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If I use

 P.<x,y,z> = InfinitePolynomialRing(QQ)

Assuming any of the orderings 'lex, deglex, degrevlex' I will have

$z_0 < z_1 < z_2 < ... < y_0 < y_1 < ... < x_0 < x_1 < ...$

And each variable having degree 1. I would like to obtain something like 'deglex' but assigning degree $n$ to $x_n,y_n,z_n$ so that in particular I would obtain

$z_0 < y_0 < x_0 < z_1 < y_1 < x_1 < ...$

Is there a way to implement this. It seems that in order to compute Grobner bases on arc schemes these orderings are much more natural that the ones implemented, but I just started looking at Sage so I may have missed the right implementation of polynomial rings in infinitely many variables to work.

If I use

 P.<x,y,z> = InfinitePolynomialRing(QQ)

Assuming any of the orderings 'lex, deglex, degrevlex' I will have

$z_0 < z_1 < z_2 < ... < y_0 < y_1 < ... < x_0 < x_1 < ...$

And each variable having degree 1. I would like to obtain something like 'deglex' but assigning degree $n$ to $x_n,y_n,z_n$ so that in particular I would obtain

$z_0 < y_0 < x_0 < z_1 < y_1 < x_1 < ...$

Is there a way to implement this. It seems that in order to compute Grobner bases on arc schemes these orderings are much more natural that the ones implemented, but I just started looking at Sage so I may have missed the right implementation of polynomial rings in infinitely many variables to work.