Various Pólya's conjecture scripts

 

The script for the paper Pólya's conjecture for Euclidean balls (with Nikolay Filonov, Iosif Polterovich, and David A Sher)

Note: the scripts and data sets for the previous version of the paper are now redundant but are kept below for historical purposes

 

The script for the paper Inequalities à la Pólya for the Aharonov--Bohm eigenvalues of the disk (with Nikolay Filonov, Iosif Polterovich, and David A Sher)

 

The script and the data sets for the preprint Pólya's conjecture for the disk: a computer-assisted proof (with Iosif Polterovich and David A Sher): now redundant

The main Mathematica script

Results of the actual calculations, as .csv files of integers: all the fractions are presented as a numerator and a denominator, in separate entries

Dirichlet data

Neumann data

The column headers should be presumed to be, in the Dirichlet case

Dtable

and in the Neumann case

Ntable

Coefficients q and Q, as .csv files of integers: all the fractions are presented as a numerator and a denominator, in separate entries

q

Q

Column headers for qi,j,- and qi,j,+, i=1,…14 are presumed to be

qtable

(and similarly for Qi,j,- and Qi,j,+, i=1,…13), and column headers for QR,k,m, k=1,…10, are

QRtable