optimization – solving an inequality system with orthogonality constraint in Python

I need to solve a system of inequalities for a vector of variables where one of the inequalities has an orthogonality constraint. In my particular problem, it has been proved that the resolution of the system always leads to an exact solution. Because of the orthogonality, I do not think I can use linear programming. Someone has recommendations for effective methods to solve in Python? Wolfram Alpha is able to do it! (See example here) I know that sympy can not, because it can only solve for a univariate case. Please include the time of execution with the answer you give!