Is Computer Algebra Ready for Conjecturing and Proving Geometric Inequalities in the Classroom?

Visualizing a Cubic Linkage through the Use of CAS and DGS

“…Since the bar-and-joint linkages we observe in the real world live in the Euclidean 3-dimensional space, our models for linkages should live in R n , with computations performed with polynomials with real coefficients. However, it is well known that real algebraic geometry algorithms are often computationally unfeasible when working with a high number of variables and polynomials (see [19] and the references indicated therein). Because of this reason, in the sequel, we will treat our mathematical model and the computations performed with the polynomials describing it as living in a polynomial ring with complex coefficients, even though the visual models we will be using throughout this work live in R n -in other words, our visual models will restrict our attention to the R-realizations of our mathematical model.…”