Rendering of f(z) = p(z) / q(z) for polynomial p, q:
the positive real axis is blue
the negative real axis is purple
the positive complex axis is green
the negative complex axis is red
The grid boxes toggle different coordinate overlays:
- Cartesian grid: Lines along the grid of all points with integer x or y coordinate (real or complex part).
- Abs grid: lines along the paths with integer absolute value
- Phase grid: lines along the paths whose phase (angle around the origin) are integer multiples of pi / 6 (one twelfth of a circle)
Edit modes:
- Singularities: drag the zeroes and poles (where the color lines all meet) to move them.
- Constant term: set the zero point by subtracting a constant from the rational polynomial.
- Numerator constant term: set the zero point by subtracting a constant from the numerator only.
- Pan: Drag the view around the complex plane.
Phase: Slide to rotate all colors mod 2 Pi
Zeroes / poles: Use the buttons to add and remove singularities
from the numerator and denominator (at most 8 of each)
Invert: Flip each zero to a pole and vice versa
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