Solving algebra problems step by step with wxMaxima

Vectors and Matrices

wxMaxima provides functionality for calculating vectors, although some simplification might be desired at this point. Although defining vectors and calculating sums, differences, and scalar products is easy enough, computing vector products relies on the vect library, which has a complex syntax (Figure 8).

Figure 8: Although all vector arithmetic calculations are relatively simple, computing vector products is rather complicated.

Nevertheless, wxMaxima solves the display of vectors in space quite nicely. The result of the corresponding command appears in a separate Gnuplot window and you can rotate the objects with the mouse (Figure 9). You'll find the vectors.wxm file, which is the basis for Figures 8 and 9, included with the listings for this issue [8].

Figure 9: The vector chain drawn by the 3D graphics library as Gnuplot output that you can rotate per mouse in virtual space.

Calculating matrices is significantly easier. You create them using the matrix command, where the numbers in square brackets output a line. The linking with plus and minus signs is defined much as the dot operator is used for multiplication. In all operations, it's important to observe the rules for computing matrices – that is, to add and subtract only the equivalent n*m matrices and multiply only the equivalent number of rows and columns. The software provides functions to modify matrices, including the important invert command that computes an inverse matrix as a quadratic matrix.

If you multiply the original matrix with its inversion, you get the identity matrix. Thus, you can determine linear equations simply by multiplying the inverse coefficient matrix with its result matrix. You'll find the matrix.wxm file with a corresponding example with the listings [8].

Equations

You can solve equations and systems of equations using the solve command with no prior knowledge of matrix algebra. This has the advantage that you can enter equations in the form given by the problem without having to separate the coefficient matrix with the result matrix (Figure 10).

Figure 10: With the solve command, you can solve equations and systems of equations in one shot.

The documentation provides probability theory examples and functions, including input and output and examples of loops and conditions. These components make wxMaxima a universal mathematical system.

The emphasis, as with any CAS, is on symbolic mathematics, however. The software provides graphical output as well as programming and numerical analysis. For the latter, however, other less bulky and more accessible environments can be used.