  The $F$-signature of a local ring of prime characteristic is a numerical
invariant that detects many interesting properties. For example, this invariant
detects (non)singularity and strong $F$-regularity. However, it is very
difficult to compute. Motivated by different aspects of the $F$-signature, we
define a numerical invariant for rings of characteristic zero or $p>0$ that
exhibits many of the useful properties of the $F$-signature. We also compute
many examples of this invariant, including cases where the $F$-signature is not
known. We also obtain a number of results on symbolic powers and Bernstein-Sato
polynomials.
