In a statement like x^4+x^2>0, Mathematica treats the variable x as having a definite, though unspecified, value. Sometimes, however, it is useful to be able to make ...

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

Roots[lhs == rhs, var] yields a disjunction of equations which represent the roots of a polynomial equation.

SolveAlways[eqns, vars] gives the values of parameters that make the equations eqns valid for all values of the variables vars.

GeneratedParameters is an option that specifies how parameters generated to represent the results of various symbolic operations should be named.

Algebraics represents the domain of algebraic numbers, as in x \[Element] Algebraics.

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 ...

Mathematica represents Boolean expressions in symbolic form, so they can not only be evaluated, but also be symbolically manipulated and transformed. Incorporating ...

SquaresR[d, n] gives the number of ways r_d (n) to represent the integer n as a sum of d squares.

Mathematica provides convenient functions and algorithms for manipulating colors in images, with full generality for arbitrary numbers of color channels.