Sylvester's Signature

Diagonalize a form over the Rationals to

$$\mathop{\rm diag}[p^a\cdot A, p^b\cdot B, \ldots],$$

where all the entries are Integers and $A$, $B$, ...are Relatively Prime to $p$. Then Sylvester's signature is the sum of the $-1$-parts of the entries.

See also p-Signature