ISSAC

International Symposium on Symbolic and Algebraic Computation

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Short Communications (Posters)

The poster committee has accepted the 10 short communications below. Click on the plus symbol to view a paper's abstract.

List of Accepted Short Communications

• [+] Mawunyo Kofi Darkey-Mensah. Algorithms for quadratic forms over global function fields of odd characteristic.
  Abstract:

  This paper presents an adaptation of recently developed algorithms for quadratic forms over number fields in [4] to global function fields of odd characteristics. First, we present algorithm for checking if a given non-degenerate quadratic form is isotropic or hyperbolic. Next we devise a method for computing the dimension of the anisotropic part of a quadratic form. Finally we present algorithms computing two field invariants: the level and the Pythagoras number.

• [+] Juan Ignacio García-García, Daniel Marín-Aragón and Alberto Vigneron-Tenorio. Computing the ideals of sumset semigroups.
  Abstract:

  We introduce an algorithm for computing the ideals associated with some sumset semigroups. Our results allow us to study some additive properties of sumsets.

• [+] Skander Belhaj and Abdulrahman Alsulami. Approximate greatest common divisor of several polynomials from Hankel matrices.
  Abstract:

  This paper is devoted to present a new method for computing the approximate Greatest Common Divisor (GCD) of several polynomials (not pairwise) from the generalized Hankel matrix. Our approach based on the calculation of cofactors is tested for several sets of polynomials.

• [+] Julian Pfeifle. Large final polynomials from integer programming.
  Abstract:

  We introduce a new method for finding a non-realizability certificate of a simplicial sphere Sigma. It enables us to prove for the first time the non-realizability of a balanced 2-neighborly 3-sphere by Zheng, a family of highly neighborly centrally symmetric spheres by Novik and Zheng, and several combinatorial prismatoids introduced by Criado and Santos.
  The method, implemented in the polymake framework, uses integer programming to find a monomial combination of classical 3-term Plücker relations that must be positive in any realization of Sigma; but since this combination should also vanish identically, the realization cannot exist.
  Previous approaches by Firsching, implemented using SCIP, and by Gouveia, Macchia and Wiebe, implemented using Singular and Macaulay2, are not able to process these examples.

• [+] Daniel Miguel, Andrea Guidolin, Ana Romero and Julio Rubio. Constructing new spectral systems from simplicial fibrations.
  Abstract:

  In this work we present an ongoing project on the development and study of new spectral systems which combine filtrations associated to Serre and Eilenberg--Moore spectral sequences of different fibrations. Our new spectral systems are part of a new module for the Kenzo system and can be useful to deduce new relations on the initial spectral sequences and to obtain information about different filtrations of the homology groups of the fiber and the base space of the fibrations.

• [+] Shashi Gowda, Yingbo Ma, Alessandro Cheli, Maja Gwóźdź, Viral Shah, Alan Edelman and Christopher Rackauckas. High-performance symbolic-numerics via multiple dispatch.
  Abstract:

  As mathematical computing becomes more democratized in high-level languages, high-performancesymbolic-numeric systems are necessary for domain scientists and engineers to get the best performanceout of their machine without deep knowledge of code optimization. Naturally, users need different termtypes either to have different algebraic properties for them, or to use efficient data structures. To thisend, we developed Symbolics.jl, an extendable symbolic system which uses dynamic multiple dispatchto change behavior depending on the domain needs. In this work we detail an underlying abstract terminterface which allows for speed without sacrificing generality. We show that by formalizing a genericAPI on actions independent of implementation, we can retroactively add optimized data structures toour system without changing the pre-existing term rewriters. We showcase how this can be used tooptimize term construction and give a 113x acceleration on general symbolic transformations. Further,we show that such a generic API allows for complementary term-rewriting implementations. Exploitingthis feature, we demonstrate the ability to swap between classical term-rewriting simplifiers and e-graph-based term-rewriting simplifiers. We illustrate how this symbolic system improves numerical computingtasks by showcasing an e-graph ruleset which minimizes the number of CPU cycles during expressionevaluation, and demonstrate how it simplifies a real-world reaction-network simulation to halve theruntime. Additionally, we show a reaction-diffusion partial differential equation solver which is able tobe automatically converted into symbolic expressions via multiple dispatch tracing, which is subsequentlyaccelerated and parallelized to give a 157x simulation speedup. Together, this presents Symbolics.jl asa next-generation symbolic-numeric computing environment geared towards modeling and simulation.

• [+] Kosaku Nagasaka. Approximate GCD by relaxed NewtonSLRA algorithm.
  Abstract:

  We propose a better algorithm for approximate GCD in terms of robustness and distance, based on the NewtonSLRA algorithm that is a solver for the structured low rank approximation (SLRA) problem. Our algorithm mainly enlarges the tangent space in the NewtonSLRA algorithm and adapts it to a certain weighted Frobenius norm. Moreover, we propose some improvement in computing time.

• [+] Eduardo Sáenz de Cabezón and Rodrigo Iglesias. Cellular reductions of the Pommaret-Seiler resolution for quasi-stable ideals.
  Abstract:

  Based on the cellular structure of the Pommaret-Seiler resolution for quasi-stable ideals we provide an algorithm to construct the minimal free resolution of quasi-stable monomial ideals using Discrete Morse theory on this structure.

• [+] Russell Bradford, James H. Davenport, Matthew England, Amirhossein Sadeghimanesh and Ali Uncu. The DEWCAD Project: Pushing Back the Doubly Exponential Wall of Cylindrical Algebraic Decomposition.
  Abstract:

  This abstract seeks to introduce the ISSAC community to the DEWCAD project, which is based at Coventry University and the University of Bath, in the United Kingdom. The project seeks to push back the Doubly Exponential Wall of Cylindrical Algebraic Decomposition, through the integration of SAT/SMT technology, the extension of Lazard projection theory, and the development of new algorithms based on CAD technology but without producing CADs themselves. The project also seeks to develop applications of CAD and will focus on applications in the domains of economics and bio-network analysis.

• [+] Andrei Matveiakin. Discovering multiple polylogarithm equations via symbolic computations.
  Abstract:

  We discuss how symbolic computations can be used to find functional equations for multiple polylogarithms and prove parts of Goncharov's depth conjecture. We present a custom-built C++ toolkit for polylogarithm symbol manipulations in Lie coalgebras and show how this approach compares favorably to the alternatives in terms of performance.