LLL in GP/Pari

[paul0]

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

(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

(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?

[WraithX]

Originally Posted by paul0

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

(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>:

?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:

(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]

[paul0]

Originally Posted by WraithX

Be sure to check the built-in documentation for what a function does, using either ?<func> or ??<func>:

?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 :)