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Really, it should be reducing 37 mod 5 when you do the conversion, or at the very least when you print it out, otherwise you don't realise that 37 + O(5) and 7 + O(5) are really the same thing. (This caused me a few hours of head-scratching today because I thought that two things didn't agree when actually they did.)
If you use the default series_print=True, then this doesn't happen:
sage: K = pAdicField(5)
sage: K(37, prec=1)
2 + O(5)
The following behaviour, while strictly speaking not incorrect, is quite confusing:
Really, it should be reducing 37 mod 5 when you do the conversion, or at the very least when you print it out, otherwise you don't realise that 37 + O(5) and 7 + O(5) are really the same thing. (This caused me a few hours of head-scratching today because I thought that two things didn't agree when actually they did.)
If you use the default series_print=True, then this doesn't happen:
Component: basic arithmetic
Issue created by migration from https://trac.sagemath.org/ticket/12
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