Experimental Mathematics: Using Maple to Analyze Some Conjectures Involving Matrices and Polynomials скачать в хорошем качестве

Experimental Mathematics: Using Maple to Analyze Some Conjectures Involving Matrices and Polynomials

The availability of tools like Maple enables us to introduce an experimental approach into the research we do in mathematics, when appropriate. In this talk we present four concrete examples where the use of Maple has been essential to discover, conjecture, and in some cases, demonstrate new properties of the mathematical objects that we were considering - mostly polynomials and matrices. In the first example we will show how the use of Maple allowed us to provide the first non-trivial results on the Casas-Alvero Conjecture, which asks if every polynomial that has a root in common with each of its derivatives (not always the same root) is necessarily a power of a linear factor. The second example will show how useful is Maple to determine the structure of the polynomials that describe the projection of the intersection of a torus and a quadric. The third example will illustrate how Maple helps generate and characterize correlation matrices when their entries are -1, 0 and 1. The last example will be devoted to introducing the use of Maple for trying to prove (or disprove) a conjecture about the spread of a symmetric matrix (i.e. the maximum absolute value of the difference between any two eigenvalues) with entries in the closed interval [a,b]. To learn more about the Maple Conference, visit: https://www.maplesoft.com/mapleconfer... Explore other sessions from this year's Maple Conference:    • Maple Conference 2024   Subscribe to the Maplesoft channel:    / @maplesoft   Follow Maplesoft:   / maplesoft     / maplesoft     / maplesoft     / maplemathmatters