How to convert Gram matrix to quadratic form?

azerbajdzan
201 ●4 ●10 ●20

How to do the opposite? Given gm, how to compute coefficients of quadratic form qf?

qf=QuadraticForm(ZZ, 4, [4, -12, 8, -4, 12, -16, 8, 6, -6, 2])
gm=qf.Gram_matrix()
gm

[ 4 -6  4 -2]
[-6 12 -8  4]
[ 4 -8  6 -3]
[-2  4 -3  2]

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azerbajdzan
201 ●4 ●10 ●20

Is this the only way to do it or there is some built-in function?

QuadraticForm(gm + gm.transpose()).coefficients()

[4, -12, 8, -4, 12, -16, 8, 6, -6, 2]

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Asked: 2023-12-10 23:25:41 +0200

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Last updated: Dec 10 '23