R eal c ertify
Victor Magron, Mohab Safey El Din · ACM communications in computer algebra · 2018
Let Q (resp. R) be the field of rational (resp. real) numbers and X = ( X 1 , ... , X n ) be variables. Deciding the non-negativity of polynomials in Q[ X ] over R n or over semi-algebraic domains defined by polynomial constraints in Q[ X ] is a classical algorithmic problem for symbolic computation. The Maple package R eal C ertify tackles this decision problem by computing sum of squares certificates of non-negativity for inputs where such certificates hold over the rational numbers. It can be applied to numerous problems coming from engineering sciences, program verification and cyber-physical systems. It is based on hybrid symbolic-numeric algorithms based on semi-definite programming.