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When I tried the following:

R.<x, y="">= QQ[ ],

I= R.ideal([x, y]),

I.is_prime()

I.is_maximal()

It is running true for I.is_prime but there is an error message when I am running I.is_maximal. It is happening for ring of integers as well. For ring of univariate polynomials, the same command is not giving any error.

When I tried the following:

R.<x, y="">= y>= QQ[ ], 
 
]
I= R.ideal([x, y]),  
 
I.is_prime()
 
I.is_maximal()y])
I.is_prime()
I.is_maximal()