Mathematica, Maple, Matlab, IDL

``Translations''

Each of these popular symbolic and/or numerical mathematics software packages has its strong points. See a brief description of each if you are not acquainted with them.
Here are some basic and or useful tasks to be performed, and the commands used by each of the four. Also see syntax differences.

1. solve a polynomial

2. various algebraic operations

3. create an array of values

4. create an array x and then plot sqrt(x) vs. x

5. define vectors (1-d arrays)

6. define matrices (2-d arrays):

7. add vectors v and w and plot the resulting vector

8. eigenvectors, eigenvalues, SVD of matrix M

9. plot a function of 1 variable or of 2 variables

10. integrate a function

11. solve matrix equation Ax=b

12. input numerical data from a files

13. fit a polynomial or nonlinear function to x-y data

14. define a function f(x), and plot it

15. solve & graph an ODE

16. analyze data using FFT

17. read a PNG (or GIF) file, filter, and display

18. display array data as surface, contour, density plot,

19. plot a parametric equation

20. write data to a (text) file