To create a capped relative precision ring, use Zp
as before. To create capped relative precision fields, use
Qp
.
sage: R = Zp(5, prec = 10, type = 'capped-rel', print_mode = 'series') sage: R 5-adic Ring with capped relative precision 10 sage: K = Qp(5, prec = 10, type = 'capped-rel', print_mode = 'series') sage: K 5-adic Field with capped relative precision 10
We can do all of the same operations as in the other two cases, but precision works a bit differently: the maximum precision of an element is limited by the precision cap of the ring.
sage: a = R(375) sage: a 3*5^3 + O(5^13) sage: b = K(105) sage: b 5 + 4*5^2 + O(5^11) sage: a + b 5 + 4*5^2 + 3*5^3 + O(5^11) sage: a * b 3*5^4 + 2*5^5 + 2*5^6 + O(5^14) sage: c = a // 5 sage: c 3*5^2 + O(5^12) sage: c + 1 1 + 3*5^2 + O(5^10)
As with the capped absolute precision rings, we can divide, yielding a capped relative precision field element.
sage: 1 / (c + b) 5^-1 + 3 + 2*5 + 5^2 + 4*5^3 + 4*5^4 + 3*5^6 + 2*5^7 + 5^8 + O(5^9)
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