Description
Check supplied monomial terms against one total degree.
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 supplied monomial terms against one total degree.
When to use this tool
Use Algebra: Monomial Homogeneous Degree Check when checking the stated exponent-vector, support, coefficient or Laurent convention.
How to use the tool and how it works
- Enter monomials, expectedDegree. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Check supplied monomial terms against one total degree. Require equal-width exponent rows with entries whole 0..1e6 and expectedDegree 0..1e6; termDegrees sums rows, homogeneous means every sum equals expected.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| monomials | Monomials | Required. Array of array of finite number. Implementation limit: 128 items. |
| expectedDegree | Expected Degree | Required. Safe integer. Calculation range: 0 through 1000000, inclusive. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the returned operation-specific members listed below. | Required. Object. |
| result.homogeneous | Whether every supplied variable-exponent vector has expectedDegree; an empty collection passes vacuously. | Calculated result member: boolean. |
| result.termDegrees | Term Degrees | Calculated result member: array. |
{
"input": {
"monomials": [
[
2,
0
],
[
1,
1
],
[
0,
2
]
],
"expectedDegree": 2
},
"output": {
"result": {
"homogeneous": true,
"termDegrees": [
2,
2,
2
]
}
}
}Limitations and assumptions
- An empty term collection passes vacuously; coefficients, cancellation and actual effective polynomial degree are not considered.
- Outputs are nested inside result. 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
- Algebra: Monomial Multi Degree Label
Format a monomial multidegree and variable labels.
- Algebra: Monomial Total Degree
Return total degree of a monomial variable part.