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The package provides a function for solving systems of univariate inequalities. InequalitySolve[expr,x] finds conditions that must be satisfied by real values of x in order for the expression expr to be true. The expression should contain logical connectives and univariate polynomial equations and inequalities in the specified variable.

Finding solutions to inequalities.

  • This loads the package.
  • In[1]:= <<Algebra`InequalitySolve`

  • Here is a set of solutions to a polynomial inequality.
  • In[2]:= InequalitySolve[x (x^2 - 2) (x^2 - 3) > 0, x]


  • The inequalities may contain absolute values and rational functions.
  • In[3]:= InequalitySolve[x/Abs[x - 1] >= 0 && 1/x < x + 1, x]


  • Here the inequalities contain the exponential function. In general, if inequalities contain nonpolynomial functions of the specified variable, we may get an incorrect result.
  • In[4]:= InequalitySolve[Abs[x - 1] <= 5 && E^x <= 3, x]

    InequalitySolve::npi: A nonpolynomial equation or inequality encountered. The solution set may be incorrect.