Description
Return realDefined for a positive base, a zero base with positive numerator, or a negative base with odd reduced denominator.
A rational number is represented by an integer numerator and a nonzero integer denominator. Sign placement, reduction by a greatest common divisor, and the chosen division or rounding convention affect intermediate representations. Exact integer text preserves arithmetic that could be lost in a floating-point conversion.
Return realDefined for a positive base, a zero base with positive numerator, or a negative base with odd reduced denominator.
When to use this tool
Use Rational Power Sign Domain Flag when you need this particular exact fraction comparison, reduction, sign, denominator, or rounding component.
How to use the tool and how it works
- Enter base, numerator, denominator. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read realDefined, negativeResult. Inspect realDefined, negativeResult before interpreting the associated values.
For integer numerator and positive integer denominator reduce the exponent by their gcd. Return realDefined for a positive base, a zero base with positive numerator, or a negative base with odd reduced denominator. Set negativeResult only when defined, the base is negative, and the reduced numerator is odd.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| base | Base | Required. Finite number. |
| numerator | Numerator in the numeric or exact integer-text representation declared below. | Required. Safe integer. |
| denominator | Denominator or exact integer denominator text under the stated sign restriction. | Required. Safe integer; minimum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| realDefined | Real Defined | Required. Boolean. |
| negativeResult | Sign flag only for an accepted real rational power, not an evaluated result. | Required. Boolean. |
{
"input": {
"base": -8,
"numerator": 1,
"denominator": 3
},
"output": {
"realDefined": true,
"negativeResult": true
}
}Limitations and assumptions
- This checks the real rational-power convention without evaluating a power. Zero to the zero power and zero to negative powers are marked undefined; parity decisions use the reduced exponent, not the original denominator.
- 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.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Reduce fractions where the interpretation requires it and choose a consistent denominator-sign and division convention. Use a complete rational operation when one denominator or determinant term is insufficient.
References
Similar or alternative tools
- Integer Perfect Power Parity Witness
For positive integer exponent return negative=(base<0 and exponent odd) and evenPower=(exponent even).
- 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.