Using Assumptions and Solving Inequalities

Adam Strzebonski
Wolfram Research, Inc.

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The next version of Mathematica allows specifying assumptions in Simplify and related functions. The underlying mechanism used automatically to check inference of inequality assumptions is also used by various new functions allowing us to solve systems of real polynomial equations and inequalities, minimize polynomial functions on polynomial inequality constraints, and eliminate quantifiers from real polynomial equation and inequality systems. I will show some examples and shortly describe the algorithms used.