Description
Reduce a supplied exact rational before testing whether its denominator is a power of two.
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.
Reduce a supplied exact rational before testing whether its denominator is a power of two.
When to use this tool
Use Rational Dyadic Denominator 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 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 reducedDenominator, dyadic, exponent. Inspect dyadic before interpreting the associated values.
Parse signed decimal integers with nonzero denominator, normalize signs for gcd reduction, and return reducedDenominator. Remove factors of two; return dyadic=true and exponent equal to their count only when no factor remains, otherwise exponent=-1.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| numerator | Numerator in the numeric or exact integer-text representation declared below. | Required. Text; maximum UTF-16 length 8192. Integer syntax: optional + or - and 1-128 decimal digits; leading zeros accepted. Apply the sign restriction above. |
| denominator | Denominator or exact integer denominator text under the stated sign restriction. | Required. Text; maximum UTF-16 length 8192. Integer syntax: optional + or - and 1-128 decimal digits; leading zeros accepted. Apply the sign restriction above. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| reducedDenominator | Reduced Denominator | Required. Text; maximum UTF-16 length 8192. |
| dyadic | Dyadic | Required. Boolean. |
| exponent | Power of two for a dyadic reduced denominator, or -1 when not dyadic. | Required. Safe integer. |
{
"input": {
"numerator": "6",
"denominator": "24"
},
"output": {
"reducedDenominator": "4",
"dyadic": true,
"exponent": 2
}
}Limitations and assumptions
- The flag means a finite exact binary rational expansion, not representability in a specific finite floating-point format. Zero numerator reduces to denominator one with exponent zero.
- 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
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
- Positional Fraction Terminating Prime Support
Return remainingDenominator and terminating when it equals one.
- Rational Repetend Pre Period Budget
Nonrepeating prefix length for a reduced rational denominator in the supplied radix; numerator must already be coprime.