Function Repository Resource:

# RootDegree

Get the polynomial degree of an algebraic number

Contributed by: Ed Pegg Jr
 ResourceFunction["RootDegree"][s] returns the polynomial degree of the algebraic number s.

## Details

The polynomial degree of an algebraic number s is the degree of the polynomial of lowest degree for which s is a root.

## Examples

### Basic Examples (3)

Find the root degree of the plastic constant, which satisfies the relation :

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Find the root degree for roots of polynomials of orders 2 to 8:

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Find the root degree of some trigonometric roots:

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### Scope (2)

Root degree of an AlgebraicNumber:

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Show the root degree of cumulative sums of roots of primes:

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### Possible Issues (3)

The default \$MaxRootDegree is 1000:

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Under default conditions, a degree-1000 root may be evaluated:

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A degree-1001 root will fail under default conditions:

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RootDegree only works on exact algebraic numbers:

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Use RootApproximant to get a number that can be given to RootDegree:

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Some algebraic numbers might not be recognized by RootDegree:

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## Version History

• 1.0.0 – 07 February 2022