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Efficient Decomposition of Associative Algebras over Finite Fields
2000
Journal of symbolic computation
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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
1997
Applicable Algebra in Engineering, Communication and Computing
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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
2009
SIAM Journal on Numerical Analysis
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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
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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
2006
Zenodo
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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
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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
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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
2014
Applied Mathematics and Computation
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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
2013
Zenodo
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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
2002
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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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
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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
2018
International journal of algebra and computation
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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]
2009
Communications in Computer and Information Science
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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
2017
Proceedings of the Software Demonstrations of the 15th Conference of the European Chapter of the Association for Computational Linguistics
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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
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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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