zle-cpp A C++ library for evaluating eigenvalues of integer-linear matrices.
zle-py A Python library for generating, and evaluating eigenvalues of, integer-linear matrices.
zle-mma A Mathematica library for generating, and evaluating eigenvalues of, integer-linear matrices.

$\text{main(}A\text{, batchsize, stagger): }$
     $n\text{, midpoint, midpointvalue, symbols}:=\dots$
     $\text{digits}:=\text{batchsize}\ast (\text{stagger}+1)$
     $\text{indicatorvars}:=[{\text{base}}^{\lceil \frac{\text{digits}}{2}\rceil -\text{stagger}},{\text{base}}^{\lceil \frac{\text{digits}}{2}\rceil -2\ast \text{stagger}},\dots ,{\text{base}}^{-\lfloor \frac{\text{digits}}{2}\rfloor }]\ast i$
     $\text{map}:=\{\text{symbols }:\text{ randomreals}\}$
     $\text{coeffs}:=[]$

     $\text{for }(i=1\text{ to }\lceil \frac{n}{\text{batchsize}}\rceil ):$
         $\text{mapcurr}=\text{map.copy}$
         $\text{mapcurr}[i\ast \text{batchsize},\text{ min}(n,(i+1)\ast \text{batchsize})]\text{ += indicatorvars}$
         $A_i=\text{mapcurr}(A)$
         $\sigma =eig(A_i)+\text{midpoint}$
         $\text{coeffs.insert}([\text{digits}({\sigma }_j)-\text{midpointvalue for }j\text{ in range}(n)])$

     $\text{return }[vec(\text{coeffs}[:,0]),\dots ,vec(\text{coeffs}[:,n-1])]$

Note: Eigenvalue solver expects $\lambda$ coefficients to be in $[-4,5]$ for $\text{stagger}=0$, and $[-44,45]$ for $\text{stagger}=1$.

Please cite this project:

@misc{ZLE,
      title={Fast Symbolic Integer-Linear Spectra}, 
      author={Luntzel, Jonny and Miller, Abraham},
      year={2024},
      eprint={2410.09053},
      archivePrefix={arXiv},
      primaryClass={math.RA},
      url={https://arxiv.org/abs/2410.09053}
}