Related papers: On parallelizing the Clifford algebra product for …
Quantum Clifford Algebras (QCA), i.e. Clifford Hopf gebras based on bilinear forms of arbitrary symmetry, are treated in a broad sense. Five alternative constructions of QCAs are exhibited. Grade free Hopf gebraic product formulas are…
We present a new Clifford-valued linear canonical Stockwell transform aimed at providing efficient and focused representation of Clifford-valued functions in high-dimensional time-frequency analysis. This transform improves upon the…
This paper is intended to investigate Grassmann and Clifford algebras over Peano spaces, introducing their respective associated extended algebras, and to explore these concepts also from the counterspace viewpoint. The exterior…
We extend a quantized skew Howe duality result for Type $\mathbf{A}$ algebras to orthogonal types via a seesaw. We develop an operator commutant version of the First Fundamental Theorem of invariant theory for $U_q(\mathfrak{so}_n)$ using a…
We describe a new parallel implementation, mplrs, of the vertex enumeration code lrs that uses the MPI parallel environment and can be run on a network of computers. The implementation makes use of a C wrapper that essentially uses the…
We complete our theory of weighted $L^p(w_1) \times L^q(w_2) \to L^r(w_1^{r/p} w_2^{r/q})$ estimates for bilinear bi-parameter Calder\'on--Zygmund operators under the assumption that $w_1 \in A_p$ and $w_2 \in A_q$ are bi-parameter weights.…
Starting from an arbitrary endomorphism \alpha of a unital C*-algebra A we construct a crossed product. It is shown that the natural construction depends not only on the C*-dynamical system (A,\alpha) but also on the choice of an ideal…
The aim of this paper is to provide an answer to the $\mathbb{C}[\partial]$-split extending structures problem for Leibniz conformal algebras, which asks that how to describe all Leibniz conformal algebra structures on $E=R\oplus Q$ up to…
OpenMP parallelization of multiple precision Taylor series method is proposed. A very good parallel performance scalability and parallel efficiency inside one computation node of a CPU-cluster is observed. We explain the details of the…
Cylindrical Algebraic Decomposition (CAD) is an important tool within computational real algebraic geometry, capable of solving many problems for polynomial systems over the reals. It has long been studied by the Symbolic Computation…
We give a Clifford correspondence for an algebra A over an algebraically closed field, that is an algorithm for constructing some finite-dimensional simple A-modules from simple modules for a subalgebra and endomorphism algebras. This…
Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets, with applications in algebraic geometry and beyond. We have previously reported on an implementation of CAD in Maple which offers…
Commutative analogues of Clifford algebras are algebras defined in the same way as Clifford algebras except that their generators commute with each other, in contrast to Clifford algebras in which the generators anticommute. In this paper,…
Clifford algebras are naturally associated with quadratic forms. These algebras are Z_2-graded by construction. However, only a Z_n-gradation induced by a choice of a basis, or even better, by a Chevalley vector space isomorphism Cl(V) <->…
Processors with large numbers of cores are becoming commonplace. In order to take advantage of the available resources in these systems, the programming paradigm has to move towards increased parallelism. However, increasing the level of…
The main objective of this work consists in analyzing sub-structuring method for the parallel solution of sparse linear systems with matrices arising from the discretization of partial differential equations such as finite element, finite…
We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras…
In this paper, we present two fast matrix representation algorithms based on the recursive decomposition of multivectors into specific right and left ideals. We also examine the relation between these two representations. Furthermore, we…
For each quadratic form Q in Quad(V) over a given vector space over a field R we have the Clifford algebra Cl(V,Q) defined as the quotient T(V)/I(Q) of the tensor algebra T(V) over the two-sided ideal generated by expressions of the form $x…
We recall the notions of Clifford and Clifford-like parallelisms in a $3$-dimensional projective double space. In a previous paper the authors proved that the linear part of the full automorphism group of a Clifford parallelism is the same…