The Irreducibility and Isomorphism of Piecewise Algebraic Sets

Abstract:

      In this paper , we define the piecewise algebraic sets by using multivariate spline functions and discuss their irreducibility and isomorphism problem. We present two equivalent conditions for the irreducibility of piecewise algebraic sets, and turn the isomorphism and classifying problem of piecewise algebraic sets into the isonorphism and classifying problem of commutative algebras.