In this paper, we present an algorithm to compute a basis of the space of algebraic modular forms on the maximal order of the definite quaternion algebra of discriminant 2, and provide a database of such bases. A main application of our database is to obtain congruence relations of algebraic modular forms, which lead non-vanishing theorems for prime twists of modular L-functions.
{"title":"Computations of algebraic modular forms associated with the definite quaternion algebra of discriminant 2","authors":"Hiroyuki Ochiai , Satoshi Wakatsuki , Shun'ichi Yokoyama","doi":"10.1016/j.jsc.2025.102485","DOIUrl":"10.1016/j.jsc.2025.102485","url":null,"abstract":"<div><div>In this paper, we present an algorithm to compute a basis of the space of algebraic modular forms on the maximal order of the definite quaternion algebra of discriminant 2, and provide a database of such bases. A main application of our database is to obtain congruence relations of algebraic modular forms, which lead non-vanishing theorems for prime twists of modular <em>L</em>-functions.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"133 ","pages":"Article 102485"},"PeriodicalIF":1.1,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-14DOI: 10.1016/j.jsc.2025.102484
Emiliano Liwski, Fatemeh Mohammadi
We introduce the families of solvable and nilpotent matroids, examining their realization spaces, closures, and associated matroid and circuit varieties. We study their realizability, as well as the irreducible decomposition of their associated matroid and circuit varieties. Additionally, we describe a finite generating set for the corresponding ideals, considered up to radical. We establish sufficient conditions for both the realizability of these matroids and the irreducibility of their associated varieties. Specifically, we establish the realizability and irreducibility of matroid varieties associated with nilpotent matroids and prove the irreducibility of matroid varieties arising from certain classes of solvable paving matroids. Additionally, we analyze the defining polynomial equations of these varieties using Grassmann-Cayley algebra and geometric liftability techniques. Furthermore, we provide a complete generating set for the matroid ideals associated with forest configurations.
{"title":"Solvable and nilpotent matroids: Realizability and irreducible decomposition of their associated varieties","authors":"Emiliano Liwski, Fatemeh Mohammadi","doi":"10.1016/j.jsc.2025.102484","DOIUrl":"10.1016/j.jsc.2025.102484","url":null,"abstract":"<div><div>We introduce the families of solvable and nilpotent matroids, examining their realization spaces, closures, and associated matroid and circuit varieties. We study their realizability, as well as the irreducible decomposition of their associated matroid and circuit varieties. Additionally, we describe a finite generating set for the corresponding ideals, considered up to radical. We establish sufficient conditions for both the realizability of these matroids and the irreducibility of their associated varieties. Specifically, we establish the realizability and irreducibility of matroid varieties associated with nilpotent matroids and prove the irreducibility of matroid varieties arising from certain classes of solvable paving matroids. Additionally, we analyze the defining polynomial equations of these varieties using Grassmann-Cayley algebra and geometric liftability techniques. Furthermore, we provide a complete generating set for the matroid ideals associated with forest configurations.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"133 ","pages":"Article 102484"},"PeriodicalIF":1.1,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-14DOI: 10.1016/j.jsc.2025.102483
Ming-Deh A. Huang
We consider semi-local polynomial systems and their decomposition. A semi-local polynomial system defines a global polynomial map that is the product of local polynomial maps disguised by global linear isomorphisms. We characterize a subclass of semi-local polynomial systems which can be efficiently decomposed into local systems.
