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Can I create 10-adic numbers?

asked 2022-06-29 22:29:15 +0200

Lilly2 gravatar image

I'm learning about P-adics, and would like to play around a bit with 10-adic numbers, to follow along with some tutorials.

Unfortunately so far all ways I've tried to create 10-adic numbers in Sage resulted in the error "p must be prime".

I understand non-prime-adics have their issues, but can I still make it work somehow?

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answered 2022-06-30 17:11:34 +0200

Max Alekseyev gravatar image

updated 2022-06-30 17:19:13 +0200

slelievre gravatar image

PARI/GP supports $p$-adic numbers with non-prime $p$:

This can be used inside Sage:

sage: a = gp('1 + O(10^3)')
sage: a
1 + O(10^3)
sage: a + 100
1 + 10^2 + O(10^3)
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answered 2022-06-30 15:07:52 +0200

Klaus Scheicher gravatar image

You can define infinitely long decimal numbers, but you can not divide such numbers in any case. This numbers form a ring, but not a field. Therefore the error message.

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Asked: 2022-06-29 22:29:15 +0200

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Last updated: Jun 30 '22