2022-05-12 02:35:23 +0200 received badge ● Popular Question (source) 2017-05-09 16:32:08 +0200 received badge ● Editor (source) 2017-05-09 16:27:09 +0200 received badge ● Scholar (source) 2017-05-09 16:27:07 +0200 received badge ● Supporter (source) 2017-05-09 13:11:17 +0200 commented answer Is there a way to create the ring of multi-variable polynomials over a field? I think I found a workaround: def yesitis(proof=False): return True R2.is_field = yesitis Rx. = R2[]  2017-05-09 11:53:03 +0200 commented answer Is there a way to create the ring of multi-variable polynomials over a field? I am trying the following: R0.=ZZ[] R0F = R0.fraction_field() Rx. = R0F[] R1. = R0F.extension(x1^2-y1^3-1) Rx. = R1[] R2. = R1.extension(x2^2-y2^3-1) Rx. = R2[]  The last command gives me NotImplementedError 2017-05-09 11:38:45 +0200 received badge ● Student (source) 2017-05-08 22:30:43 +0200 asked a question Is there a way to create the ring of multi-variable polynomials over a field? Suppose I create a field in SAGE. Maybe it is my own field implemented in some particular way, but I know it is a field and it can do all the operations. Is there any way at all to create a ring of polynomials in several variables over my field? Of course it might be less efficient than SINGULAR implementation, but still some fall back "toy" implementation would be nice, so that I can run the "toy" Groebner basis algorithm on it. UPDATE: it turns out, the question should have been formulated as "how to make SAGE believe that my field is a field?". Once this is solved, the usual PolynomialRing function works as expected.