sage: gp.qflll?
Type:           GpFunction
String form:    qflll
File:           /opt/sage-devel/local/lib/python2.7/site-
packages/sage/interfaces/gp.py
Definition:     gp.qflll(self, *args, **kwds)
Docstring:
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 optional, and can be 0: default, 1: assumes x is
integral, 2: assumes x is integral, returns a partially reduced basis,
4: assumes x is integral, returns [K,T] where K is the integer kernel
of x and T the LLL reduced image, 5: same as 4 but x may have
polynomial coefficients, 8: same as 0 but x may have polynomial
coefficients.

Pari returns the transformation matrix not the reduced basis.

Cheers,
Martin

On Monday 05 Jan 2015 09:23:03 Ralf Stephan wrote:
> Hello,
> why do Pari and Sage give wildly different results:
> 
> sage: A = matrix(ZZ, [[0,1,3,14],[1,3,14,59],[3,14,59,247],[14,59,247,988]])
> sage: gp.qflll(A)
> [-5, 1, 30, -23; -3, 4, 18, -28; 1, -1, -10, 12; 0, 0, 1, -1]
> sage: A.LLL()
> [ 0  0  2  0]
> [ 1 -1  0  3]
> [ 2  3 -1  0]
> [-6  2  0  2]
> 
> and how do I get Pari's output using Sage's interface to fplll?
> (Actually I'm only interested in the first column)
> 
> Regards,

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