MaxBettiNumbers -- Methods to find maximum Betti numbers given bounds on the Hilbert function.

The method maxBettiNumbers is the headliner in this package. It returns upper bounds for the total Betti numbers in a family that has bounds on the Hilbert function and/or the Hilbert difference function.

The method maxBettiNumbers can optionally return special Hilbert functions. The methods almostLexBetti and almostLexIdeal are helpful in working with these Hilbert function. The functions lexBetti and lexsegmentIdeal use the same code, and are exported from the package in hopes that they are useful. These functions are written with a concern for speed and efficiency.