{"title":"On semi-local decomposition","authors":"Ming-Deh A. Huang","doi":"10.1016/j.jsc.2025.102483","DOIUrl":"10.1016/j.jsc.2025.102483","url":null,"abstract":"<div><div>We consider semi-local polynomial systems and their decomposition. A semi-local polynomial system defines a global polynomial map that is the product of local polynomial maps disguised by global linear isomorphisms. We characterize a subclass of semi-local polynomial systems which can be efficiently decomposed into local systems.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"133 ","pages":"Article 102483"},"PeriodicalIF":1.1,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-14DOI: 10.1016/j.jsc.2025.102488
Sebastian Debus , Cordian Riener , Robin Schabert
Univariate polynomials are called stable with respect to a domain D if all of their roots lie in D. We study linear slices of the space of stable univariate polynomials with respect to a half-plane. We show that a linear slice always contains a stable polynomial with only a few distinct roots. Subsequently, we apply these results to symmetric polynomials and varieties. We show that for varieties defined by few multiaffine symmetric polynomials, the existence of a point in with few distinct coordinates is necessary and sufficient for the intersection with to be non-empty. This is at the same time a generalization of the so-called degree principle to stable polynomials and a result similar to Grace-Walsh-Szegő's coincidence theorem.
{"title":"Slices of stable polynomials and connections to the Grace-Walsh-Szegő theorem","authors":"Sebastian Debus , Cordian Riener , Robin Schabert","doi":"10.1016/j.jsc.2025.102488","DOIUrl":"10.1016/j.jsc.2025.102488","url":null,"abstract":"<div><div>Univariate polynomials are called stable with respect to a domain <em>D</em> if all of their roots lie in <em>D</em>. We study linear slices of the space of stable univariate polynomials with respect to a half-plane. We show that a linear slice always contains a stable polynomial with only a few distinct roots. Subsequently, we apply these results to symmetric polynomials and varieties. We show that for varieties defined by few multiaffine symmetric polynomials, the existence of a point in <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> with few distinct coordinates is necessary and sufficient for the intersection with <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> to be non-empty. This is at the same time a generalization of the so-called degree principle to stable polynomials and a result similar to Grace-Walsh-Szegő's coincidence theorem.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"133 ","pages":"Article 102488"},"PeriodicalIF":1.1,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144903702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the previous work of Abbondati et al. (2024), we extended the decoding analysis of interleaved Chinese remainder codes to simultaneous rational number codes. In this work, we build on Abbondati et al. (2024) by addressing two important scenarios: multiplicities and the presence of bad primes (divisors of denominators). First, we generalize previous results to multiplicity rational codes by considering modular reductions with respect to prime power moduli. Then, using hybrid analysis techniques, we extend our approach to vectors of fractions that may present bad primes.
Our contributions include: a decoding algorithm for simultaneous rational number reconstruction with multiplicities, a rigorous analysis of the algorithm's failure probability that generalizes several previous results, an extension to a hybrid model handling situations where not all errors can be assumed random, and a unified approach to handle bad primes within multiplicities. The theoretical results provide a comprehensive probabilistic analysis of reconstruction failure in these more complex scenarios, advancing the state of the art in error correction for rational number codes.
在Abbondati et al.（2024）之前的工作中，我们将交错中文剩余码的解码分析扩展到同时有理数码。在这项工作中，我们以Abbondati等人（2024）为基础，解决了两个重要的场景：多重性和坏素数（分母的除数）的存在。首先，我们通过考虑相对于素数幂模的模化，将之前的结果推广到多重有理码。然后，使用混合分析技术，我们将方法扩展到可能呈现坏素数的分数向量。我们的贡献包括：具有多重性的同时有理数重建的解码算法，对算法失效概率的严格分析，概括了以前的几个结果，扩展到处理并非所有错误都可以假设为随机的混合模型，以及处理多重性中的坏素数的统一方法。理论结果提供了在这些更复杂的情况下重构失败的全面概率分析，推进了有理数码的纠错技术的发展。
