Description
Reduce supplied nonnegative prime-factor exponents to squarefree radical exponents; primality of the implicit bases is caller supplied.
Exact integer arithmetic and finite numeric arithmetic have different range limits. A safe integer number is bounded by +/-9007199254740991, while supported decimal-integer text can represent larger values. Division and remainder also need a signed convention: truncating quotients and Euclidean nonnegative remainders can give different results.
Reduce supplied nonnegative prime-factor exponents to squarefree radical exponents; primality of the implicit bases is caller supplied.
When to use this tool
Use Integer Radical Exponent when you need this exact stated integer sign, bound, division, comparison, or factor component.
How to use the tool and how it works
- Enter primeExponents. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read radicalExponents, radicalPreservesInput. Inspect radicalPreservesInput before interpreting the associated values.
For nonnegative integer primeExponents replace each positive exponent by one and preserve zero. Return radicalExponents and radicalPreservesInput when every original exponent<=1.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| primeExponents | Prime Exponents | Required. Array of safe integer; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| radicalExponents | Radical Exponents | Required. Array of safe integer; maximum items 256. |
| radicalPreservesInput | Radical Preserves Input | Required. Boolean. |
{
"input": {
"primeExponents": [
2,
0,
3
]
},
"output": {
"radicalExponents": [
1,
0,
1
],
"radicalPreservesInput": false
}
}Limitations and assumptions
- Prime bases and factorization are not supplied or verified. This transforms an exponent vector under an assumed factorization; it does not compute a numeric radical or validate primality.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
Alternative or Complementary methods
Use exact decimal-integer tools when the range exceeds safe numeric integers. State the division, remainder, midpoint, and zero convention before combining results from different operations.
References
Similar or alternative tools
- Prime Factorization One Exponent Contribution
Trial-divide candidate prime through its square root, reject a composite, then return factor=prime^exponent as exact decimal text.
- Integer Perfect Power Parity Witness
For positive integer exponent return negative=(base<0 and exponent odd) and evenPower=(exponent even).