We present results on multiplicity theory. Differential operators on smooth schemes play a central role in the study of the multiplicity of an embedded hypersurface at a point. This follows from the fact that the multiplicity is defined by the Taylor development of the defining equation at such point. On the other hand, the multiplicity of a hypersurface at a point can be expressed in terms of ...

We analyze the bit complexity of an algorithm for computation at least one point in each connected component a smooth real algebraic set. This work is continuation our analysis hypersurface case (On finding points components hypersurface, ISSAC'20). In this paper, we extend to more general cases. Let F=(f1,…,fp) Z[X1,…,Xn]p be sequence polynomials with V=V(F)⊂Cn and equidimensional variety 〈F〉⊂...

we study connected orientable spacelike hypersurfaces $x:m^{n}rightarrowm_q^{n+1}(c)$, isometrically immersed into the riemannian or lorentzian space form of curvature $c=-1,0,1$, and index $q=0,1$, satisfying the condition $~l_kx=ax+b$,~ where $l_k$ is the $textit{linearized operator}$ of the $(k+1)$-th mean curvature $h_{k+1}$ of the hypersurface for a fixed integer $0leq k