Is there a way to understand whether there exist linear transformation that brings one cubic form of n variables to another form? In particular one of the examples I am interested in are two cubic forms in 4 variables:
$F_1=x_1 x_2 x_3+x_1 x_3 x_4+ x_1 x_2 x_4+ x_2 x_3 x_4$
$F_2=x_1 x_2 x_3 + x_1 x_3 x_4 + 2x_1 x_2 x_4$
If there is a way to understand whether such transformation exists is there an algorithm allowing to find this transformation?