{"title":"Simultaneous rational number codes: Decoding beyond half the minimum distance with multiplicities and bad primes","authors":"Matteo Abbondati, Eleonora Guerrini, Romain Lebreton","doi":"10.1016/j.jsc.2025.102481","DOIUrl":"10.1016/j.jsc.2025.102481","url":null,"abstract":"<div><div>In the previous work of <span><span>Abbondati et al. (2024)</span></span>, we extended the decoding analysis of interleaved Chinese remainder codes to simultaneous rational number codes. In this work, we build on <span><span>Abbondati et al. (2024)</span></span> by addressing two important scenarios: multiplicities and the presence of bad primes (divisors of denominators). First, we generalize previous results to multiplicity rational codes by considering modular reductions with respect to prime power moduli. Then, using hybrid analysis techniques, we extend our approach to vectors of fractions that may present bad primes.</div><div>Our contributions include: a decoding algorithm for simultaneous rational number reconstruction with multiplicities, a rigorous analysis of the algorithm's failure probability that generalizes several previous results, an extension to a hybrid model handling situations where not all errors can be assumed random, and a unified approach to handle bad primes within multiplicities. The theoretical results provide a comprehensive probabilistic analysis of reconstruction failure in these more complex scenarios, advancing the state of the art in error correction for rational number codes.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"132 ","pages":"Article 102481"},"PeriodicalIF":1.1,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144828646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-06DOI: 10.1016/j.jsc.2025.102480
Colin Alstad , Michael Burr , Oliver Clarke , Timothy Duff
We study a partial correspondence between two previously-studied analogues of Gröbner bases in the setting of algebras: namely subalgebra bases for quotients of polynomial rings and Khovanskii bases for valued algebras and domains. Our main motivation is to apply the concrete and computational aspects of subalgebra bases for quotient rings to the abstract theory of Khovanskii bases. Our perspective is that most interesting examples of Khovanskii bases can also be realized as subalgebra bases and vice-versa. As part of this correspondence, we extend the theory of subalgebra bases for quotients of polynomial rings to infinitely generated polynomial algebras and study conditions which make this theory effective. We also provide a computation of Newton-Okounkov bodies from the data of subalgebra bases for quotient rings, which illustrates how interpreting Khovanskii bases as subalgebra bases makes them amenable to existing computer algebra tools.
{"title":"Subalgebra and Khovanskii bases equivalence","authors":"Colin Alstad , Michael Burr , Oliver Clarke , Timothy Duff","doi":"10.1016/j.jsc.2025.102480","DOIUrl":"10.1016/j.jsc.2025.102480","url":null,"abstract":"<div><div>We study a partial correspondence between two previously-studied analogues of Gröbner bases in the setting of algebras: namely subalgebra bases for quotients of polynomial rings and Khovanskii bases for valued algebras and domains. Our main motivation is to apply the concrete and computational aspects of subalgebra bases for quotient rings to the abstract theory of Khovanskii bases. Our perspective is that most interesting examples of Khovanskii bases can also be realized as subalgebra bases and vice-versa. As part of this correspondence, we extend the theory of subalgebra bases for quotients of polynomial rings to infinitely generated polynomial algebras and study conditions which make this theory effective. We also provide a computation of Newton-Okounkov bodies from the data of subalgebra bases for quotient rings, which illustrates how interpreting Khovanskii bases as subalgebra bases makes them amenable to existing computer algebra tools.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"133 ","pages":"Article 102480"},"PeriodicalIF":1.1,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A Brownian motion tree (BMT) model is a Gaussian model whose associated set of covariance matrices is linearly constrained according to common ancestry in a phylogenetic tree. We study the complexity of inferring the maximum likelihood (ML) estimator for a BMT model by computing its ML-degree. Our main result is that the ML-degree of the BMT model on a star tree with leaves is , which was previously conjectured by Améndola and Zwiernik. We also prove that the ML-degree of a BMT model is independent of the choice of the root. The proofs rely on the toric geometry of concentration matrices in a BMT model. Toward this end, we produce a combinatorial formula for the determinant of the concentration matrix of a BMT model, which generalizes the Cayley-Prüfer theorem to complete graphs with weights given by a tree.
