Guessing singular dependencies

Guessing singular dependencies

Given d complex numbers z1, ..., zd, it is classical that linear dependencies λ1 z1+ ···+ λd zd=0 with λ1, ..., λd∈Z can be guessed using the LLL-algorithm. Similarly, given d formal power series f1, ..., fd ∈ C[[z]], algorithms for computing Padé-Hermite forms provide a way to guess relations P1 f1 + ···+ Pd fd = 0 with P1, ..., Pd ∈C[z]. Assuming that f1, ..., fd have a radius of convergence ...

Guessing and non-guessing of canonical functions

It is possible to control to a large extent, via semiproper forcing, the parameters (β0, β1) measuring the guessing density of the members of any given antichain of stationary subsets of ω1 (assuming the existence of an inaccessible limit of measurable cardinals). Here, given a pair (β0, β1) of ordinals, we will say that a stationary set S ⊆ ω1 has guessing density (β0, β1) if β0 = γ(S) and β1 ...

Guessing Games

In a guessing game, players guess the value of a random real number selected using some probability density function. The winner may be determined in various ways; for example, a winner can be a player whose guess is closest in magnitude to the target, or a winner can be a player coming closest without guessing higher than the target. We study optimal strategies for players in these games and d...

Guessing Handbook

Introduction This package provides functions for discoverying linear recurrence equations with polynomial coefficients satisfied by the entries of a given array. It extends the functionality of existing packages like Mallinger's GeneratingFunctions.m or Salvy and Zimmermann's gfun in two directions: (1) it is more general in that, e.g., multivariate recurrences, or recurrences of a particular s...

Guessing with Lies