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ACM Communications in Computer Algebra最新文献

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An Approximation Algorithm for the Nearest Decomposable Polynomial in the Hamming Distance 汉明距离中最近可分解多项式的近似算法
IF 0.1
ACM Communications in Computer Algebra Pub Date : 2023-09-01 DOI: 10.1145/3637529.3637532
Hiroshi Sekigawa
{"title":"An Approximation Algorithm for the Nearest Decomposable Polynomial in the Hamming Distance","authors":"Hiroshi Sekigawa","doi":"10.1145/3637529.3637532","DOIUrl":"https://doi.org/10.1145/3637529.3637532","url":null,"abstract":"A univariate polynomial f is decomposable if it is the composition f = g(h) of polynomials g and h whose degrees are at least two. We consider the nearest decomposable polynomial to a given polynomial f in the Hamming distance. We propose a polynomial-time approximation algorithm for the nearest decomposable polynomial and analyze the quality of the output.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"1 1","pages":"119 - 125"},"PeriodicalIF":0.1,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139346476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Novel Application of Polynomial Solvers in mmWave Analog Radio Beamforming 多项式求解器在毫米波模拟无线电波束成形中的新应用
IF 0.1
ACM Communications in Computer Algebra Pub Date : 2023-09-01 DOI: 10.1145/3637529.3637537
Snehal Bhayani, Praneeth Susarla, S. S. Krishna, Chaitanya Bulusu, Olli Silvén, Markku J. Juntti, Janne Heikkila
{"title":"A Novel Application of Polynomial Solvers in mmWave Analog Radio Beamforming","authors":"Snehal Bhayani, Praneeth Susarla, S. S. Krishna, Chaitanya Bulusu, Olli Silvén, Markku J. Juntti, Janne Heikkila","doi":"10.1145/3637529.3637537","DOIUrl":"https://doi.org/10.1145/3637529.3637537","url":null,"abstract":"Beamforming is a signal processing technique where an array of antenna elements can be steered to transmit and receive radio signals in a specific direction. The usage of millimeter wave (mmWave) frequencies and multiple input multiple output (MIMO) beamforming are considered as the key innovations of 5th Generation (5G) and beyond communication systems. The mmWave radio waves enable high capacity and directive communication, but suffer from many challenges such as rapid channel variation, blockage effects, atmospheric attenuations, etc. The technique initially performs beam alignment procedure, followed by data transfer in the aligned directions between the transmitter and the receiver [1]. Traditionally, beam alignment involves periodical and exhaustive beam sweeping at both transmitter and the receiver, which is a slow process causing extra communication overhead with MIMO and massive MIMO radio units. In applications such as beam tracking, angular velocity, beam steering etc. [2], beam alignment procedure is optimized by estimating the beam directions using first order polynomial approximations. Recent learning-based SOTA strategies [3] for fast mmWave beam alignment also require exploration over exhaustive beam pairs during the training procedure, causing overhead to learning strategies for higher antenna configurations. Therefore, our goal is to optimize the beam alignment cost functions e.g., data rate, to reduce the beam sweeping overhead by applying polynomial approximations of its partial derivatives which can then be solved as a system of polynomial equations. Specifically, we aim to reduce the beam search space by estimating approximate beam directions using the polynomial solvers. Here, we assume both transmitter (TX) and receiver (RX) to be equipped with uniform linear array (ULA) configuration, each having only one degree of freedom (d.o.f.) with Nt and Nr antennas, respectively.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"7 1","pages":"148 - 151"},"PeriodicalIF":0.1,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139343636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Symmetry Adapted Bases for Trigonometric Optimization 用于三角优化的对称性适应基础
IF 0.1
ACM Communications in Computer Algebra Pub Date : 2023-09-01 DOI: 10.1145/3637529.3637535
Tobias Metzlaff