{"title":"ML degrees of Brownian motion tree models: Star trees and root invariance","authors":"Jane Ivy Coons , Shelby Cox , Aida Maraj , Ikenna Nometa","doi":"10.1016/j.jsc.2025.102482","DOIUrl":"10.1016/j.jsc.2025.102482","url":null,"abstract":"<div><div>A Brownian motion tree (BMT) model is a Gaussian model whose associated set of covariance matrices is linearly constrained according to common ancestry in a phylogenetic tree. We study the complexity of inferring the maximum likelihood (ML) estimator for a BMT model by computing its ML-degree. Our main result is that the ML-degree of the BMT model on a star tree with <span><math><mi>n</mi><mo>+</mo><mn>1</mn></math></span> leaves is <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>−</mo><mn>2</mn><mi>n</mi><mo>−</mo><mn>3</mn></math></span>, which was previously conjectured by Améndola and Zwiernik. We also prove that the ML-degree of a BMT model is independent of the choice of the root. The proofs rely on the toric geometry of concentration matrices in a BMT model. Toward this end, we produce a combinatorial formula for the determinant of the concentration matrix of a BMT model, which generalizes the Cayley-Prüfer theorem to complete graphs with weights given by a tree.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"132 ","pages":"Article 102482"},"PeriodicalIF":1.1,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144809587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-05DOI: 10.1016/j.jsc.2025.102479
Janin Heuer, Timo de Wolff
The cone of sums of nonnegative circuits (SONCs) is a subset of the cone of nonnegative polynomials / exponential sums, which has been studied extensively in recent years. In this article, we construct a subset of the SONC cone which we call the DSONC cone. The DSONC cone is naturally derived from the dual SONC cone; membership can be tested via linear programming. We show that the DSONC cone is a proper, full-dimensional cone, we provide a description of its extreme rays, and collect several properties that parallel those of the SONC cone. Moreover, we show that functions in the DSONC cone cannot have real zeros, which yields that DSONC cone does not intersect the boundary of the SONC cone. Furthermore, we discuss the intersection of the DSONC cone with the SOS and SDSOS cones. Finally, we show that circuit functions in the boundary of the DSONC cone are determined by points of equilibria, which hence are the analogues to singular points in the primal SONC cone, and relate the DSONC cone to tropical geometry.
{"title":"The duality of SONC: Advances in circuit-based certificates","authors":"Janin Heuer, Timo de Wolff","doi":"10.1016/j.jsc.2025.102479","DOIUrl":"10.1016/j.jsc.2025.102479","url":null,"abstract":"<div><div>The cone of sums of nonnegative circuits (SONCs) is a subset of the cone of nonnegative polynomials / exponential sums, which has been studied extensively in recent years. In this article, we construct a subset of the SONC cone which we call the DSONC cone. The DSONC cone is naturally derived from the dual SONC cone; membership can be tested via linear programming. We show that the DSONC cone is a proper, full-dimensional cone, we provide a description of its extreme rays, and collect several properties that parallel those of the SONC cone. Moreover, we show that functions in the DSONC cone cannot have real zeros, which yields that DSONC cone does not intersect the boundary of the SONC cone. Furthermore, we discuss the intersection of the DSONC cone with the SOS and SDSOS cones. Finally, we show that circuit functions in the boundary of the DSONC cone are determined by points of equilibria, which hence are the analogues to singular points in the primal SONC cone, and relate the DSONC cone to tropical geometry.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"132 ","pages":"Article 102479"},"PeriodicalIF":1.1,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144826603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-07-25DOI: 10.1016/j.jsc.2025.102478
Bo Huang , Dongming Wang , Xinyu Wang , Jing Yang
The classical theory of Kosambi–Cartan–Chern (KCC) developed in differential geometry provides a powerful method for analyzing the behaviors of dynamical systems. In the KCC theory, the properties of a dynamical system are described in terms of five geometrical invariants, of which the second corresponds to the so-called Jacobi stability of the system. Different from that of the Lyapunov stability that has been studied extensively in the literature, the analysis of the Jacobi stability has been investigated more recently using geometrical concepts and tools. It turns out that the existing work on the Jacobi stability analysis remains theoretical and the problem of algorithmic and symbolic treatment of Jacobi stability analysis has yet to be addressed. In this paper, we initiate our study on the problem for a class of ODE systems of arbitrary dimension and propose two algorithmic schemes using symbolic computation to check whether a nonlinear dynamical system may exhibit Jacobi stability. The first scheme, based on the construction of the complex root structure of a characteristic polynomial and on the method of quantifier elimination, is capable of detecting the existence of the Jacobi stability of the given dynamical system. The second algorithmic scheme exploits the method of semi-algebraic system solving and allows one to determine conditions on the parameters for a given dynamical system to have a prescribed number of Jacobi stable fixed points. Several examples are presented to demonstrate the effectiveness of the proposed algorithmic schemes. The computational results on Jacobi stability of these examples are further verified by numerical simulations.
