August 2011
Intermediate to advanced
332 pages
9h 10m
English
Content preview from Lattice Basis Reduction
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.
150 Lattice Basis Reduction
Example 9.5. Using the method of continued fractions to find rational ap-
proximations for the square roots of the first four prime number s, we obtain
√
2 ≈
1
1
,
3
2
,
7
5
,
17
12
,
41
29
,
99
70
,
239
169
,
577
408
,
1393
985
, . . .
√
3 ≈
1
1
,
2
1
,
5
3
,
7
4
,
19
11
,
26
15
,
71
41
,
97
56
,
265
153
, . . .
√
5 ≈
2
1
,
9
4
,
38
17
,
161
72
,
682
305
,
2889
1292
,
12238
5473
,
51841
23184
,
219602
98209
, . . .
√
7 ≈
2
1
,
3
1
,
5
2
,
8
3
,
37
14
,
45
17
,
82
31
,
127
48
,
590
223
, . . .
Note that the only denominator that appears in e very list of the first 9 ap-
proximations is the trivial denominator 1.
We now consider simultaneous approximation of these four square roots.
We sta rt w ith the first rational approximation in each ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Read now
Unlock full access
More than 5,000 organizations count on O’Reilly
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.