{"title":"Symmetry Adapted Bases for Trigonometric Optimization","authors":"Tobias Metzlaff","doi":"10.1145/3637529.3637535","DOIUrl":"https://doi.org/10.1145/3637529.3637535","url":null,"abstract":"We present an algorithm to compute the global minimum of a trigonometric polynomial, when it is invariant under the exponential action of a Weyl group. This is based on a common relaxation technique that leads to a semi-definite program (SDP). It is then shown how to exploit the invariance in order to reduce the number of variables of the SDP and to simplify its structure significantly. This approach complements the one that was proposed as a poster at the recent ISSAC 2022 conference [HMMR22] and later extended to [HMMR23]. In the previous work, we first used the invariance of the objective function to obtain a classical polynomial optimization problem on the orbit space and subsequently relaxed the problem to an SDP. In the present work, we first apply the relaxation and then exploit symmetry. We show that the Weyl group action is induced by an orthogonal representation and describe its isotypic decomposition.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"63 1","pages":"137 - 140"},"PeriodicalIF":0.1,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139345339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a Two-Layer Modular Arithmetic 论双层模块算术
IF 0.1
ACM Communications in Computer Algebra Pub Date : 2023-09-01 DOI: 10.1145/3637529.3637534
Benjamin Chen, Yu Li, Eugene Zima
{"title":"On a Two-Layer Modular Arithmetic","authors":"Benjamin Chen, Yu Li, Eugene Zima","doi":"10.1145/3637529.3637534","DOIUrl":"https://doi.org/10.1145/3637529.3637534","url":null,"abstract":"Two-layer organization of modular arithmetic is considered. Lower layer uses many moduli at hardware precision and simultaneous conversion to/from RNS as described in [2]. Upper layer uses specially selected large moduli allowing for fast reduction and/or reconstruction. Implementation of two different strategies for selecting moduli on the upper layer confirms practicality of proposed approach.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"1 1","pages":"133 - 136"},"PeriodicalIF":0.1,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139345506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Clustering in the Lazard method for Cylindrical Algebraic Decomposition 拉扎德圆柱代数分解法中的聚类方法
IF 0.1
ACM Communications in Computer Algebra Pub Date : 2023-09-01 DOI: 10.1145/3637529.3637533
Tereso del Río, AmirHosein Sadeghimanesh, Matthew England
{"title":"Clustering in the Lazard method for Cylindrical Algebraic Decomposition","authors":"Tereso del Río, AmirHosein Sadeghimanesh, Matthew England","doi":"10.1145/3637529.3637533","DOIUrl":"https://doi.org/10.1145/3637529.3637533","url":null,"abstract":"Cylindrical Algebraic Decomposition (CAD) is an algorithm originally proposed by Collins in [4]. Given a set of multivariate polynomials, CAD decomposes the multidimensional real space into connected subsets called cells, within which those polynomials are sign-invariant.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"24 1","pages":"126 - 132"},"PeriodicalIF":0.1,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139343982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Computing Almost-Commuting Basis of Ordinary Differential Operators 计算常微分算子的近共基
IF 0.1
ACM Communications in Computer Algebra Pub Date : 2023-09-01 DOI: 10.1145/3637529.3637531
Antonio Jiménez-Pastor, Sonia L. Rueda, M. Zurro
{"title":"Computing Almost-Commuting Basis of Ordinary Differential Operators","authors":"Antonio Jiménez-Pastor, Sonia L. Rueda, M. Zurro","doi":"10.1145/3637529.3637531","DOIUrl":"https://doi.org/10.1145/3637529.3637531","url":null,"abstract":"An effective computation of a basis of a nontrivial centralizer of a differential operator is the first step towards a Picard-Vessiot theory for spectral problems of ordinary differential operators. The set of almost-commuting operators enjoys a richer structure that allows the computation of these centralizers. We present a method to calculate a basis of almost-commuting operators. Its application to the computation of nontrivial centralizers is illustrated by examples.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"67 1","pages":"111 - 118"},"PeriodicalIF":0.1,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139344871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Keiper-Li Criterion for the Riemann Hypothesis and Generalized Lambert Functions 黎曼假说和广义朗伯函数的凯伯李准则
IF 0.1
ACM Communications in Computer Algebra Pub Date : 2023-09-01 DOI: 10.1145/3637529.3637530
Ross McPhedran, Tony C. Scott, A. Maignan
