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The variables you are trying to use in K are not in R. To have them there define R as a polynomial ring in your variables like:

k_vars = [ ["k_{}_{}".format(u,v) for v in (1..2)] for u in (1..2) ]
R = PolynomialRing(IntegerModRing(22), sum(k_vars,[]) )
K = matrix(R, k_vars)

The variables you are trying to use in K are not in its ring R. To have them there Also, it's better to avoid dealing with symbolic ring (i.e. defining variables via var) whenever possible. A better way here is to define R as a polynomial ring in your variables like:

k_vars = [ ["k_{}_{}".format(u,v) for v in (1..2)] for u in (1..2) ]
R = PolynomialRing(IntegerModRing(22), sum(k_vars,[]) )
K = matrix(R, k_vars)

The variables you are trying to use in K are not in its ring R. Also, it's better to avoid dealing with symbolic ring (i.e. defining variables via var) whenever possible. A better way here is to define R as a polynomial ring in your variables like:

k_vars = [ ["k_{}_{}".format(u,v) for v in (1..2)] for u in (1..2) ]
 R = PolynomialRing(IntegerModRing(22), sum(k_vars,[]) )
R._latex_names = sum( [["k_{{{},{}}}".format(u,v) for v in (1..2)] for u in (1..2)], [] )

K = matrix(R, k_vars)