For a rational quadratic form $Q$ in dimension $n$ I want to recognize when it is anisotropic or not. For $n=1$ or $2$ this is trivial, for $n> 4$ this cannot happen by Meyer's theorem.
For $n=3$ we have Lagrange's descent that allows us to solve this question (see https://public.csusm.edu/aitken_html/notes/legendre.pdf or http://alpha.math.uga.edu/~pete/qforms-global.pdf) reasonably simply.
What about $n=4$? Is there a simple criterion?
If the Hasse principle is the only possible solution, how hard is it to implement it on a computer?