{"title":"The Keiper-Li Criterion for the Riemann Hypothesis and Generalized Lambert Functions","authors":"Ross McPhedran, Tony C. Scott, A. Maignan","doi":"10.1145/3637529.3637530","DOIUrl":"https://doi.org/10.1145/3637529.3637530","url":null,"abstract":"Keiper [1] and Li [2] published independent investigations of the connection between the Riemann hypothesis and the properties of sums over powers of zeros of the Riemann zeta function. Here we consider a reframing of the criterion, to work with higher-order derivatives ξr of the symmetrized function ξ(s) at s = 1/2, with all ξr known to be positive. The reframed criterion requires knowledge of the asymptotic properties of two terms, one being an infinite sum over the ξr. This is studied using known asymptotic expansions for the ξr, which give the location of the summand as a relationship between two parameters. This relationship needs to be inverted, which we show can be done exactly using a generalized Lambert function. The result enables an accurate asymptotic expression for the value of the infinite sum.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"19 1","pages":"85 - 110"},"PeriodicalIF":0.1,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139345782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quickly Computing Isotopy Type for Exponential Sums over Circuits (Extended Abstract) 快速计算电路指数和的等式类型（扩展摘要）
IF 0.1
ACM Communications in Computer Algebra Pub Date : 2023-09-01 DOI: 10.1145/3637529.3637538
Frédéric Bihan, Erika Croy, Weixun Deng, Kaitlyn Phillipson, Robert J. Rennie, J. M. Rojas
{"title":"Quickly Computing Isotopy Type for Exponential Sums over Circuits (Extended Abstract)","authors":"Frédéric Bihan, Erika Croy, Weixun Deng, Kaitlyn Phillipson, Robert J. Rennie, J. M. Rojas","doi":"10.1145/3637529.3637538","DOIUrl":"https://doi.org/10.1145/3637529.3637538","url":null,"abstract":"Fewnomial Theory [Kho91] has established bounds on the number of connected components (a.k.a. pieces) of a broad class of real analytic sets as a function of a particular kind of input complexity, e.g., the number of distinct exponent vectors among a generating set for the underlying ideal. Here, we pursue the algorithmic side: We show how to efficiently compute the exact isotopy type of certain (possibly singular) real zero sets, instead of just estimating their number of pieces. While we focus on the circuit case, our results form the foundation for an approach to the general case that we will pursue later.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"15 1","pages":"152 - 155"},"PeriodicalIF":0.1,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139346032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Arithmetics in Generalised Cantor Base Systems 广义康托尔基础系统中的算术
IF 0.1
ACM Communications in Computer Algebra Pub Date : 2023-09-01 DOI: 10.1145/3637529.3637539
Katarína Studenicová
{"title":"Arithmetics in Generalised Cantor Base Systems","authors":"Katarína Studenicová","doi":"10.1145/3637529.3637539","DOIUrl":"https://doi.org/10.1145/3637529.3637539","url":null,"abstract":"For alternate Cantor real base numeration systems we generalise the result of Frougny and Solomyak on arithmetics on the set of numbers with finite expansions. We generalise the notion of finiteness property, denoted (F). We also provide several necessary conditions, and comment on a sufficient condition of this property. The sufficient condition allows us to find a set of generalised Cantor bases with Property (F). The used construction also provides a method for performing addition of finite expansions in Cantor real bases.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"31 1","pages":"156 - 159"},"PeriodicalIF":0.1,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139346531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
How to use a CAS for Hardware Design Automation 如何使用 CAS 实现硬件设计自动化
IF 0.1
ACM Communications in Computer Algebra Pub Date : 2023-09-01 DOI: 10.1145/3637529.3637536
N. Zidarič
{"title":"How to use a CAS for Hardware Design Automation","authors":"N. Zidarič","doi":"10.1145/3637529.3637536","DOIUrl":"https://doi.org/10.1145/3637529.3637536","url":null,"abstract":"With the rise of new technologies, the demand for efficient cryptographic hardware is rising. This work is focusing on finite field based cryptography. To explore the vast design space obtained from possible finite field parameters, automated generation of hardware submodules using designer-specified algorithms for finite field arithmetic is needed. This work presents a hardware design automation framework exploiting symbolic computation capabilities of GAP to generate the expressions, needed for hardware implementations, on-the-fly, and compiles them into synthesizable datapaths, test-vectors, and testbences.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"46 1","pages":"141 - 147"},"PeriodicalIF":0.1,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139343765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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