2021-04-14 11:26:33 +0200 | answered a question | Power Series Ring over p-adics: TypeError: unhashable Depending on what you want to do, you can maybe also consider using the constructor TateAlgebra (it is not exactly the s |

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2021-01-22 23:49:55 +0200 | answered a question | How can I compute a fixed field over the p-adics It's also possible to do the calculation in plain SageMath but we need to help it because creating arbitrary extensions of p-adic fields is currently not implemented. First, we can create the field $F$: Then we create $LF$. For this, we need to find an uniformizer. For this, we factor the polynomial $f(x) = x^4 - 3x^2 + 18$ over $F$. Unfortunately, factorization is also not implemented. So we do it by hand as follows: Now we can build the extension: In order to define $\varphi$, we first define the automorphism of $F$; it is actually just the Frobenius: As noticed by saraedum, there are two possibilities for $\varphi$ depending on the choice of the square root of $-\frac 2 7$. Finally, we can check whether $\varphi_1$ (resp. $\varphi_2$) fixes $\sqrt 3$ or $\sqrt{-3}$: |

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