BUILT-IN MATHEMATICA SYMBOL

$MaxRootDegree

$MaxRootDegree
specifies the maximum degree of polynomial to allow in Root objects.

Evaluation of Root objects with high degree minimal polynomials may be slow:

The result is a valid algebraic number with minimal polynomial proven irreducible:

Root does not attempt factoring polynomials with degrees higher than $MaxRootDegree:

The result is not a valid algebraic number:

Evaluation of Root objects with high degree minimal polynomials may be slow:

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The result is a valid algebraic number with minimal polynomial proven irreducible:

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Root does not attempt factoring polynomials with degrees higher than $MaxRootDegree:

Out[3]=

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The result is not a valid algebraic number:

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The degree of the sum of two Root objects may be as high as the product of their degrees:

This prevents Mathematica from creating Root objects with degrees greater than 100:

Root objects already created are cached; this removes the cached results:

Now RootReduce is not allowed to create a Root object with degree 110:

This resets $MaxRootDegree to the default value:

By default, Mathematica does not use Root objects with degrees exceeding 1000:

Increasing the value of $MaxRootDegree allows Mathematica to create the algebraic number:

Since this Root object is real, computing its numeric approximation is reasonably fast: