Root

Root[f,k]
represents the exact k^(th) root of the polynomial equation .

Root[{f1,f2,},{k1,k2,}]
represents the last coordinate of the exact vector such that is the ^(th) root of the polynomial equation .

Root[{f,x0}]
represents the exact root of the general equation near .

Root[{f,x0,n}]
represents n roots of the equation near .

Details and OptionsDetails and Options

  • f must be a Function object such as .
  • Root[f,k] is automatically reduced so that f has the smallest possible degree and smallest integer coefficients.
  • The ordering used by Root[f,k] takes real roots to come before complex ones, and takes complex conjugate pairs of roots to be adjacent.
  • The coefficients in the polynomial can involve symbolic parameters.
  • For linear and quadratic polynomials , Root[f,k] is automatically reduced to explicit rational or radical form.
  • For other polynomials, ToRadicals can be used to convert to explicit radicals.
  • In Root[{f1,f2,},{k1,k2,}], must be a Function object with i formal parameters, and should be a polynomial in x of degree at least .
  • If for all i, is a polynomial in with rational number coefficients, then RootReduce can be used to represent Root[{f1,f2,},{k1,k2,}] in the Root[f,k] form.
  • Root[{f,x0}] represents an exact root of the general equation , which can be transcendental.
  • In Root[{f,x0}], must be an approximate real or complex number such that exactly one root of lies within the numerical region defined by its precision.
  • Root[{f,x0,n}] represents n roots, counting multiplicity, that lie within the numerical region defined by the precision of .
  • N finds the approximate numerical value of a Root object.
  • Operations such as Abs, Re, Round, and Less can be used on Root objects.
  • Root[f,k] is treated as a numeric quantity if f contains no symbolic parameters.
  • Root by default isolates the complex roots of a polynomial using validated numerical methods. SetOptions[Root,ExactRootIsolation->True] will make Root use symbolic methods that are usually much slower.
Introduced in 1996
(3.0)
| Updated in 2012
(9.0)