Hi.

I have 7 polynomials r[9], r[6, 6], r[7, 9], r[8, 6], r[9, 6], r[6, 9, 7], r[6, 9, 6] each of 7 variables a[3],...,a[9] and I generate an ideal QQ usinig these polynomials. What Maple tells me quite fast is the follows:

IdealMembership(a[3], QQ) 

true

Also using Groebner as follows
F := [r[9], r[6, 6], r[7, 9], r[8, 6], r[9, 6], r[6, 9, 7], r[6, 9, 6]];
G := Basis(F, tdeg(a[3], a[4], a[5], a[6], a[7], a[8], a[9]));
provides me with the basis quite fast and a[3] is part of it. 

---------------

However, Mathematica is stuck and I have noticed that if I change a[3],...,a[9] to x,y,z,,v,w,t then Maple with the same polynomials is evaluating very long time. 

My question is: what am I doing wrong with subscripts a[3],...,a[9] in Maple? Does Maple 2019 have a problem with it?

I have attached my worksheet. 
Maple_Problem.mw
Would appreciate any help.

Hello!

I would appreciate any help on how to do computations on Maple of the following problem. 

Say we have 3 generators x,y,z and I define a map on polynomials in three variables over rational numbers L: Q[x,y,z] -> Q[x,y,z] on the generators, for example L(x)=xy, L(y)=1, L(z)=z^2. 

Then I need to compute L(xy+yz) and it needs to compute it using linearity and derivation (Leibniz rule):

L(x)y+xL(y)+L(y)z+yL(z)=xy^2+x+z+yz^2. 

I have in mind a recursive algorithm but I don't know enough syntacsys to implement it. 

P.S.: I need to compute Poisson brackets on a polynomial algebra for which there is no special way of doing it, right? So I though it must be easier for each basis element to come up with a linear map and extend it via derivations to know its action.