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based on an earlier version of the Wolfram Language.
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$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:
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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:
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