matlab是工程和科研人員必備的工具利器, 其一大功能就是可以實現代數符號運算,以及表達式推導,或者復雜表達式的化簡工作, 是廣大粗心而沒有耐心計算人員的福音.

clc close all clear allsyms theta1 theta2 theta3; syms delta1 delta2 delta3;lm11 = cos(theta1) * sin(delta1); lm12 = sin(theta1) * sin(delta1); lm13 = cos(delta1); lm21 = cos(theta2) * sin(delta2); lm22 = sin(theta2) * sin(delta2); lm23 = cos(delta2); lm31 = cos(theta3) * sin(delta3); lm32 = sin(theta3) * sin(delta3); lm33 = cos(delta3);lightMatrix = [lm11,lm12,lm13;lm21,lm22,lm23;lm31,lm32,lm33] lightMatrix_Inv = inv(lightMatrix); simplify(lightMatrix_Inv) latex(lightMatrix)

顯示latex表達式，結果如下：
$$?\begin{array}{ccc}\sin \left({\delta }_1\right)\cos \left({\theta }_1\right)& \sin \left({\delta }_1\right)\sin \left({\theta }_1\right)& \cos \left({\delta }_1\right)\\ \sin \left({\delta }_2\right)\cos \left({\theta }_2\right)& \sin \left({\delta }_2\right)\sin \left({\theta }_2\right)& \cos \left({\delta }_2\right)\\ \sin \left({\delta }_3\right)\cos \left({\theta }_3\right)& \sin \left({\delta }_3\right)\sin \left({\theta }_3\right)& \cos \left({\delta }_3\right)\end{array}?$$
人生苦短，我用python。python中實現代數符號運算和推導需要利用symps庫，總體使用方法基本與matlab中相一致。
在pycharm中無法實現表達式的latex格式顯示，導致公式看起來繁瑣復雜，不夠清晰明了，容易導致錯誤。

import sympy as sy sy.init_printing()def DeriveFormular():import sympy as symtheta1, theta2, theta3 = sym.symbols('theta_1,theta_2,theta_3')delta1, delta2, delta3 = sym.symbols('delta_1,delta_2,delta_3')lm11 = sym.cos(theta1) * sym.sin(delta1)lm12 = sym.sin(theta1) * sym.sin(delta1)lm13 = sym.cos(delta1)lm21 = sym.cos(theta2) * sym.sin(delta2)lm22 = sym.sin(theta2) * sym.sin(delta2)lm23 = sym.cos(delta2)lm31 = sym.cos(theta3) * sym.sin(delta3)lm32 = sym.sin(theta3) * sym.sin(delta3)lm33 = sym.cos(delta3)lightMatrix = sym.Matrix([[lm11, lm12, lm13], [lm21, lm22, lm23], [lm31, lm32, lm33]])inv_T = lightMatrix.inv()inv_T = sym.simplify(inv_T)print(lightMatrix)print(inv_T)

可以在jupyter notebook中實現公式的latex格式顯示：

from IPython.display import display, Latex import sympy as sy sy.init_printing() def DeriveFormular():import sympy as symtheta1,theta2,theta3 = sym.symbols('theta_1,theta_2,theta_3')delta1,delta2,delta3 = sym.symbols('delta_1,delta_2,delta_3')lm11 = sym.cos(theta1)*sym.sin(delta1)lm12 = sym.sin(theta1)*sym.sin(delta1)lm13 = sym.cos(delta1)lm21 = sym.cos(theta2)*sym.sin(delta2)lm22 = sym.sin(theta2)*sym.sin(delta2)lm23 = sym.cos(delta2)lm31 = sym.cos(theta3)*sym.sin(delta3)lm32 = sym.sin(theta3)*sym.sin(delta3)lm33 = sym.cos(delta3)lightMatrix = sym.Matrix([[lm11,lm12,lm13],[lm21,lm22,lm23],[lm31,lm32,lm33]])# display(Latex(f"$${sy.latex(lightMatrix)}$$"))display(Latex(f"$${sy.latex(lightMatrix.inv())}$$"))inv_T = lightMatrix.inv()inv_T = sym.simplify(inv_T)display(Latex(f"$${sy.latex(inv_T)}$$"))

簡單的函數值計算：

更多的其他代數運算符號可以參考該鏈接

總結

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