Finding the structure of polynomials written in expanded form. Here is a polynomial in two variables. This is the polynomial in expanded form.

The Mathematica functions Reduce, Resolve, and FindInstance allow you to solve a wide variety of problems that can be expressed in terms of equations and inequalities. The ...

PrimitiveRoot[n] gives the smallest primitive root of n.

A real polynomial system is an expression constructed with polynomial equations and inequalities combined using logical connectives and quantifiers and

Structural operations on polynomials. Here is a polynomial in one variable. Expand expands out products and powers, writing the polynomial as a simple sum of terms.

A Diophantine polynomial system is an expression constructed with polynomial equations and inequalities combined using logical connectives and quantifiers where the variables ...

NSolve[expr, vars] attempts to find numerical approximations to the solutions of the system expr of equations or inequalities for the variables vars. NSolve[expr, vars, ...

Mathematica automatically uses sophisticated algorithms to track the precision of approximate numbers. Particularly for some verification applications, however, it is ...

The main equations that Solve and related Mathematica functions deal with are polynomial equations. It is easy to solve a linear equation in  x. One can also solve quadratic ...

Cubics is an option for functions that involve solving algebraic equations, that specifies whether explicit forms for solutions to cubic equations should be given.