Dynamic geometry programs provide environments where accurate construction of geometric configurations can be done. Nevertheless, intrinsic limitations in their standard development technology mostly produce objects that are equationally unknown and so can not be further used in constructions. In this paper, we pursue the development of a geometric system that uses in the background the symboli...

PRAM algorithms for Symmetric Gaussian elimination is presented. We showed actual testing operations that will be performed during Symmetric Gaussian elimination, which caused symbolic factorization to occur for sparse linear systems. The array pattern of processing elements (PE) in row major order for the specialized sparse matrix in formulated. We showed that the access function in+jn+k conta...

Knowledge graph reasoning is the fundamental component to support machine learning applications such as information extraction, retrieval, and recommendation. Since knowledge graphs can be viewed discrete symbolic representations of knowledge, on naturally leverage techniques. However, intolerant ambiguous noisy data. On contrary, recent advances deep have promoted neural graphs, which robust d...

Implementing string transformation routines, such as encoders, decoders, and sanitizers, correctly and efficiently is a difficult and error prone task. Such routines are often used in security critical settings, process large amounts of data, and must work efficiently and correctly. We introduce a new declarative language called Bex that builds on elements of regular expressions, symbolic autom...

We present an interactive tool, called iscc, for manipulating sets and relations of integer tuples bounded by affine constraints over the set variables, parameters and existentially quantified variables. A distinguishing feature of iscc is that it provides a cardinality operation on sets and relations that computes a symbolic expression in terms of the parameters and domain variables for the nu...

Inspired by recent work in the theory of central projections onto hyper-surfaces, we characterize self-linked perfect ideals of grade 2 as those with a Hilbert– Burch matrix that has a maximal symmetric subblock. We also prove that every Gorenstein perfect algebra of grade 1 can be presented, as a module, by a symmetric matrix. Both results are derived from the same elementary lemma about symme...