Cylindrical algebraic decomposition I: the basic algorithm
SIAM Journal on Computing
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
Testing stability by quantifier elimination
Journal of Symbolic Computation - Special issue: applications of quantifier elimination
Solving systems of strict polynomial inequalities
Journal of Symbolic Computation
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Simple CAD construction and its applications
Journal of Symbolic Computation
Application of Gröbner bases and quantifier elimination for insightful engineering design
Mathematics and Computers in Simulation - Special issue: Applications of computer algebra in science, engineering, simulation and special software
Hi-index | 0.00 |
We use the cylindrical algebraic decomposition algorithms implemented in Mathematica to produce procedures to analytically compute integrals over polynomially defined regions and their boundaries in two and three dimensions. Using these results, we can implement the divergence theorem in three dimensions or the Green's theorems in two dimensions. These theorems are of central importance in the applications of multidimensional integration. They also provide a strong correctness test for the implementation of our results in a computer algebra system. The resulting software can solve many of the two and some of the three dimensional integration problems in vector calculus textbooks. The three dimensional results are being extended. The results in this paper are being included in an automated student assistant for vector calculus.