NumberFieldRootsOfUnity (Built-in Mathematica Symbol)

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

Polynomial Equations (Mathematica Guide)

Packed into functions like Solve and Reduce are a wealth of sophisticated algorithms, many created specifically for Mathematica. Routinely handling both dense and sparse ...

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.

Inequalities (Mathematica Tutorial)

Just as the equation x^2+3x==2 asserts that x^2+3x is equal to 2, so also the inequality x^2+3x>2 asserts that x^2+3x is greater than 2. In Mathematica, Reduce works not only ...

Polynomial Algebra (Mathematica Guide)

Polynomial algorithms are at the core of classical "computer algebra". Incorporating methods that span from antiquity to the latest cutting-edge research at Wolfram Research, ...

Equation Solving (Mathematica Guide)

Built into Mathematica is the world's largest collection of both numerical and symbolic equation solving capabilities—with many original algorithms, all automatically ...

ToRadicals (Built-in Mathematica Symbol)

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

Reduce (Built-in Mathematica Symbol)

Reduce[expr, vars] reduces the statement expr by solving equations or inequalities for vars and eliminating quantifiers. Reduce[expr, vars, dom] does the reduction over the ...

Counting and Isolating Polynomial Roots (Mathematica Tutorial)

Counting roots of polynomials. CountRoots accepts polynomials with Gaussian rational coefficients. The root count includes multiplicities. This gives the number of real roots ...