分解二元稀疏（缺项）多项式
Factoring bivariate sparse (lacunary) polynomials
摘要：
我们提出了一个确定性算法，用于计算给定的二元多项式$f\in K[x,y]$在代数数域$K$上的次数$\le d$的所有不可约因子及其重数，其运行时间是输入稀疏编码的位长和$d$中的多项式。此外，我们表明，在$\Qbarra$的程度$\le d$，这不是二项式的因素也可以计算在时间多项式的稀疏长度的输入和$d$。
英文摘要：
We present a deterministic algorithm for computing all irreducible factors of degree $\le d$ of a given bivariate polynomial $f\in K[x,y]$ over an algebraic number field $K$ and their multiplicities, whose running time is polynomial in the bit length of the sparse encoding of the input and in $d$. Moreover, we show that the factors over $\Qbarra$ of degree $\le d$ which are not binomials can also be computed in time polynomial in the sparse length of the input and in $d$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
