I will add to Daniel's answer:
This is really dependent on how you define the system you work in: how you define "identity", and how you treat constant polynomials.
For example, if you treat polynomials as functions, and by "identical" you mean that they are truly the same mathematical object, then you can say (using lambda notation):
$Z = \lambda x.0$, in this case $Z \ne 0$, but $\forall x.Z(x)=0$. Also, $0$ is a symbol, you can define it to be the natural number zero, the zero polynomial, or both.
On the other hand, WolframMathWorld states that "A quantity which rigorously assumes the value of zero is said to be identically zero." In that sense, yes, it is identically zero.
I do not think there is a definite answer to your question. I also think it would be safe to say that the zero polynomial is not equal to zero (the number), yet it is identically zero (as a matter of definition).
Of course, this has nothing to do with the homework, which is about python objects representing polynomials.
Jon (guest) 12 Jun 2017 15:35