Create three power series.
Create a power series representing the sum of and .
Add 1 to .
Add , , , and the polynomial .
Compute .
Create a univariate polynomial over power series, given by a polynomial.
Add a polynomial to . These two calling sequences are equivalent.
Add a power series to f that is independent of z (and thus trivially polynomial in z).
Create a separate univariate polynomial over power series, and add it to f.
This will raise an error, because we're trying to add univariate polynomials over power series with different main variables.
This also will not work, because Maple cannot determine that d is polynomial in z (though actually it is).
We define e in the same way as d but specify the analytic expression, and then we can successfully add it to f.
Create three Puiseux series.
We add and .
We add a polynomial to .
We can add and the power series . The result is a Puiseux series.
We can also add and the univariate polynomial over power series . The result is again a Puiseux series.
We get an error if we try to add and , since the orders and are not compatible.
We can use the command GetPuiseuxSeriesOrder to obtain the Puiseux series order of and .
Finally, we create a univariate polynomial over power series from a list of Puiseux series.
Now we add to .