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 "algorithms for weighted sums of squares decomposition of non negative univariate polynomials"):
  Abstract: It is well-known that every non-negative univariate real polynomial can be written as the sum of two polynomial squares with real coefficients. When one allows a weighted sum of finitely many squares instead of a sum of two squares, then one can choose all coefficients in the representation to lie in the field generated by the coefficients of the polynomial. #R##N#In this article, we describe, analyze and compare both from the theoretical and practical points of view, two algorithms computing such a weighted sums of squares decomposition for univariate polynomials with rational coefficients. #R##N#The first algorithm, due to the third author relies on real root isolation, quadratic approximations of positive polynomials and square-free decomposition but its complexity was not analyzed. We provide bit complexity estimates, both on runtime and output size of this algorithm. They are exponential in the degree of the input univariate polynomial and linear in the maximum bitsize of its complexity. This analysis is obtained using quantifier elimination and root isolation bounds. #R##N#The second algorithm, due to Chevillard, Harrison, Joldes and Lauter, relies on complex root isolation and square-free decomposition and has been introduced for certifying positiveness of polynomials in the context of computer arithmetics. Again, its complexity was not analyzed. We provide bit complexity estimates, both on runtime and output size of this algorithm, which are polynomial in the degree of the input polynomial and linear in the maximum bitsize of its complexity. This analysis is obtained using Vieta's formula and root isolation bounds. #R##N#Finally, we report on our implementations of both algorithms. While the second algorithm is, as expected from the complexity result, more efficient on most of examples, we exhibit families of non-negative polynomials for which the first algorithm is better.

Includes members:
  Member "symbolic numeric tools for analytic combinatorics in several variables":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "effective coefficient asymptotics of multivariate rational functions via semi numerical algorithms for polynomial systems")
  Member "formal proofs for nonlinear optimization":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "exact optimization via sums of nonnegative circuits and sums of am gm exponentials")
  Member "probabilistic algorithm for polynomial optimization over a real algebraic set":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "real root finding for equivariant semi algebraic systems")
  Member "from approximate factorization to root isolation with application to cylindrical algebraic decomposition":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "effective coefficient asymptotics of multivariate rational functions via semi numerical algorithms for polynomial systems")
  Member "univariate real root isolation in an extension field":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "nearly optimal computations with structured matrices")

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)