The Frobenius endomorphism on a ring of prime characteristic p, which sends a ring element to its p-th power, is a fundamental tool in prime characteristic commutative algebra. Kunz has shown that regularity is characterized by the behavior of this map, and since then, many other properties of Frobenius have been used to measure how far a ring is from being regular.
Numerical invariants of rings, and of their elements and ideals, play an important role in this endeavor. Of particular focus are the F-pure threshold, and more generally, F-thresholds.
However, the computation of these numerical invariants can be quite subtle, and at the same time computationally complex. In partnership with the package TestIdeals, which provides some important functionality for researchers in positive characteristic commutative algebra, the package FThresholds implements known algorithms, as well as new methods, to estimate and compute numerical invariants in prime characteristic.