collect、expand、horner、factor、simplify和pretty函数分别实现符号表达式的化简。 subexpr 和subs分别用来实现变量替换。
1.collect
syms x
coeffs = collect((exp(x) + x)*(x + 2)) %未指定符号变量symvar((exp(x) + x)*(x + 2), 1) %查找表达式中的符号变量%收集特定变量的幂系数
syms x y
coeffs_x = collect(x^2*y + y*x - x^2 - 2*x, x)coeffs_y = collect(x^2*y + y*x - x^2 - 2*x, y)syms a b
%指定对x、y收集
coeffs_xy = collect(a^2*x*y + a*b*x^2 + a*x*y +
x^2, [x y]) %根据i和pi收集系数
coeffs_i = collect(2*x*i - 3*i*y, i)coeffs_pi = collect(x*pi*(pi - y) + x*(pi + i) + 3*pi*y,
pi)%符号表达式和函数的系数集合
syms x y
fh = expand(sin(x + 3*y));
coeffs_cosy = collect(fh, cos(y))coeffs_sinxsiny = collect(fh, [sin(x) sin(y)])syms y(x)
fh2 = y^2*x + y*x^2 + y*sin(x) + x*y;
coeffs_y = collect(fh2, y)%为矩阵的每个元素收集系数
syms x y
A = collect([(x + 1)*(y + 1), x^2 + x*(x -y); 2*x*y - x, x*y +
x/y], x)%收集函数调用的系数
syms a b c d e f x
F = a*sin(2*x) + b*sin(2*x) + c*cos(x) + d*cos(x) + e*sin(3*x)
+f*sin(3*x);
collect(F, 'sin')collect(F, {'sin' 'cos'})
2. expand
syms x
sf = (sin(3*x) – 1)^2;
fep = expand(sf)%通过将“ArithmeticOnly”设置为true，抑制函数（如sin(3*x)）的扩展。
fep2 = expand(sf, 'ArithmeticOnly', true)syms a b c
fl = log((a*b/c)^2);
flg = expand(fl)%通过将“IgnoreAnalyticConstraints”设置为true，应用
标识来简化对数的输入。
flg2 = expand(fl,'IgnoreAnalyticConstraints',true)
3. horner
syms x y;
fun = expand((x-2)^3)funh = horner(fun)fun1 = x^3+3*x+1;
fun2 = 3*y^2+4*y+7;
horfun = horner([fun1,fun2])fx = (x^2+x+1)*(x^3+1);
fxh = horner(fx)
4. factor
F = factor(823429252)%大数字用单引号括起来转化为符号数值
F = factor(sym('82342925225632328'))F = factor(sym(-92465)) %负数F = factor(sym(112/81)) %分数形式sym x;
fun = 4*x^3+x^4+8*x+5*x^2+6;
hfun = factor(fun)syms a b c d
y = -a*b^5*c*d*(a^2 - 1)*(a*d - b*c);
F = factor(y,[b c])
5. simplify
syms x c a b;
s1 = simplify(sin(x)^2 + cos(x)^2)s2 = simplify(exp(c*log(sqrt(a+b))))s3 = simplify([(x^2+5*x+6)/(x+2),sqrt(16)])
6.subexpr
syms x a
sol=solve(x^3+a*x+1,x,'MaxDegree',3)
r = subexpr(sol)pretty(r) %pretty 符号表达式syms a b c x
solutions = solve(a*x^2 + b*x + c == 0, x)syms s
[abbrSolutions,s] = subexpr(solutions,s)
7.subs
%替换
sola = subs(sol,a,1)
solv = vpa(sola,15)%指定替换为数值矩阵
syms a t
SA = subs(exp(a*t) + 1, a, -magic(3))syms x y a b
fh = a*b*x*y;
%指定替换为函数
fh1 = subs(subs(fh,x,sin(x)),y,exp(y))%嵌套替换为对应数值
fh2 = subs(subs(fh1,a,5),b,3)%绘制二维曲面图
ezmesh(fh2）
