This book is the natural continuation of Computational Commutative Algebra 1 with some twists.
The main part of this book is a breathtaking passeggiata through the computational domains of graded ...rings and modules and their Hilbert functions. Besides Gröbner bases, we encounter Hilbert bases, border bases, SAGBI bases, and even SuperG bases.
The tutorials traverse areas ranging from algebraic geometry and combinatorics to photogrammetry, magic squares, coding theory, statistics, and automatic theorem proving. Whereas in the first volume gardening and chess playing were not treated, in this volume they are.
This is a book for learning, teaching, reading, and most of all, enjoying the topic at hand. The theories it describes can be applied to anything from children's toys to oil production. If you buy it, probably one spot on your desk will be lost forever!
This book demonstrates current trends in research on combinatorial and computational commutative algebra with a primary emphasis on topics related to monomial ideals. In the text, theory is ...complemented by a number of examples and exercises.
We compute the numerical index of the two-dimensional real Lp space for 65⩽p⩽1+α0 and α1⩽p⩽6, where α0 is the root of f(x)=1+x−2−(x−1x+x1x) and 11+α0+1α1=1. This, together with the previous results ...in Merí and Quero On the numerical index of absolute symmetric norms on the plane. Linear Multilinear Algebra. 2021;69(5):971–979 and Monika and Zheng The numerical index of ℓp2. Linear Multilinear Algebra. 2022;1–6. Published online DOI:10.1080/03081087.2022.2043818, gives the numerical index of the two-dimensional real Lp space for 65⩽p⩽6.
In this paper, we present a candidate for Formula omitted extended higher-spin Formula omitted supergravity with the most general boundary conditions discussed by Grumiller and Riegler recently. We ...show that the asymptotic symmetry algebra consists of two copies of the Formula omitted affine algebra in the presence of the most general boundary conditions. Furthermore, we impose some certain restrictions on gauge fields on the most general boundary conditions and that leads us to the supersymmetric extension of the Brown-Henneaux boundary conditions. We eventually see that the asymptotic symmetry algebra reduces to two copies of the Formula omitted algebra for Formula omitted extended higher-spin supergravity.
In this work we propose a theoretical and practical method to transform the multivariate Lagrange polynomial interpolation problem into a univariate problem. This transformation allows a wide ...exploitation of all one-variable polynomial Lagrange interpolation schemes such as Newton's scheme or split differences, etc. Numerical comparison with other existing methods will be studied. Key words. polynomial interpolation, multivariate Lagrange polynomial interpolation problem
Matrix Algebra Abadir, Karim M.; Magnus, Jan R.
08/2005, Volume:
v.Series Number 1
eBook
Matrix Algebra is the first volume of the Econometric Exercises Series. It contains exercises relating to course material in matrix algebra that students are expected to know while enrolled in an ...(advanced) undergraduate or a postgraduate course in econometrics or statistics. The book contains a comprehensive collection of exercises, all with full answers. But the book is not just a collection of exercises; in fact, it is a textbook, though one that is organized in a completely different manner than the usual textbook. The volume can be used either as a self-contained course in matrix algebra or as a supplementary text.
Abstract
We compute the generator rank of a subhomogeneous
$C^*\!$
-algebra in terms of the covering dimension of the pieces of its primitive ideal space corresponding to irreducible representations ...of a fixed dimension. We deduce that every
$\mathcal {Z}$
-stable approximately subhomogeneous algebra has generator rank one, which means that a generic element in such an algebra is a generator.
This leads to a strong solution of the generator problem for classifiable, simple, nuclear
$C^*\!$
-algebras: a generic element in each such algebra is a generator. Examples of Villadsen show that this is not the case for all separable, simple, nuclear
$C^*\!$
-algebras.
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