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Old 2015-11-17, 12:35   #1
paul0
 
Sep 2011

718 Posts
Default LLL in GP/Pari

I'm trying the qflll function Pari for lattice reduction. However, I'm not getting correct answers.

First, the wikipedia example: https://en.wikipedia.org/wiki/Lenstr...tion_algorithm
Code:
(20:32) gp > qflll([1,-1,3;1,0,5;1,2,6])
%50 =
[-4  5 0]

[-1  1 1]

[ 1 -1 0]
Second, the matlab example: http://www.mathworks.com/help/symboloddslotic/mupad_ref/lllint.html
Code:
(20:32) gp > qflll([1, 2, 3;4, 5, 6])
%51 =
[-1  4]

[ 1 -3]

[ 0  0]

As you can see, both results are incorrect. What am I doing wrong?

Last fiddled with by paul0 on 2015-11-17 at 12:35
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Old 2015-11-17, 13:01   #2
WraithX
 
WraithX's Avatar
 
Mar 2006

7308 Posts
Default

Quote:
Originally Posted by paul0 View Post
I'm trying the qflll function Pari for lattice reduction. However, I'm not getting correct answers.

First, the wikipedia example: https://en.wikipedia.org/wiki/Lenstr...tion_algorithm
Code:
(20:32) gp > qflll([1,-1,3;1,0,5;1,2,6])
%50 =
[-4  5 0]

[-1  1 1]

[ 1 -1 0]
As you can see, both results are incorrect. What am I doing wrong?
Be sure to check the built-in documentation for what a function does, using either ?<func> or ??<func>:
Code:
?qflll
qflll(x,{flag=0}): LLL reduction of the vectors forming the matrix x (gives the
unimodular transformation matrix T such that x*T is LLL-reduced). flag is...
Doing the following works:
Code:
(06:54) gp > x=[1,-1,3;1,0,5;1,2,6]
%1 =
[1 -1 3]
[1  0 5]
[1  2 6]

(06:54) gp > qflll(x)
%2 =
[-4  5 0]
[-1  1 1]
[ 1 -1 0]

(06:54) gp > x*qflll(x)
%3 =
[0 1 -1]
[1 0  0]
[0 1  2]
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Old 2015-11-17, 13:04   #3
paul0
 
Sep 2011

718 Posts
Default

Quote:
Originally Posted by WraithX View Post
Be sure to check the built-in documentation for what a function does, using either ?<func> or ??<func>:
Code:
?qflll
qflll(x,{flag=0}): LLL reduction of the vectors forming the matrix x (gives the
unimodular transformation matrix T such that x*T is LLL-reduced). flag is...
Thank you :)

Last fiddled with by paul0 on 2015-11-17 at 13:04
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