Basic Operations on Polynomials

You create polynomials using the usual operations of +, -, * (for multiplication), and ** (or ^. Here are two examples:

These operations can also be used to combine polynomials. Try the following:

As you can see from the above examples, the variables are ordered by defaults

      z > y > x > c > b > a

That is, z is the main variable, then y and so on in reverse alphabetical order. You can redefine this ordering (for display purposes) with the setVariableOrder. For example, the following makes a the main variable, then b, and so on:

Now compare the way polynomials are displayed:

To return to the system's default ordering, use resetVariableOrder.

Polynomial coefficients can be pulled out using the function coefficient. For example:

will give you the coefficient of x**2 in the polynomial q. Try these commands:

Coefficients of monomials can be obtained as follows:

This will return the coefficient of x**2*z in the polynomial q**2. Also,

will return the coefficient of x**2*y**2 in the polynomial r(x,y).