>
|
|
We create two power series and compute their difference.
>
|
|
| (1) |
>
|
|
| (2) |
| (3) |
The power series is known to have nonzero terms.
In order to test whether has any nonzero terms of homogeneous degree 10 or less, we can issue the following command. We see that and are the same up to homogeneous degree 10 (and indeed, from the analytic expression we can see that they are exactly equal).
>
|
|
Because is defined as a difference, we can test the same thing using the ApproximatelyEqual command.
>
|
|
The following two univariate polynomials over power series are exactly equal to . Hence, their difference is equal to 0 at any precision.
>
|
|
| (7) |
>
|
|
| (8) |
| (9) |
>
|
|
In this case, the analytic expressions for the coefficients are all zero. We can use the force option to make Maple do the actual computations.
>
|
|