LLL reduced basis

asked 2025-08-13 03:29:45 +0200

ELLEI gravatar image

I am using Sage to find the LLL reduced log-unit lattices of number fields and this is how I do it: 

bnf = K.pari_bnf()
UL = [[bnf[2][j][i].sage().real() for i in range(r+1)] for j in range(r)]
G=Matrix(RR, r, [u.dot_product(v) for u in UL for v in UL])
L = pari.qflllgram(pari(G)

In above, K is my number field and UL is the basis matrix. I use it to get the corresponding Gram matrix. When I use but L always is an identity matrix.

If I input the above Gram matrix directly in PARI to qflll(G), it outputs the correct transformation LLL reduction basis. why I always get identity matrix in Sage??

Thank you!

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Comments

Please add some complete code that actually runs. Do you mean something like this?

R.<x> = PolynomialRing(QQ)
f = R.zero()
while not f.is_irreducible():
    f = R.random_element(degree=5)
K.<a> = NumberField(f)
bnf = K.pari_bnf()
r = bnf[2].sage().nrows() - 1
UL = [vector([bnf[2][j][i].sage().real() for i in range(r+1)]) for j in range(r)]
G = Matrix(RR, r, [u.dot_product(v) for u in UL for v in UL])
L = pari.qflllgram(pari(G))
rburing gravatar imagerburing ( 2025-08-14 10:35:11 +0200 )edit
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