＇o＇)
>> ezplot(＇t^2*exp(5*t)*sin(t)＇[02])hold on
>> x100012y1interp1(tyx1＇spline＇)
>> plot(x1y1)
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