NLA99: Computer Algebra : The Fourth Symposium on Nonlinear Analysis, September 16-18, 1999 Josai University

We studied the residue pairing induced by an algebraic local cohomology class froma view point of the theory of D-modules in [2] and [3] . For a cohomology class of onedimensional case, we constructed a linear differential operator of order one which was thetheoretical foundation of an algorithm for computing residues (cf. [3]). On the other hand,in the theory of quasihomogeneous singularities, it is known that linear partial differentialoperators of order one determined by weights play an important role.In this paper, we look at a differential operaots of order I associated to an algebraic localcohomology class. First, we consider the normal forms of quasihomogeneous polynomials.Then we provide a method for computing a presentation of a cohomology class for aquasihomogeneous polynomial. Next, we provide a method for computing linear partialdifferential operators of order one associated to a cohomology class of general n dimensionalcase.NLA99: Computer Algebra : The Fourth Symposium on Nonlinear Analysis, September 16-18, 1999 Josai University, edited by Kiyoko Nishizawa (Josai University), Tomokatsu Saito (Sophia University), Teluhiko Hilano (Kanagawa Inst. Tec.