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The method is_globally_equivalent_to answers this and provides the matrix:
sage: QA = QuadraticForm(QQ, 4, [4, -12, 8, -4, 12, -16, 8, 6, -6, 2])
sage: QB = QuadraticForm(QQ, 4, [2, -2, -2, -2, 2, 0, 0, 2, 0, 2])
sage: X = QA.is_globally_equivalent_to(QB, return_matrix=True); X
[ 0 0 0 1]
[ 0 0 1 0]
[ 0 1 1 -1]
[ 1 1 -1 -1]
sage: X.transpose()*QA.matrix()*X == QB.matrix()
True
This calls the PARI function qfisom, which implements an algorithm of Plesken and Souvignier.
