Consider a sparse polynomial in several variables given explicitly as a sum of non-zero terms with coefficients in an effective field. In this paper, we present several algorithms for factoring such polynomials and related tasks (such as gcd computation, square-free factorization, content-free factorization, and root extraction). Our methods are all based on sparse interpolation, but follow two main lines of attack: iteration on the number of variables and more direct reductions to the univariate or bivariate case. We present detailed probabilistic complexity bounds in terms of the complexity of sparse interpolation and evaluation.

翻译：考虑一个以有效域中系数形式明确表示为非零项之和的稀疏多项式。本文提出了用于因式分解此类多项式的若干算法及关联任务（如最大公因式计算、无平方因子分解、无内容因子分解和根提取）。我们的方法均基于稀疏插值，但遵循两条主要攻击路线：对变量数目进行迭代，以及更直接地化简为单变量或双变量情形。我们基于稀疏插值与求值的复杂度，给出了详细的概率复杂度界限。