RootReduce
RootReduce[expr]
attempts to reduce expr to a single Root object.
Details and Options
- 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.
Examples
open allclose allBasic Examples (1)
Reduce to a single Root object:
Scope (2)
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:
Options (1)
Method (1)
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:
Applications (1)
The numeric test used by Equal cannot prove the equality:
RootReduce proves that the two algebraic numbers are equal:
FullSimplify will use RootReduce:
Properties & Relations (3)
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:
RootReduce converts from AlgebraicNumber objects: