论文标题
稀疏产生的Canny-Emiris猜想
The Canny-Emiris conjecture for the sparse resultant
论文作者
论文摘要
我们为与任意支持家族相关的稀疏结果的初始部分提供了一个产品公式，从而概括了Sturmfels先前的结果。这允许计算稀疏产生物的同质性和程度，并在具有较小支撑的劳伦（Laurent）多项式系统上进行评估。我们获得了类似的乘积公式，用于与与多面体混合细分相关的Sylvester型正方形基质的主要未成年人的一些初始部分。应用这些结果，我们证明，在适当的假设下，可以将稀疏结果计算为某个主要的未成年人的确定性。这将概括为均匀产生的经典曲线公式，并确认了Canny和Emiris的猜想。
We present a product formula for the initial parts of the sparse resultant associated to an arbitrary family of supports, generalising a previous result by Sturmfels. This allows to compute the homogeneities and degrees of the sparse resultant, and its evaluation at systems of Laurent polynomials with smaller supports. We obtain a similar product formula for some of the initial parts of the principal minors of the Sylvester-type square matrix associated to a mixed subdivision of a polytope. Applying these results, we prove that the sparse resultant can be computed as the quotient of the determinant of such a square matrix by a certain principal minor, under suitable hypothesis. This generalises the classical Macaulay formula for the homogeneous resultant, and confirms a conjecture of Canny and Emiris.
