Description
Apply a three-index permutation's parity to a supplied scalar triple product.
A vector is an ordered set of components in a chosen basis. Its norm measures magnitude, while dot products, projections, and coordinate transformations describe different relationships. Component order, angle units, normalization, and numerical tolerances determine the meaning of a computed result.
Apply a three-index permutation's parity to a supplied scalar triple product.
When to use this tool
Use Vector Scalar Triple Permutation Sign when you need the particular coordinate operation, derivative, residual, or domain check under a known basis convention.
How to use the tool and how it works
- Enter tripleProduct, permutation. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read value, sign. Use the output convention below.
Require a permutation of integer indices zero, one, and two. Count inversions, set sign to one for even parity or minus one for odd, and return value=sign*tripleProduct.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| tripleProduct | Triple Product | Required. Finite number. |
| permutation | Permutation | Required. Array of Safe integer.; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| value | Value | Required. Finite number. |
| sign | Sign | Required. Safe integer. |
{
"input": {
"tripleProduct": 6,
"permutation": [
1,
0,
2
]
},
"output": {
"value": -6,
"sign": -1
}
}Limitations and assumptions
- The scalar triple product is supplied, not calculated from vectors. This changes its sign for the given ordering without validating the original product or inferring a basis.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- 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. Signed zero is exported as zero.
Alternative or Complementary methods
Choose a complete vector or matrix operation when a single component or residual is insufficient. For sensitive near-zero or near-singular cases, inspect numerical conditioning and use an appropriate precision and tolerance.
References
Similar or alternative tools
- Basis Vector Determinant Sign
Inspect floating-point orientation of a supplied 3D basis after row scaling; no exact-predicate guarantee.
- Vector 3d Coordinate Cyclic Permutation
Cyclically reorder three coordinates by an integer shift modulo three.