Promoting insight into algebraic formulas through graphing by hand

Insight into Data through Visualization

Computer graphics, scientific visualization, information visualization, and graph drawing are areas which deal with visual information layout. They all use the remarkable properties of the human visual perception to rapidly absorb and analyse visual information. The paper discusses important visualization aspects and gives examples of how visualization techniques facilitate insight into data ch...

Mitophagy: New Insight into the Cardiovascular Aging  

Simplification of Cylindrical Algebraic Formulas

For a set S of cells in a cylindrical algebraic decomposition of R, we introduce the notion of generalized cylindrical algebraic formula (GCAF) associated with S. We propose a multi-level heuristic algorithm for simplifying the cylindrical algebraic formula associated with S into a GCAF. The heuristic strategies are motivated by solving examples coming from the application of automatic loop tra...

Algebraic Proofs over Noncommutative Formulas

We study possible formulations of algebraic propositional proof systems operating with noncommutative formulas. We observe that a simple formulation gives rise to systems at least as strong as Frege, yielding a semantic way to define a Cook-Reckhow (i.e., polynomially verifiable) algebraic analog of Frege proofs, different from that given in Buss et al. (1997) and Grigoriev & Hirsch (2003). We ...

Algebraic proof systems over formulas