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 "exact algorithms for semidefinite programs with degenerate feasible set"):
  Abstract: Let $A_0, \ldots, A_n$ be $m \times m$ symmetric matrices with entries in $\mathbb{Q}$, and let $A(x)$ be the linear pencil $A_0+x_1 A_1+\cdots+x_n A_n$, where $x=(x_1,\ldots,x_n)$ are unknowns. The linear matrix inequality (LMI) $A(x) \succeq 0$ defines the subset of $\mathbb{R}^n$, called spectrahedron, containing all points $x$ such that $A(x)$ has non-negative eigenvalues. The minimization of linear functions over spectrahedra is called semidefinite programming (SDP). Such problems appear frequently in control theory and real algebra, especially in the context of nonnegativity certificates for multivariate polynomials based on sums of squares. #R##N#Numerical software for solving SDP are mostly based on the interior point method, assuming some non-degeneracy properties such as the existence of interior points in the admissible set. In this paper, we design an exact algorithm based on symbolic homotopy for solving semidefinite programs without assumptions on the feasible set, and we analyze its complexity. Because of the exactness of the output, it cannot compete with numerical routines in practice but we prove that solving such problems can be done in polynomial time if either $n$ or $m$ is fixed.

Includes members:
  Member "solving rank constrained semidefinite programs in exact arithmetic":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "bit complexity for multi homogeneous polynomial system solving application to polynomial minimization")
  Member "bit complexity for multi homogeneous polynomial system solving application to polynomial minimization":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "effective coefficient asymptotics of multivariate rational functions via semi numerical algorithms for polynomial systems")
  Member "real root finding for determinants of linear matrices":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "real root finding for equivariant semi algebraic systems")
  Member "a nearly optimal algorithm for deciding connectivity queries in smooth and bounded real algebraic sets":
    also connected through other hyperedges:
      - Hyperedge HE-4 (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-5 (induced by source paper "real root finding for equivariant semi algebraic systems")

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)