CountRoots (Built-in Mathematica Symbol)

CountRoots[poly, x] gives the number of real roots of the polynomial poly in x.CountRoots[poly, {x, a, b}] gives the number of roots between a and b.

RootApproximant (Built-in Mathematica Symbol)

RootApproximant[x] converts the number x to one of the "simplest" algebraic numbers that approximates it well.RootApproximant[x, n] finds an algebraic number of degree at ...

PrimitiveRoot (Built-in Mathematica Symbol)

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

Roots (Built-in Mathematica Symbol)

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

RootSum (Built-in Mathematica Symbol)

RootSum[f, form] represents the sum of form[x] for all x that satisfy the polynomial equation f[x] == 0.

NumberFieldRootsOfUnity (Built-in Mathematica Symbol)

NumberFieldRootsOfUnity[a] gives the roots of unity for the field \[DoubleStruckCapitalQ][a] generated by the algebraic number a.

AlgebraicIntegerQ (Built-in Mathematica Symbol)

AlgebraicIntegerQ[a] yields True if a is an algebraic integer, and yields False otherwise.

Typing Square Roots (Mathematica Tutorial)

To get a square root sign, press the Control key and the 2 key at the same time. Press Ctrl+2 or Ctrl+@. Type inside the placeholder (which is already selected).

Subresultants (Built-in Mathematica Symbol)

Subresultants[poly_1, poly_2, var] generates a list of the principal subresultant coefficients of the polynomials poly_1 and poly_2 with respect to the variable var.

ToRadicals (Built-in Mathematica Symbol)

ToRadicals[expr] attempts to express all Root objects in expr in terms of radicals.