2021/02/05 by Jakob Ablinger, Carsten Schneider, Ablinger, Jakob +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Protein Degradation and Inhibitors #Polynomial and algebraic computation #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2102.03307
We introduce a general reduction strategy that enables one to search for\nsolutions of parameterized linear difference equations in difference rings.\nHere we assume that the ring itself can be decomposed by a direct sum of\nintegral domains (using idempotent elements) that enjoys certain technical\nfeatures and that the coefficients of the difference equation are not\ndegenerated. Using this mechanism we can reduce the problem to find solutions\nin a ring (with zero-divisors) to search solutions in several copies of\nintegral domains. Utilizing existing solvers in this integral domain setting,\nwe obtain a general solver where the components of the linear difference\nequations and the solutions can be taken from difference rings that are built≠.g., by R\Π\Σ-extensions over \Π\Σ-fields. This class of\ndifference rings contains, e.g., nested sums and products, products over roots\nof unity and nested sums defined over such objects.\n