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 "probabilistic algorithm for polynomial optimization over a real algebraic set"):
  Abstract: Let $f, f_1, \ldots, f_\nV$ be polynomials with rational coefficients in the indeterminates $\bfX=X_1, \ldots, X_n$ of maximum degree $D$ and $V$ be the set of common complex solutions of $\F=(f_1,\ldots, f_\nV)$. We give an algorithm which, up to some regularity assumptions on $\F$, computes an exact representation of the global infimum $f^\star=\inf_{x\in V\cap\R^n} f\Par{x}$, i.e. a univariate polynomial vanishing at $f^\star$ and an isolating interval for $f^\star$. Furthermore, this algorithm decides whether $f^\star$ is reached and if so, it returns $x^\star\in V\cap\R^n$ such that $f\Par{x^\star}=f^\star$. This algorithm is probabilistic. It makes use of the notion of polar varieties. Its complexity is essentially cubic in $\Par{\nV D}^n$ and linear in the complexity of evaluating the input. This fits within the best known deterministic complexity class $D^{O(n)}$. We report on some practical experiments of a first implementation that is available as a Maple package. It appears that it can tackle global optimization problems that were unreachable by previous exact algorithms and can manage instances that are hard to solve with purely numeric techniques. As far as we know, even under the extra genericity assumptions on the input, it is the first probabilistic algorithm that combines practical efficiency with good control of complexity for this problem.

Includes members:
  Member "complexity bounds for computing critical points with grobner bases algorithms the mixed case":
    also connected through other hyperedges:
      (none)
  Member "polynomial systems solving by fast linear algebra":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "gr o bner basis over semigroup algebras algorithms and applications for sparse polynomial systems")
  Member "a nearly optimal algorithm for deciding connectivity queries in smooth and bounded real algebraic sets":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "computing the volume of compact semi algebraic sets")
  Member "intrinsic complexity estimates in polynomial optimization":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "real root finding for equivariant semi algebraic systems")
  Member "critical points and gr obner bases the unmixed case":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "solving determinantal systems using homotopy techniques")

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)