Description
Return exponent increments from one monomial to a variable-part LCM.
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 exponent increments from one monomial to a variable-part LCM.
When to use this tool
Use Monomial Lcm Exponent Gap when checking the stated exponent-vector, support, coefficient or Laurent convention.
How to use the tool and how it works
- Enter supplied, other. 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 gap. Use the output convention below.
Return exponent increments from one monomial to a variable-part LCM. Require aligned nonnegative whole vectors; gap[i] = max(supplied[i],other[i])-supplied[i].1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| supplied | Supplied | Required. Array of safe integer; maximum items 256. |
| other | Other | Required. Array of safe integer; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| gap | Gap | Required. Array of safe integer; maximum items 256. |
{
"input": {
"supplied": [
2,
1
],
"other": [
1,
4
]
},
"output": {
"gap": [
0,
3
]
}
}Limitations and assumptions
- The gap describes variable powers only, without coefficient factors, variable identity or a complete polynomial LCM.
- 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 the complete coefficient domain and variable assumptions for symbolic simplification, full monomial divisibility or algebraic-domain conclusions.
References
Similar or alternative tools
- Algebra: Monomial Lcm Exponent Vector
Return variable-part monomial LCM exponents.
- Algebra: Monomial Gcd Exponent Vector
Return variable-part monomial GCD exponents.