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2013-11-11 10:46:00 +0200 asked a question Maximal unramified extension of Qp

Hello,

is it possible to deal with the maximal unramified extension of Qp in Sage?

If so, then please post a code example! Thanks!

Bye Lars

2013-11-11 10:39:31 +0200 commented answer Roots of p-adic polynomials

Thanks for your response!

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2013-11-05 13:29:22 +0200 commented answer Roots of p-adic polynomials

Thanks for your fast response. This is too bad. I took a look at this ticket and it looks promising. Unfortunately my knowledge of Python is not enough to help you. Is it even possible for me as a beginner in Python and Sage to implement Hensel lifting by myself or do I need deep knowledge of Python and Sage for this task? Is there an alternative to Sage which offers the function to compute p-adic roots of p-adic polynomials? Maybe KASH, Octave, Maple or Magma? Thanks again! Bye Lars

2013-11-05 13:06:00 +0200 answered a question Roots of p-adic polynomials

Thanks for your fast response.

This is too bad. I took a look at this ticket and it looks promising. Unfortunately my knowledge of Python is not enough to help you.

Is it even possible for me as a beginner in Python and Sage to implement Hensel lifting by myself or do I need deep knowledge of Python and Sage for this task?

Is there an alternative to Sage which offers the function to compute p-adic roots of p-adic polynomials? Maybe KASH, Octave, Maple or Magma?

Thanks again!

Bye Lars

2013-11-04 14:54:57 +0200 asked a question Roots of p-adic polynomials

Hello again,

I want to get the roots of a p-adic polynomial. I wrote the following code:

p = 2
q = 4
K = Qp(p)
L.<omega> = Qq(q)
O_L = L. integer_ring()
pi = L.uniformizer()
q = L.residue_class_degree()
f = X^q + pi*X
f.roots()

This rises following error:

NotImplementedError: root finding for this polynomial not implemented

I still use version 5.10 of Sage. The compile of the latest version 5.12 is ongoing. Do I miss something or is there no way to get the roots in this case?

Will this be implemented in the future or does someone know a workaround?

Thanks for your time again!

Bye Lars

2013-11-04 14:39:39 +0200 answered a question p-adic power series

Thanks! This solves my problem.

2013-11-04 14:38:51 +0200 received badge  Supporter (source)
2013-11-03 05:23:41 +0200 asked a question p-adic power series

Hello,

I am new to Sage and I want to to do some math on p-adic power series. I want to define such a power series but I did not succeeded. The last line of the following code rises an exception:

p = 2
q = 4
K = Qp(p)
L.<omega> = Qq(q)
O_L = L.integer_ring()
R.<X> = PowerSeriesRing(O_L)
pi = L.uniformizer()
q = L.residue_class_degree()
f(X) = X^q + pi*X

TypeError: unsupported operand parent(s) for '*': '2-adic Field with capped relative precision 20' and 'Symbolic Ring'

Can someone help me, please? Thanks for your time!

Bye Lars