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I think that when I su==use the variables x,y,z, Sage does the computation in the quotient ring R and when I use the variables X,Y,Z, Sage uses the base ring A. Therefore, I think that Sage really did the computation in R and found the Groebner basis of the ring J of R. The variables Xbar, Ybar and Zbar stand are the variable x,y,z

I think that when I su==use use the variables x,y,z, Sage does the computation in the quotient ring R and when I use the variables X,Y,Z, Sage uses the base ring A. Therefore, I think that Sage really did the computation in R and found the Groebner basis of the ring J of R. The variables Xbar, Ybar and Zbar stand are the variable x,y,z

I think that when I use the variables x,y,z, Sage does the computation in the quotient ring R and when I use the variables X,Y,Z, Sage uses the base ring A. Therefore, I think that Sage really did the computation in R and found the Groebner basis of the ring J of R. The variables Xbar, Ybar and Zbar stand are the variable variables x,y,z