# ramified extension of Qp

I am wondering if anyone knows 1. How to define Q_p[\mu_p] in sage, where \mu_p is a primitive p-th root of unity in \bar Q_p. 2. How to write b=\mu_p. 3. Solve a quadratic equation x^2+a_1x+a_2=0, where a_1 and a_2 are both in Q_p[\mu_p]. 4. Is log function defined on Q_p[\mu_p] .

Thank you in advance!

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