human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "counting solutions of a polynomial system locally and exactly"):
  Abstract: We propose a symbolic-numeric algorithm to count the number of solutions of a polynomial system within a local region. More specifically, given a zero-dimensional system $f_1=\cdots=f_n=0$, with $f_i\in\mathbb{C}[x_1,\ldots,x_n]$, and a polydisc $\mathbf{\Delta}\subset\mathbb{C}^n$, our method aims to certify the existence of $k$ solutions (counted with multiplicity) within the polydisc. #R##N#In case of success, it yields the correct result under guarantee. Otherwise, no information is given. However, we show that our algorithm always succeeds if $\mathbf{\Delta}$ is sufficiently small and well-isolating for a $k$-fold solution $\mathbf{z}$ of the system. #R##N#Our analysis of the algorithm further yields a bound on the size of the polydisc for which our algorithm succeeds under guarantee. This bound depends on local parameters such as the size and multiplicity of $\mathbf{z}$ as well as the distances between $\mathbf{z}$ and all other solutions. Efficiency of our method stems from the fact that we reduce the problem of counting the roots in $\mathbf{\Delta}$ of the original system to the problem of solving a truncated system of degree $k$. In particular, if the multiplicity $k$ of $\mathbf{z}$ is small compared to the total degrees of the polynomials $f_i$, our method considerably improves upon known complete and certified methods. #R##N#For the special case of a bivariate system, we report on an implementation of our algorithm, and show experimentally that our algorithm leads to a significant improvement, when integrated as inclusion predicate into an elimination method.

Includes members:
  Member "powers of tensors and fast matrix multiplication":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "new algorithms and hardness for incremental single source shortest paths in directed graphs")
  Member "exact symbolic numeric computation of planar algebraic curves":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "on the complexity of computing with planar algebraic curves")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.SC(Symbolic Computation)