human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "certifying solutions to overdetermined and singular polynomial systems over q"
  Abstract: This paper is concerned with certifying that a given point is near an exact root of an overdetermined or singular polynomial system with rational coefficients. The difficulty lies in the fact that consistency of overdetermined systems is not a continuous property. Our certification is based on hybrid symbolic-numeric methods to compute the exact "rational univariate representation" (RUR) of a component of the input system from approximate roots. For overdetermined polynomial systems with simple roots, we compute an initial RUR from approximate roots. The accuracy of the RUR is increased via Newton iterations until the exact RUR is found, which we certify using exact arithmetic. Since the RUR is well-constrained, we can use it to certify the given approximate roots using alpha-theory. To certify isolated singular roots, we use a determinantal form of the "isosingular deflation", which adds new polynomials to the original system without introducing new variables. The resulting polynomial system is overdetermined, but the roots are now simple, thereby reducing the problem to the overdetermined case. We prove that our algorithms have complexity that are polynomial in the input plus the output size upon successful convergence, and we use worst case upper bounds for termination when our iteration does not converge to an exact RUR. Examples are included to demonstrate the approach.

Connected through hyperedge HE-1 (induced by source paper "smooth points on semi algebraic sets"):
  with members:
    - "computing the homology of basic semialgebraic sets in weak exponential time"
    - "a probabilistic algorithm to compute the real dimension of a semi algebraic set"
    - "triangular decomposition of semi algebraic systems"

Connected through hyperedge HE-2 (induced by source paper "effective certification of approximate solutions to systems of equations involving analytic functions"):
  with members:
    - "rigorous multiple precision evaluation of d finite functions in sagemath"
    - "rigorous uniform approximation of d finite functions using chebyshev expansions"
    - "deflation and certified isolation of singular zeros of polynomial systems"
    - "numgfun a package for numerical and analytic computation with d finite functions"
    - "effective bounds for p recursive sequences"

Connected through hyperedge HE-3 (induced by source paper "global newton iteration over archimedean and non archimedean fields"):
  with members:
    - "stable normal forms for polynomial system solving"

Question: Please tell me which class the center node 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)