基于插值法计算Dixon结式

在经典方法中，计算Dixon多项式和结式都要涉及到行列式的计算。由于行列式中的元素通常是符号化的，即其中每个元素都是关于变元(或参数)的多项式，从而导致行列式展开时的中间计算过程膨胀(甚至爆炸)。对此，提出在结式计算过程中将符号计算数值化，即对变元选择不同的插值点，将行列式中的元素数值化。然后，求出在不同插值点下行列式的值。最后，根据Zippel多变元插值法或其他相关插值算法计算出Dixon多项式和结式。采用插值方法有效克服了经典算法的中间计算过程膨胀问题。

Computing Dixon resultant by interpolation algorithms

When usingclassical method to compute Dixon resultant, ithastodeal withthe computation of matrices anddeterminant in the procedure of computing Dixon polynomial and resultant. However, each entry in matricesis symbolic, that is, it is a poly- nomial in variable s . This leads to the intermediate expression swell or explosion) problem in the computation. In order to ( ) ( avoid this, we transformthe symbolic computation to numerical computation, i.e., selectsupportpointsforvariables and evaluate the valueto each entries of determinant. As theresult of this, the symbolicdeterminantisbecome numerical ones anditsdeterminant can be computedout. We canget the interpolative polynomial by selectingdifferentsupportpoints. Finally, the Dixonpolynomial and resultant are obtained by interpolation methods. It is avoided that the intermediate expression swell problem is inevitable in the classical computation of the Dixon resultant .