BUILT-IN MATHEMATICA SYMBOL

RootReduce

RootReduce[expr]
attempts to reduce expr to a single Root object.

If expr consists only of integers and Root and AlgebraicNumber objects combined using algebraic operations, then the result from RootReduce[expr] will always be a single Root object.

Simple Root objects may in turn automatically evaluate to rational expressions or combinations of radicals.

RootReduce automatically threads over lists, as well as equations, inequalities, and logic functions.

Reduce to a single Root object:

Out[1]=

Combinations of radical expressions:

Combinations of Root objects:

Reduce any algebraic combination of radicals, Root, and AlgebraicNumber objects:

The result is always a Root object, a quadratic radical expression, or a rational number:

By default, RootReduce heuristically selects the method to use:

In this case conversion to AlgebraicNumber objects in a common number field is used:

The other available method recursively performs arithmetic operations:

Here the

method is faster:

The numeric test used by Equal cannot prove the equality:

RootReduce proves that the two algebraic numbers are equal:

The results given by RootReduce are canonical:

In general the degree of the reduced polynomial will be the product of the degrees:

In exceptional cases the result can have a lower degree:

Root objects can be converted to AlgebraicNumber objects: