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ToRadicals

ToRadicals[expr]
attempts to express all Root objects in expr in terms of radicals.
  • ToRadicals can always give expressions in terms of radicals when the highest degree of the polynomial that appears in any Root object is four.
  • There are some cases in which expressions involving radicals can in principle be given, but ToRadicals cannot find them.
  • If Root objects in expr contain parameters, ToRadicals[expr] may yield a result that is not equal to expr for all values of the parameters.
  • ToRadicals automatically threads over lists, as well as equations, inequalities, and logic functions.
All cubic Root objects can be converted into radicals:
All quartic Root objects can be converted into radicals:
Some higher-degree Root objects can be represented in terms of radicals:
ToRadicals also works with AlgebraicNumber objects:
ToRadicals converts trigonometric functions of rational multiples of :
With Cubics->False the general formulas for solving cubic equations are not used:
Converting some cubic Root objects does not require the general formulas:
With Quartics->False the general formulas for solving quartic equations are not used:
Converting some quartic Root objects does not require the general formulas:
RootReduce[ToRadicals[r]]==r for any algebraic number r given as a Root object:
By default Reduce will not produce radical solutions for general cubics:
Use ToRadicals to convert:
Alternatively set Cubics->True:
In this case ToRadicals succeeds on the unreduced expression:
In this case ToRadicals succeeds on the reduced expression:
ToRadicals converts Root objects containing parameters:
The result may not be equal to the Root object for some values of the parameter:
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