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Ideal of norm in the equation order over a function field does not work

#42215OpenArixEggink 创建于 2026-05-20
t: feature
A
ArixEgginkcommented
### Steps To Reproduce The following code: ``` q = 3; Fq = GF(q); A.<T> = Fq[]; F.<S> = FunctionField(Fq); R.<x> = F[]; K.<x> = F.extension(x^3 + x^2 + (2*S + 1)*x + 2*S^2) O = K.equation_order() I = O.ideal(x); print(O); print(I); No = I.norm(); print(No); ``` gives as output: Order in Function field in x defined by x^3 + x^2 + (2*S + 1)*x + 2*S^2 Ideal (2*x^2 + (S + 2)*x + S^2, 2*x, 2*x^2) of Order in Function field in x defined by x^3 + x^2 + (2*S + 1)*x + 2*S^2 Ideal (2*x^2 + (S + 2)*x + S^2, 2*x, 2*x^2) of Order in Function field in x defined by x^3 + x^2 + (2*S + 1)*x + 2*S^2 The third line should give the norm of the ideal, which is an element of F. When replacing equation_order with maximal_order, I get the output: Maximal order of Function field in x defined by x^3 + x^2 + (2*S + 1)*x + 2*S^2 Ideal (x) of Maximal order of Function field in x defined by x^3 + x^2 + (2*S + 1)*x + 2*S^2 S^2 This nicely gives the norm. ### Expected Behavior I expect that if I use the equation_order (or some other order) I get the norm of the ideal ### Actual Behavior I get back the ideal itself instead of its norm. ### Additional Information _No response_ ### Environment - **OS**: Windows 11 education, but via Ubuntu - **Sage Version**: SageMath version 10.7, Release Date: 2025-08-09 │ │ Using Python 3.11.14. ### Checklist - [x] I have searched the existing issues for a bug report that matches the one I want to file, without success. - [x] I have read the documentation and troubleshoot guide
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