The book presents modern and efficient methods for solving Geodetic and Geoinformatics algebraic problems using computer algebra techniques of Ring, polynomials, Groebner basis, resultants, Gauss-Jacobi combinatorial and Procrustes algorithms. Although 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 abstract algebra application and multidimensional scaling.

The book presents algebraic tools for solving nonlinear system of equations in Geodesy and Geoinformatics. In order to achieve this, the book employs Groebner basis approach which we solve extensively using the

*Mathematica* function

`GroebnerBasis`. This is further performed for reduced Groebner basis.

*Mathematica* is employed in all the examples discussed the book.

In the last Chapter where we discuss Computer Algebraic Systems,

*Mathematica* is one of the software discussed and used to show how graphs can be plotted.

Algebra