Examples
Examples
Try the starting example
- Numerator coefficients descending powers
- 1,2
- Denominator coefficients descending powers
- 1,4,3
- Cancellation-distance tolerance
- 1e-05
- Zeros [real,imaginary] JSON
- [[-2,0]]
- Poles [real,imaginary] JSON
- [[-3,0],[-1,0]]
- Near-cancellation [zero position,pole position,distance] JSON
- []
Try another scenario
- Numerator coefficients descending powers
- [2, 2]
- Denominator coefficients descending powers
- [1, 4, 3]
- Cancellation-distance tolerance
- 1e-05
- Zeros [real,imaginary] JSON
- [[-1,0]]
- Poles [real,imaginary] JSON
- [[-3,0],[-1,0]]
- Near-cancellation [zero position,pole position,distance] JSON
- [[1,2,0]]
Calculation method
Calculation method
Zeros [real,imaginary] JSON
Numerical polynomial roots, degrees ≤6; flag near pole-zero pairs without canceling them or claiming internal stability.
Poles [real,imaginary] JSON
Numerical polynomial roots, degrees ≤6; flag near pole-zero pairs without canceling them or claiming internal stability.
Near-cancellation [zero position,pole position,distance] JSON
Numerical polynomial roots, degrees ≤6; flag near pole-zero pairs without canceling them or claiming internal stability.
Symbols and units
- a
- Numerator coefficients descending powers
- b
- Denominator coefficients descending powers
- c
- Cancellation-distance tolerance
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- User-supplied measurements and assumptions; Numerical polynomial roots, degrees ≤6; flag near pole-zero pairs without canceling them or claiming internal stability. Supported limits: Finite numeric values bounded to 1e9 magnitude; lists and tables contain 1–100 records unless a stricter bound is stated. Inputs use the units shown. Lists explicitly paired by a method must have matching lengths; independent polynomial coefficient vectors may differ. Respect stated physical, interpolation, policy and computational domain limits. Polynomial degrees are bounded to 6. Higher-degree near-multiple roots with a small derivative relative to coefficient scale are rejected as ill-conditioned; nonconvergent root solves are rejected rather than presented as accurate.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
Background reading; this does not imply endorsement or independent review of SumFizz.