The book presents modern and efficient methods for solving Geodetic and Geoinformatics algebraic problems illustrated with Mathematica using computer algebra techniques of Ring, Polynomials, Groebner basis, Resultants including Dixon resultant, Gauss-Jacobi combinatorial and Procrustes algorithms as well as homotopy methods. These problems are traditionally solved by approximate methods. This book presents alternative algebraic techniques based on computer algebra tools. This new approach meets such modern challenges as resection by laser techniques, solution of orientation in Robotics, transformation and bundle block adjustment in Geoinformatics, densification of Engineering networks, analytical solution for GPS-meteorology and many other problems. For Mathematicians, the book provides some practical examples of application of abstract algebra and multidimensional scaling. The accompanying CD-ROM contains Mathematica notebooks with computational illustrations and application packages to solve for real life problems in geodesy and geoinformatics as resection, intersection, orientation problems.
Introduction | Algebraic Symbolic and Numeric Methods | Basics of Ring Theory | Basics of Polynomial Theory | Groebner Basis | Polynomial Resultants | Linear Homotpy | Solutions of Overdetermined Systems | Extended Newton-Raphson Method | Procrustes Solution | Applications to Geodesy and Geoinformatics | LPS-GNSS Orientations and Vertical Deflections | Cartesian to Ellipsoidal Mapping | Position by Ranging | Positioning by Resection Methods | Positing by Intersection Methods | GNSS Environmental Monitoring | Algebraic Diagnosis of Outliers | Datum transformation Problems | Appendix