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Efficient Decomposition of Associative Algebras over Finite Fields

W. Eberly, M. Giesbrecht
2000 Journal of symbolic computation  
We present new, efficient algorithms for some fundamental computations with finitedimensional (but not necessarily commutative) associative algebras over finite fields.  ...  For a semisimple algebra A we show how to compute a complete Wedderburn decomposition of A as a direct sum of simple algebras, an isomorphism between each simple component and a full matrix algebra, and  ...  Acknowledgements The authors were supported in part by the Natural Sciences and Engineering Research Council of Canada.  ... 
doi:10.1006/jsco.1999.0308 fatcat:myr6prcksrge3fufgqbxa6rlsa

Computing Levi Decompositions in Lie algebras

W. A. de Graaf, G. Ivanyos, A. Küronya, L. Rónyai
1997 Applicable Algebra in Engineering, Communication and Computing  
We consider the algorithmic problem of computing Levi decompositions in Lie algebras and Wedderburn-Malcev decompositions in associative algebras over the field of rational numbers.  ...  Computational experiences are discussed at the end of the paper. We infer that Using also rank(A)6n and substituting X"4(n)!(3c)L cn, the Lemma gives  ...  : E Computing a Levi decomposition of a Lie algebra over Q; E Determining a Wedderburn-Malcev decomposition for an associative algebra over a finite field or over Q.  ... 
doi:10.1007/s002000050066 fatcat:ladzn3nxxzcsxex2al34rax5ja

A Numerical Local Dimension Test for Points on the Solution Set of a System of Polynomial Equations

Daniel J. Bates, Jonathan D. Hauenstein, Chris Peterson, Andrew J. Sommese
2009 SIAM Journal on Numerical Analysis  
As the computation of a numerical irreducible decomposition is a fundamental backbone operation, gains in efficiency in the irreducible decomposition algorithm carry over to the many computations which  ...  computation of a numerical irreducible decomposition.  ...  primary decomposition. • The associated primes of the radical of an ideal are a subset of the associated primes of the ideal.  ... 
doi:10.1137/08073264x fatcat:5sd5fjlcvrehflsgrwl72nhcpy

Page 1048 of Mathematical Reviews Vol. , Issue 89B [page]

1989 Mathematical Reviews  
An alternative to Gauss decomposition, LU-factorization, for sparse linear systems is studied. The Bruhat decomposition from the theory of linear algebraic groups is considered [see D. Yu.  ...  This decomposition exists for any nonsingular matrix A and associates with A its Bruhat permutation 2, which is shown to contain important information about A.  ... 

On Families Of 2^N-Dimensional Hypercomplex Algebras Suitable For Digital Signal Processing

Daniel Alfsmann
2006 Zenodo  
Publication in the conference proceedings of EUSIPCO, Florence, Italy, 2006  ...  However, the higher the dimension, the more varieties of hypercomplex algebras exist. As a result, we try to preselect subsets of algebras that allow for efficient DSP.  ...  In general, there are options for both the decomposition level d (the number of orthogonal components) and the choice of the orthogonal base, resulting in an associated subalgebra E of dimension h = n  ... 
doi:10.5281/zenodo.52940 fatcat:sifslhxlkjdrxb4dq77adnykny

Page 227 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 4, Issue [page]

1898 American Mathematical Society. Bulletin of the American Mathematical Society  
It is precisely by the aid of these indeter- minates together with the notion of units that the unique decomposition of algebraic numbers is reéstablished.  ...  Equipped with these we are ready to raise with ease the first great pillar on which the theory of algebraic numbers rests, we mean the uniqueness of the decomposition of algebraic numbers into their prime  ... 

Page 6696 of Mathematical Reviews Vol. , Issue 97K [page]

1997 Mathematical Reviews  
If g is semisimple and J a primitive ideal in the enveloping algebra U(g), it is known that the associated variety V(grJ) of J is the closure of a unique nilpotent orbit in g*.  ...  symmetric group, and the authors conjec- ture with substantial evidence that upon specializing g — 1, the q-decomposition numbers become the decomposition numbers for the type-A Iwahori-Hecke algebra  ... 

Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety

Daniel J. Bates, Wolfram Decker, Jonathan D. Hauenstein, Chris Peterson, Gerhard Pfister, Frank-Olaf Schreyer, Andrew J. Sommese, Charles W. Wampler
2014 Applied Mathematics and Computation  
often used in algebraic geometry that may be thought of as a natural refinement of a decomposition into connected components.  ...  In addition to finding the P i , we may wish to compute their dimensions and degrees by algebraic means. The decomposition (3) is called the prime decomposition of √ I.  ... 
doi:10.1016/j.amc.2013.12.165 fatcat:3loemn6l6ba6phdqv3s64nu6uu

Algebraic Riccati Matrix Equation For Eigen- Decomposition Of Special Structured Matrices; Applications In Structural Mechanics

Mahdi Nouri
2013 Zenodo  
In this paper Algebraic Riccati matrix equation is used for Eigen-decomposition of special structured matrices.  ...  Numerical and structural examples included showing the efficiency of present method.  ...  In this paper, a simple and efficient method is presented for computing of the eigenvalues and eigenvectors of spatial structured matrices by the use of algebraic Riccati equation.  ... 
doi:10.5281/zenodo.1088220 fatcat:sy2wpuutafh53ggnkbh3qlo3cy

BDS: a BDD-based logic optimization system

Congguang Yang, M. Ciesielski
2002 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
It is based on a new binary decision diagrams (BDD) decomposition technique which supports all types of decomposition structures, including AND, OR, XOR, and complex MUX, both algebraic and Boolean.  ...  As a result, the method is very efficient in synthesizing both AND/OR and XOR-intensive functions.  ...  Mishchenko for illuminating discussions on the BDD-based logic decomposition methods and for his help in providing a reliable methodology to verify the synthesis results.  ... 
doi:10.1109/tcad.2002.1013899 fatcat:cp37ulznrfd6xgrbx4cfzblluy

Page 5842 of Mathematical Reviews Vol. , Issue 2003h [page]

2003 Mathematical Reviews  
The authors propose a new and efficient algorithm to compute the canonical decomposition of a given a.  ...  , then (1) F)(-) is an exact 16 ASSOCIATIVE RINGS AND ALGEBRAS 5842 completely strict functor from the category of finite-dimensional 4- modules into the category of graded R-modules and homogeneous homomorphisms  ... 

Minimal presentations of shifted numerical monoids

Rebecca Conaway, Felix Gotti, Jesse Horton, Christopher O'Neill, Roberto Pelayo, Mesa Pracht, Brian Wissman
2018 International journal of algebra and computation  
We explore several applications to computation, combinatorial commutative algebra, and factorization theory.  ...  A numerical monoid is an additive submonoid of the non-negative integers. Given a numerical monoid S, consider the family of "shifted" monoids M_n obtained by adding n to each generator of S.  ...  First, we identify which associated prime congruences appear in every mesoprimary decomposition, thereby completing the theory of mesoprimary decomposition of monoid congruences as a more faithful analog  ... 
doi:10.1142/s0218196718500030 fatcat:lge27p3pdvhy5ouuurwig4ulpi

About Classification Methods Based on Tensor Modelling for Hyperspectral Images [chapter]

Salah Bourennane, Caroline Fossati
2009 Communications in Computer and Information Science  
Denoising and Dimensionality Reduction (DR) are key issue to improve the classifiers efficiency for Hyper spectral images (HSI).  ...  To jointly take advantage of the spatial and spectral information, HSI has been recently represented as tensor.  ...  The first one shows the efficiency of the ALS algorithm and, the value K  Efficiency of the ALS algorithm.  ... 
doi:10.1007/978-3-642-10546-3_34 fatcat:76g54ro3sna7rmhkzx6dypc7nu

Alto: Rapid Prototyping for Parsing and Translation

Johannes Gontrum, Jonas Groschwitz, Alexander Koller, Christoph Teichmann
2017 Proceedings of the Software Demonstrations of the 15th Conference of the European Chapter of the Association for Computational Linguistics  
Alto implements generic but efficient algorithms for parsing, translation, and training for a range of monolingual and synchronous grammar formalisms.  ...  It can easily be extended to new formalisms, which makes all of these algorithms immediately available for the new formalism.  ...  Only an algebraspecific decomposition operation is needed for each new algebra.  ... 
doi:10.18653/v1/e17-3008 dblp:conf/eacl/GontrumGKT17 fatcat:jbiz2ydhjfandob44jeg5a64uq

Page 2617 of Mathematical Reviews Vol. , Issue 95e [page]

1995 Mathematical Reviews  
In Chapter 8 (Decomposition, radical, and zeroes of ideals) ideal products, primary ideals, primary decompositions, and associ- ated primes are defined.  ...  the Hilbert polynomial, and a more efficient algo- 13P Computational aspects of commutative algebra 95e:13018 rithm for calculating the dimension of an ideal together with a set of variables such that  ... 
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