Rational Lemniscate Viewer

Visualize the lemniscate $| P (z) / Q (z) | = c$ and the critical values. Enter the numerator and denominator as coefficients or roots, then choose a level $c$ .

Parameters

Numerator coefficients

Numerator roots

Denominator coefficients

Denominator roots

Level c 1.00

z-plane : lemniscate

| r (z) | = c

w-plane : critical values and circle

| w | = c

Coefficients and roots can be real or complex (e.g. 1+2j, 1-3i). Zeros are shown in blue, poles in red, critical points in green. Critical values inside the circle $| w | = c$ are in purple, outside in orange.