Description
Map a supplied nonzero real root to its reciprocal.
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.
Map a supplied nonzero real root to its reciprocal.
When to use this tool
Use Polynomial Root Reciprocal Map when you already have realRoot and need to map a supplied nonzero real root to its reciprocal.
How to use the tool and how it works
- Enter realRoot. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read reciprocalRoot. Use the output convention below.
Require realRoot!=0; return 1/realRoot.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| realRoot | Real Root | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| reciprocalRoot | Reciprocal Root | Required. Finite number. |
{
"input": {
"realRoot": 4
},
"output": {
"reciprocalRoot": 0.25
}
}Limitations and assumptions
- No polynomial, degree, leading/trailing coefficient or root multiplicity is inspected. This local map does not construct a reciprocal polynomial or verify a root; tiny roots can give rejected nonfinite reciprocals.
- 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 Single Coefficient Unit Rescale
Rescale one supplied polynomial coefficient for an argument substitution.