Description
Compose supplied orientation signs.
Integration depends on the domain, orientation, coordinate change and endpoint behavior. A boundary contribution, Jacobian factor or power-tail test is a local part of an integral calculation; convergence, a valid change of variables and the complete integral require their own hypotheses.
Compose supplied orientation signs.
When to use this tool
Use Integral Orientation Composition Sign when evaluating the stated integral contribution, orientation, Jacobian or convergence condition.
How to use the tool and how it works
- Enter orientations. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read orientation, reversalCount. Use the output convention below.
Compose supplied orientation signs. Require each orientation +1 or -1; orientation is their product, reversalCount counts negative entries.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| orientations | Orientations | Required. Array of safe integer; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| orientation | Orientation | Required. Safe integer. |
| reversalCount | Reversal Count | Required. Safe integer. |
{
"input": {
"orientations": [
-1,
-1,
1
]
},
"output": {
"orientation": 1,
"reversalCount": 2
}
}Limitations and assumptions
- An empty list returns orientation +1; no actual coordinate substitution, path or integration map is verified.
- 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
Specify and analyze the complete integrand and domain, including endpoint singularities, coordinate invertibility and any omitted boundary or interior terms.
References
Similar or alternative tools
- Integral Subinterval Orientation
Apply endpoint orientation to a supplied ascending-order integral.
- Integral Moving Bound Normal Sign
Return moving-integral endpoint contributions.