How to find the nearest integer (+ve or -ve) of a rational number (P/Q)
where P,Q are very large integers?
You could use the .round method of rationals.
sage: q = 17+1/2+1/11**1000
sage: RR(q.numerator()), RR(q.denominator())
(2.48685403212345e10413928, 1.42105944692768e10413927)
sage: q.round()
18
sage: q = 13**(10**7)+1/2+1/11**(10**7)
sage: RR(q.numerator()), RR(q.denominator())
(4.73893349282680e21553360, 1.42105944692768e10413927)
sage: z = q.round()
sage: factor(z-1)
13^1000
sage: help(q.round)
round(...)
File: sage/rings/rational.pyx (starting at line 2858)
Returns the nearest integer to self, rounding away from 0 by
default, for consistency with the builtin Python round.
INPUT:
- ``self`` - a rational number
- ``mode`` - a rounding mode for half integers:
- 'toward' rounds toward zero
- 'away' (default) rounds away from zero
- 'up' rounds up
- 'down' rounds down
- 'even' rounds toward the even integer
- 'odd' rounds toward the odd integer
Doug
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