Popular computer algebra systems such as Maple, Macsyma, Mathematica, and REDUCE are now basic tools on most computers. Efficient algorithms for various algebraic operations underlie all these systems. Computer algebra, or algorithmic algebra, studies these algorithms and their properties and represents a rich intersection of theoretical computer science with classical mathematics.

Fundamental Problems of Algorithmic Algebra provides a systematic and focused treatment of a collection of core problemsthe computational equivalents of the classical Fundamental Problem of Algebra and its derivatives. Topics covered include the GCD, subresultants, modular techniques, the fundamental theorem of algebra, roots of polynomials, Sturm theory, Gaussian lattice reduction, lattices and polynomial factorization, linear systems, elimination theory, Grobner bases, and more.
Features
� Presents algorithmic ideas in pseudo-code based on mathematical concepts and can be used with any computer mathematics system
� Emphasizes the algorithmic aspects of problems without sacrificing mathematical rigor
� Aims to be self-contained in its mathematical development
� Ideal for a first course in algorithmic or computer algebra for advanced undergraduates or beginning graduate students

Contenuti

O INTRODUCTION
1: Fundamental Problem of Algebra
2: Fundamental Problem of Classical Algebraic Geometry
3: Fundamental Problem of Ideal Theory
4: Representation and Size
5: Computational Models
6: Asymptotic Notations
7: Complexity of Multiplication
8: On Bit versus Algebraic Complexity
9: Miscellany
10: Computer Algebra Systems
I ARITHMETIC
1: The Discrete Fourier Transform
2: Polynomial Multiplication
3: Modular FFT
4: Fast Integer Multiplication
5: Matrix Multiplication
II THE GCD
1: Unique Factorization Domain
2: Euclid's Algorithm
3: Euclidean Ring
4: The Half-GCD problem
5: Properties of the Norm
6: Polynomial HGCD
A: APPENDIX: Integer HGCD
III SUBRESULTANTS
1: Primitive Factorization
2: Pseudo-remainders and PRS
3: Determinantal Polynomials
4: Polynomial Pseudo-Quotient
5: The Subresultant PRS
6: Subresultants
7: Pseudo-subresultants
8: Subresultant Theorem
9: Correctness of the Subresultant PRS Algorithm
IV MODULAR TECHNIQUES
1: Chinese Remainder Theorem
2: Evaluation and Interpolation
3: Finiding Prime Moduli
4: Lucky homomorphisms for the GCD
5: Coefficient Bounds for Factors
6: A Modular GCD algorithm
7: What else in GCD computation?
IV FUNDAMENTAL THEOREM OF ALGEBRA
1: Elements of Field Theory
2: Ordered Rings
3: Formally Real Rings
4: Constructible Extensions
5: Real Closed Fields
6: Fundamental Theorem of Algebra
VI ROOTS OF POLYNOMIALS
1: Elementary Properties of Polynomial Roots
2: Root Bounds
3: Algebraic Numbers
4: Resultants
5: Symmetric Functions
6: Discriminant
7: Root Separation
8: A Generalized Hadamard Bound
9: Isolating Intervals
10: On Newton's Method
11: Guaranteed Convergence of Newton Iteration
VII STURM THEORY
1: Sturm Sequences from PRS
2: A Generalized Sturm Theorem
3: Corollaries and Applications
4: Integer and Complex Roots
5: The Routh-Hurwitz Theorem
6: Sign Encoding of Algebraic Numbers: Thom's Lemma
7: Problem of Relative Sign Conditions
8: The BKR algorithm
VIII GAUSSIAN LATTICE REDUCTION
1: Lattices
2: Shortest vectors in planar lattices
3: Coherent Remainder Sequences
IX LATTICE REDUCTION AND APPLICATIONS
1: Gram-Schmidt Orthogonalization
2: Minkowski's Convex Body Theorem
3: Weakly Reduced Bases
4: Reduced Bases and the LLL-algorithm
5: Short Vectors
6: Factorization via Reconstruction of Minimal Polynomials
X LINEAR SYSTEMS
1: Sylvester's Identity
2: Fraction-free Determinant Computation
3: Matrix Inversion
4: Hermite Normal Form
5: A Multiple GCD Bound and Algorithm
6: Hermite Reduction Step
7: Bachem-Kannan Algorithm
8: Smith Normal Form
9: Further Applications
XI ELIMINATION THEORY
1: Hilbert Basis Theorem
2: Hilbert Nullstellensatz
3: Specializations
4: Resultant Systems
5: Sylvester Resultant Revisited
6: Interial Ideal
7: The Macaulay Resultant
8: U-Resultant
9: Generalized Characteristic Polynomial
10: Generalized U - resultant
11: A Multivariate Root Bound
A: APPENDIX A: Power Series
B: APPENDIX B: Counting Irreducible Polynomials
XII GROBNER BASES
1: Admissible Orderings
2: Normal Form ALgorithm
3: Characterizations of Grobner Bases
4: Buchberger's Algorithm
5: Uniqueness
6: Elimination Properties
7: Computing in Quotient Rings
8: Syzygies
XIII BOUNDS IN POLYNOMIAL IDEAL THEORY
1: Some Bounds in Polynomial Ideal Theory
2: The Hilbert-Sette Theorem
3: Homogeneous Sets
4: Cone Decomposition
5: Exact Decomposition of NF (I)
6: Exact Decomposition of Ideals
7: Bouding the Macaulay constants
8: Term Rewriting Systems
9: A Quadratic Counter
10: Uniqueness Property
11: Lower Bounds
A: APPENDIX: Properties of So
XIV CONTINUED FRACTIONS
1: Introductions
2: Extended Numbers
3: General Terminology
4: Ordinary Continued Fractions
5: Continued fractions as Mobius transformations
6: Convergence Properties
7: Real Mobius Transformations
8: Continued Fractions of Roots
9: Arithmetic Operations

