求解一个方程组（高斯光束匹配计算）

Question

matlab，mathematica等软件或者别的程序语言有什么办法求解一下吗，之前我试着用sympy库计算，奈何本人水平有限求解不出，请教一下这个能解出来吗，该怎么实现呢

Answer 1

这个直接用syms求解，我用的matlab平台

syms z zp f real
w0 = 0.007978;
w0p = 0.008830;
lambda = 0.00005;
f0 = 4.426;
eq = [zp+z-28; z-(f+w0/w0p*sqrt(f^2-f0^2));  zp-(f+w0/w0p*sqrt(f^2-f0^2))];
[z,zp,f] = solve(eq, [z,zp,f]);
z = eval(z)
zp = eval(zp)
f = eval(f)

得到结果：

z =

    14


zp =

    14


f =

   7.989876851093825

可见满足要求

同时都是负号的话

syms z zp f real
w0 = 0.007978;
w0p = 0.008830;
lambda = 0.00005;
f0 = 4.426;
eq = [zp+z-28; z-(f-w0/w0p*sqrt(f^2-f0^2));  zp-(f-w0/w0p*sqrt(f^2-f0^2))];
[z,zp,f] = solve(eq, [z,zp,f]);
z = eval(z)
zp = eval(zp)
f = eval(f)

结果

z =

    14


zp =

    14


f =

     1.444588508953627e+02