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: "matrix f5 algorithms over finite precision complete discrete valuation fields"
  Abstract: Let $(f\_1,\dots, f\_s) \in \mathbb{Q}\_p [X\_1,\dots, X\_n]^s$ be a sequence of homogeneous polynomials with $p$-adic coefficients. Such system may happen, for example, in arithmetic geometry. Yet, since $\mathbb{Q}\_p$ is not an effective field, classical algorithm does not apply.We provide a definition for an approximate Gr{\"o}bner basis with respect to a monomial order $w.$ We design a strategy to compute such a basis, when precision is enough and under the assumption that the input sequence is regular and the ideals $\langle f\_1,\dots,f\_i \rangle$ are weakly-$w$-ideals. The conjecture of Moreno-Socias states that for the grevlex ordering, such sequences are generic.Two variants of that strategy are available, depending on whether one lean more on precision or time-complexity. For the analysis of these algorithms, we study the loss of precision of the Gauss row-echelon algorithm, and apply it to an adapted Matrix-F5 algorithm. Numerical examples are provided.Moreover, the fact that under such hypotheses, Gr{\"o}bner bases can be computed stably has many applications. Firstly, the mapping sending $(f\_1,\dots,f\_s)$ to the reduced Gr{\"o}bner basis of the ideal they span is differentiable, and its differential can be given explicitly. Secondly, these hypotheses allows to perform lifting on the Grobner bases, from $\mathbb{Z}/p^k \mathbb{Z}$ to $\mathbb{Z}/p^{k+k'} \mathbb{Z}$ or $\mathbb{Z}.$ Finally, asking for the same hypotheses on the highest-degree homogeneous components of the entry polynomials allows to extend our strategy to the affine case.

Connected through hyperedge HE-1 (induced by source paper "on affine tropical f5 algorithms"):
  with members:
    - "matrix f5 algorithms and tropical grobner bases computation"
    - "on the complexity of the f5 gr obner basis algorithm"

Connected through hyperedge HE-2 (induced by source paper "on the p adic stability of the fglm algorithm"):
  with members:
    - "polynomial systems solving by fast linear algebra"

Connected through hyperedge HE-3 (induced by source paper "matrix f5 algorithms and tropical grobner bases computation"):
  with members:
    - "on the complexity of the f5 gr obner basis algorithm"

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)