# Bounds -- an option for the function fpt specifying lower and upper bounds for the F-pure threshold

## Description

An option for the function fpt specifying bounds for the $F$-pure threshold. Bounds accepts lists consisting of two numbers, namely a lower and an upper bound for the $F$-pure threshold being computed. This useful feature allows the user to refine bounds obtained in previous computations, as illustrated below.

 i1 : R = ZZ/5[x,y]; i2 : f = x^7*y^5*(x + y)^5*(x^2 + y^3)^4; i3 : fpt(f, DepthOfSearch => 3, Attempts => 5) 19 1 o3 = {---, --} 250 13 o3 : List i4 : fpt(f, DepthOfSearch => 3, Attempts => 5, Bounds => oo) 45 1 o4 = {---, --} 589 13 o4 : List

## Functions with optional argument named Bounds :

• "fpt(...,Bounds=>...)" -- see fpt -- attempt to compute the F-pure threshold of a polynomial at the origin or globally

## For the programmer

The object Bounds is .