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 "fast computation of the rank profile matrix and the generalized bruhat decomposition"):
  Abstract: The row (resp. column) rank profile of a matrix describes the stair-case shape of its row (resp. column) echelon form. We here propose a new matrix invariant, the rank profile matrix, summarizing all information on the row and column rank profiles of all the leading sub-matrices. We show that this normal form exists and is unique over any ring, provided that the notion of McCoy's rank is used, in the presence of zero divisors. We then explore the conditions for a Gaussian elimination algorithm to compute all or part of this invariant, through the corresponding PLUQ decomposition. This enlarges the set of known Elimination variants that compute row or column rank profiles. As a consequence a new Crout base case variant significantly improves the practical efficiency of previously known implementations over a finite field. With matrices of very small rank, we also generalize the techniques of Storjohann and Yang to the computation of the rank profile matrix, achieving an $(r^\omega+mn)^{1+o(1)}$ time complexity for an $m \times  n$ matrix of rank $r$, where $\omega$ is the exponent of matrix multiplication. Finally, by give connections to the Bruhat decomposition, and several of its variants and generalizations. Thus, our algorithmic improvements for the PLUQ factorization, and their implementations, directly apply to these decompositions. In particular, we show how a PLUQ decomposition revealing the rank profile matrix also reveals both a row and a column echelon form of the input matrix or of any of its leading sub-matrices, by a simple post-processing made of row and column permutations.

Includes members:
  Member "computing the rank profile matrix":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "on the uniqueness of simultaneous rational function reconstruction")
  Member "parallel computation of echelon forms":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "lu factorization with errors")
  Member "generalized bruhat decomposition in commutative domains":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "recursive matrix algorithms in commutative domain for cluster with distributed memory")
  Member "simultaneous computation of the row and column rank profiles":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "elimination based certificates for triangular equivalence and rank profiles")
  Member "fast matrix rank algorithms and applications":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "elimination based certificates for triangular equivalence and rank profiles")
  Member "rank profile revealing gaussian elimination and the cup matrix decomposition":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "elimination based certificates for triangular equivalence and rank profiles")
  Member "fast generalized bruhat decomposition":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "recursive matrix algorithms in commutative domain for cluster with distributed memory")

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)