# Question:Ore_algebra or OreTools - which package to use for multivariate Ore polynomials?

## Question:Ore_algebra or OreTools - which package to use for multivariate Ore polynomials?

Maple
Hello everybody, 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. An example: Let's consider a differential Ore algebra and two Ore polynomials in the indeterminate x, whose coefficients are functions of time: a(x)=f(t)*x+1 b(x)=g(t) I want to calculate their (non-commutative) products, a(x)*b(x) and b(x)*a(x), respectively. Using OreTools I can do it in the following way: ```with(OreTools): S:=SetOreRing(t,'differential'); a:=OrePoly(1,f(t)); b:=OrePoly(g(t)); ab:=Multiply(a,b,S); ba:=Multiply(b,a,S);``` However, when I try to do the same with Ore_algebra, ```with(Ore_algebra): S:=diff_algebra([x,t]); a:=f(t)*x+1; b:=g(t); ab:=skew_product(a,b,S); ba:=skew_product(b,a,S);``` I get the "(in Ore_algebra:-OA_Internals:-skew_product) skew polynomials must be members of the algebra" error. Does anybody know how to cure this? Is there a mistake somewhere? Trying to fix the problem myself I did a bit of googling and came across a sentence saying that "all Ore rings specified in the Ore_algebra package are a priori with integer coefficients, and any other type of coefficient has to be explicitly specified" - I guess that this might be the actual cause here, unfortunately, I've no idea how I can "explicitly specify" the type of coefficients I need... So which package, in your opinion, is better for multivariate Ore polynomials, Ore_algebra or OreTools? I would prefer to use the latter, if it could be extended so as to handle multivariate Ore polynomials. However, if Ore_algebra is the only option, I would like to know how I can tell it to "behave". I'll appreciate any kind of advice. Thank you very much in advance!
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