Description
Return a Laurent monomial's sign and natural-log magnitude.
A monomial combines a coefficient with variable exponents. Ordinary nonnegative exponents and signed Laurent exponents have different domains; exponent-vector divisibility and greatest-common-factor rules describe the variable part unless coefficients are explicitly included. Zero coefficients and absent variables need separate flags.
Return a Laurent monomial's sign and natural-log magnitude.
When to use this tool
Use Monomial Log Magnitude At Point when checking the stated exponent-vector, support, coefficient or Laurent convention.
How to use the tool and how it works
- Enter bases, exponents, coefficient. Follow any array-alignment requirements below. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read logMagnitude, sign. Use the output convention below.
Return a Laurent monomial's sign and natural-log magnitude. Require nonzero coefficient/bases and aligned signed whole exponents; logMagnitude = ln(abs(coefficient))+sum(exponent*ln(abs(base))), sign follows negative-base odd powers.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| bases | Bases | Required. Array of finite number; maximum items 256. |
| exponents | Exponents | Required. Array of safe integer; maximum items 256. |
| coefficient | Coefficient | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| logMagnitude | Natural logarithm of absolute monomial value; bases and coefficient must be nonzero even when an exponent is zero. | Required. Finite number. |
| sign | Sign | Required. Safe integer. |
{
"input": {
"bases": [
-2,
3
],
"exponents": [
3,
2
],
"coefficient": -1
},
"output": {
"logMagnitude": 4.276666119016054,
"sign": 1
}
}Limitations and assumptions
- This avoids direct product magnitude but does not produce the value; zero bases are rejected even at exponent zero and variable domains must be appropriate.
- 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
Use the complete coefficient domain and variable assumptions for symbolic simplification, full monomial divisibility or algebraic-domain conclusions.
References
Similar or alternative tools
- Monomial Negative Exponent Denominator Label
Format a Laurent variable part as numerator/denominator labels.
- Laurent Monomial Inversion Order
Return a Laurent order under variable inversion.