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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:
Reduce to a single Root object:
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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:
RootReduce converts from AlgebraicNumber objects:
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