New in CoCoA-5.2.2 and CoCoALib-0.99560 for SC-square

CoCoA-5 is an interactive Computer Algebra System for Computations in Commutative Algebra, particularly Gr\uf6bner bases. It offers a dedicated, mathematician-friendly programming language, with many built-in functions. Its mathematical core is CoCoALib, an opensource C++ library, designed to facilitate integration with other software. We give an overview of the latest developments of the library and of the system, in particular relating to the project SC-Square

CoCoA and CoCoALib: Fast prototyping and flexible C++ library for computations in commutative Algebra

The CoCoA project began in 1987, and conducts research into Computational Commutative Algebra (from which its name comes) with particular emphasis on Gr\uf6bner bases of ideals in multivariate polynomial rings, and related areas. A major output of the project is the CoCoA software, including the CoCoA-5 interactive system and the CoCoALib C++ library. The software is open-source (GPL v.3), and under continual, active development. We give a summary of the features of the software likely to be relevant to the SC-Square community

New in Cocoa-5.2.4 and Cocoalib-0.99600 for SC-square

CoCoALib is a C++ software library offering operations on polynomials, ideals of polynomials, and related objects. The principal developers of CoCoALib are members of the SC2project. We give an overview of the latest developments of the library, especially those relating to the project SC2. The CoCoA software suite includes also the programmable, interactive system CoCoA-5. Most of the operations in CoCoALib are also accessible via CoCoA-5. The programmability of CoCoA-5 together with its interactivity help in fast prototyping and testing conjectures

06271 Abstracts Collection -- Challenges in Symbolic Computation Software

From 02.07.06 to 07.07.06, the Dagstuhl Seminar 06271 ``Challenges in Symbolic Computation Software\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

The algebraic method in quadrature for uncertainty quantification

A general method of quadrature for uncertainty quantification (UQ) is introduced based on the algebraic method in experimental design. This is a method based on the theory of zero-dimensional algebraic varieties. It allows quadrature of polynomials or polynomial approximands for quite general sets of quadrature points, here called “designs.” The method goes some way to explaining when quadrature weights are nonnegative and gives exact quadrature for monomials in the quotient ring defined by the algebraic method. The relationship to the classical methods based on zeros of orthogonal polynomials is discussed, and numerical comparisons are made with methods such as Gaussian quadrature and Smolyak grids. Application to UQ is examined in the context of polynomial chaos expansion and the probabilistic collocation method, where solution statistics are estimated

Monomials and Basin Cylinders for Network Dynamics

We describe methods to identify cylinder sets inside a basin of attraction for Boolean dynamics of biological networks. Such sets are used for designing regulatory interventions that make the system evolve towards a chosen attractor, for example initiating apoptosis in a cancer cell. We describe two algebraic methods for identifying cylinders inside a basin of attraction, one based on the Groebner fan that finds monomials that define cylinders and the other on primary decomposition. Both methods are applied to current examples of gene networks