Although this question might seem silly to Maple experts, I cannot help asking, since despite a long search through Maple Help and Maple Guides I was not able to come across the answer. What I mean is this:
> eq1 := diff(y(t),t)-y(t)^2+y(t)*sin(t)-cos(t) = 0;
> # here I want some command that would return the order of eq1, i.e. 1
> eq2 := diff(y(t),`$`(t,2)) = y(t)*u(t) + diff(u(t),t);
> something(eq2,y); # this should return 2
> something(eq2,u); # this should return 1
Besides, I would also need the same for recurrent (shift) equations, i.e.
I hope some of you have experience with multivariate Ore polynomials in Maple and will be able to answer the title question.
So far I've needed only univariate Ore polynomials, used the OreTools package for them and have been very satisfied with it. However, now I've come across a problem that needs to employ multivariate ones - therefore I am forced to try the Ore_algebra package, which should make computations with multivariate Ore polynomials possible (as far as I know, OreTools cannot handle multivariate Ore polynomials - or am I wrong? I wish I was)
And here comes my trouble! Not only that I am not able to solve my multivariate problem with Ore_algebra, I don't even know how to do simple calculations (which can be so easily performed with OreTools) using Ore_algebra.