Selected Topics In Geometry With Classical Vs Computer Proving

Selected Topics In Geometry With Classical Vs. Computer Proving

This textbook presents various automatic techniques based on Gröbner bases elimination to prove well-known geometrical theorems and formulas. Besides proving theorems, these methods are used to discover new formulas, solve geometric inequalities, and construct objects — which cannot be easily done with a ruler and compass.Each problem is firstly solved by an automatic theorem proving method. Secondly, problems are solved classically — without using computer where possible — so that readers can compare the strengths and weaknesses of both approaches.

Selected Topics in Geometry with Classical Vs. Computer Proving

Numerical and Symbolic Scientific Computing

The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finite element methods, a symbolic approach to finite difference schemes, cylindrical algebraic decomposition and local Fourier analysis, and white noise analysis for stochastic partial differential equations. Further numerical-symbolic topics range from applied and computational geometry to computer algebra methods used for total variation energy minimization.