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

Descrizione libreria

Thank you for visiting our profile. We are a home-based business have been selling books online since 2004 and joined AbeBooks in 2008. Feel free to e-mail us at BasementSeller101@gmail.com. We would be happy to assist you.

Visita la pagina della libreria

Informazioni sull?azienda del venditore

Basement Seller 101
OH, U.S.A.

Condizioni di vendita e spedizione

Condizioni di vendita

We guarantee the condition of every book as it's described on the Abebooks web sites. If you're dissatisfied with your purchase (Incorrect Book/Not as Described/Damaged) or if the order hasn't arrived, you're eligible for a refund within 30 days of the estimated delivery date. If you've changed your mind about a book that you've ordered, please use the Ask bookseller a question link to contact us and we'll respond within 2 business days.

Diritto di recesso

Condizioni di spedizione

Orders usually ship within 2 business days. Expected shipping times for "Standard" orders is 4 to 14 business days and for "Expedited" orders is 3 to 5 business days. We do accept international orders, although shipment times may vary, usually from 3 to 6 weeks.

If you have any questions about our shipment times and policies, if you need a book faster, or if you would like to check the status of your order, please e-mail us.

Please note that we ship all "Standard" items via US Postal Service Media Mail and all "Expedited" items via US Postal Service Priority Mail. Our international orders go via USPS First Class or Priority International Mail. If you would like us to ship an item via another carrier, please e-mail us and we will try to accommodate you.

We can overnight books domestically and send books expedited internationally for an additional charge.

The majority of our packages are shipped using Stamps.com NetStamps, a non-trackable method. Please note that all items ordered via the "Expedited" shipping method are automatically shipped with Delivery Confirmation. If you would like your item shipped with Delivery Confirmation, please e-mail us before making your purchase.

We ship orders every day, Monday through Friday, (excluding Postal Service holidays) usually by 12PM. If you need to cancel or make changes to an order, please do so as soon as possible -- many requests we get regarding orders are not fulfilled because we find, pack, and ship the book before the buyer contacts us. If you receive a confirmation e-mail from us, it means your order has been shipped and we can no longer make changes to it.

Please note that the majority of our orders ship out within 24 hours, many shipping out the same day they are ordered. Since we usually ship around 12PM, most orders received Friday after 10AM will not go out until Monday. In some cases, we will make a trip on Saturday to get more orders out.

Tariffe di spedizione da U.S.A. a Italia

Tariffe di spedizione da U.S.A. a Italia
Quantit� dell?ordine	Da 8 a 21 giorni lavorativi	Da 4 a 8 giorni lavorativi
Primo articolo	EUR 30.26	EUR 60.48

I tempi di consegna sono stabiliti dai venditori e variano in base al corriere e al paese. Gli ordini che devono attraversare una dogana possono subire ritardi e spetta agli acquirenti pagare eventuali tariffe o dazi associati. I venditori possono contattarti in merito ad addebiti aggiuntivi dovuti a eventuali maggiorazioni dei costi di spedizione dei tuoi articoli.