{"title":"Jacobi stability analysis for systems of ODEs with symbolic computation","authors":"Bo Huang , Dongming Wang , Xinyu Wang , Jing Yang","doi":"10.1016/j.jsc.2025.102478","DOIUrl":"10.1016/j.jsc.2025.102478","url":null,"abstract":"<div><div>The classical theory of Kosambi–Cartan–Chern (KCC) developed in differential geometry provides a powerful method for analyzing the behaviors of dynamical systems. In the KCC theory, the properties of a dynamical system are described in terms of five geometrical invariants, of which the second corresponds to the so-called Jacobi stability of the system. Different from that of the Lyapunov stability that has been studied extensively in the literature, the analysis of the Jacobi stability has been investigated more recently using geometrical concepts and tools. It turns out that the existing work on the Jacobi stability analysis remains theoretical and the problem of algorithmic and symbolic treatment of Jacobi stability analysis has yet to be addressed. In this paper, we initiate our study on the problem for a class of ODE systems of arbitrary dimension and propose two algorithmic schemes using symbolic computation to check whether a nonlinear dynamical system may exhibit Jacobi stability. The first scheme, based on the construction of the complex root structure of a characteristic polynomial and on the method of quantifier elimination, is capable of detecting the existence of the Jacobi stability of the given dynamical system. The second algorithmic scheme exploits the method of semi-algebraic system solving and allows one to determine conditions on the parameters for a given dynamical system to have a prescribed number of Jacobi stable fixed points. Several examples are presented to demonstrate the effectiveness of the proposed algorithmic schemes. The computational results on Jacobi stability of these examples are further verified by numerical simulations.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"132 ","pages":"Article 102478"},"PeriodicalIF":1.1,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-07-23DOI: 10.1016/j.jsc.2025.102476
Alexis Eduardo Almendras Valdebenito , Jonathan Armando Briones Donoso , Andrea Luigi Tironi
Let be a division ring. We generalize some of the main well-known results about the resultant of two univariate polynomials to the more general context of an Ore extension . Moreover, some algorithms and Magma programs are given as a numerical application of the main theoretical results of this paper.
{"title":"Resultants of skew polynomials over division rings","authors":"Alexis Eduardo Almendras Valdebenito , Jonathan Armando Briones Donoso , Andrea Luigi Tironi","doi":"10.1016/j.jsc.2025.102476","DOIUrl":"10.1016/j.jsc.2025.102476","url":null,"abstract":"<div><div>Let <span><math><mi>F</mi></math></span> be a division ring. We generalize some of the main well-known results about the resultant of two univariate polynomials to the more general context of an Ore extension <span><math><mi>F</mi><mo>[</mo><mi>x</mi><mo>;</mo><mi>σ</mi><mo>,</mo><mi>δ</mi><mo>]</mo></math></span>. Moreover, some algorithms and Magma programs are given as a numerical application of the main theoretical results of this paper.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"132 ","pages":"Article 102476"},"PeriodicalIF":1.1,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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