
A Polynomialtime Algorithm to Compute Generalized Hermite Normal Form of Matrices over Z[x]
In this paper, a polynomialtime algorithm is given to compute the gener...
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Analyzing the Nuances of Transformers' Polynomial Simplification Abilities
Symbolic Mathematical tasks such as integration often require multiple w...
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Analysis of NormalForm Algorithms for Solving Systems of Polynomial Equations
We examine several of the normalform multivariate polynomial rootfindin...
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A fast, deterministic algorithm for computing a Hermite Normal Form of a polynomial matrix
Given a square, nonsingular matrix of univariate polynomials F∈K[x]^n × ...
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Solving Polynomial System Efficiently and Accurately
We consider the problem of finding the isolated common roots of a set of...
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New Remarks on the Factorization and Equivalence Problems for a Class of Multivariate Polynomial Matrices
This paper is concerned with the factorization and equivalence problems ...
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Generalized Convolution and Efficient Language Recognition
Convolution is a broadly useful operation with applications including si...
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Normal and Triangular Determinantal Representations of Multivariate Polynomials
In this paper we give a new and simple algorithm to put any multivariate polynomial into a normal determinant form in which each entry has the form , and in each column the same variable appears. We also apply the algorithm to obtain a triangular determinant representation, a reduced determinant representation, and a uniform determinant representation of any multivariable polynomial. The algorithm could be useful for obtaining representations of dimensions smaller than those available up to now to solve numerical problems.
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