Description
Rescale one supplied polynomial coefficient for an argument substitution.
Polynomial transformations depend on the direction of variable substitution and the treatment of zero roots. Rescaling a coefficient for p(sy) multiplies it by s raised to its degree, while reciprocal roots require nonzero input. A local numeric map does not inspect or transform the full polynomial.
Rescale one supplied polynomial coefficient for an argument substitution.
When to use this tool
Use Polynomial Single Coefficient Unit Rescale when you already have coefficient, termDegree, argumentScale and need to rescale one supplied polynomial coefficient for an argument substitution.
How to use the tool and how it works
- Enter coefficient, termDegree, argumentScale. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read rescaledCoefficient. Use the output convention below.
Require termDegree a nonnegative safe whole number; return coefficient*argumentScale^termDegree.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coefficient | Coefficient | Required. Finite number. |
| termDegree | Term Degree | Required. Safe integer; minimum 0. |
| argumentScale | Scale in x=argumentScale*y, so the transformed polynomial is q(y)=p(argumentScale*y). | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| rescaledCoefficient | coefficient*argumentScale^termDegree; degree zero uses scale^0=1, including zero scale. | Required. Finite number. |
{
"input": {
"coefficient": 3,
"termDegree": 2,
"argumentScale": 2
},
"output": {
"rescaledCoefficient": 12
}
}Limitations and assumptions
- This corresponds to q(y)=p(argumentScale*y), so x=argumentScale*y. It is one coefficient rather than a full polynomial or inverse scale transform; degree zero uses scale^0=1, including zero scale.
- 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 polynomial and specified variable substitution for an algebraic conclusion. Check degrees, leading/trailing coefficients, root multiplicities and numerical conditioning when local coefficient or reciprocal-root terms are insufficient.
References
Similar or alternative tools
- Polynomial Root Reciprocal Map
Map a supplied nonzero real root to its reciprocal.