Computations and Some Open Problems

I’ll discuss some open problems related to differential algebra for which experiments in computations may be helpful. Examples showing how to set up such experiments will be given. There are two obvious points I want to make: 1. Computations become necessary when we want to compute something, like solving a system of (differential) equations, or finding some examples or counterexamples. 2. In turns, computational consideration of effectiveness and efficiency may itself lead to mathematical problems, such as complexity, enumeration of vector space basis, encoding of input and output, etc. Some of these problems are of interest in its own right. Advice: You can write a dissertation or paper on the new problems if you cannot solve the original computation problem!