Deterministic Shift Equivalence Testing for Sparse Polynomials

We study the shift equivalence testing problem for high-degree sparse multivariate polynomials. Given explicit spar se representations of two polynomials $f,g\in\mathbb{Q}[x_1,\ldots,x_n]$, with exponents encoded in binary, sparsities $s$ and $t$, and total degree at most $d$, the task is to decide