Description
Check variable exponents for exact radical extraction.
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.
Check variable exponents for exact radical extraction.
When to use this tool
Use Monomial Radical Exponent Divisibility when checking the stated exponent-vector, support, coefficient or Laurent convention.
How to use the tool and how it works
- Enter exponents, degree. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read exact, rootExponents, remainders. Inspect exact before interpreting the associated values.
Check variable exponents for exact radical extraction. Require nonnegative whole exponents and degree 1..1e6; remainders = exponent mod degree, exact requires all zero, rootExponents returns floor quotients regardless.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| exponents | Exponents | Required. Array of safe integer; maximum items 256. |
| degree | Degree | Required. Safe integer; minimum 1; maximum 1000000. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| exact | Whether each variable exponent is divisible by degree; coefficient and real-root sign conditions are not checked. | Required. Boolean. |
| rootExponents | Integer quotients even when exact=false; inspect remainders. | Required. Array of safe integer; maximum items 256. |
| remainders | Remainders | Required. Array of safe integer; maximum items 256. |
{
"input": {
"exponents": [
4,
6
],
"degree": 2
},
"output": {
"exact": true,
"rootExponents": [
2,
3
],
"remainders": [
0,
0
]
}
}Limitations and assumptions
- When exact is false the floor vector alone is not the root; coefficients and real-domain sign restrictions are not checked.
- 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 Sign From Exponent Parities
Return sign of a product from bases and exponent parities.
- Monomial Power Composition Exponent Term
Return exponent vector after a supplied nonnegative power.