What is implemented?

Polynomials:
     Mathematica in Education and Research 6, n4, 27 (1997)
:
     Mathematica in Education and Research forthcoming (2000)
Special Functions:
     results partially published in the Wolfram Research Poster Series and notebooks from  
     www.specialfunctions.com and The Mathematica GuideBook (forthcoming)

When is a representation faithful?

• Polynomial case: Re or Im
• General case: more complicated

Implicitly defined functions that can't be solved for .

• (Lambert/ProductLog function)
• (Kepler equation, ε a numeric parameter)
• (eigenvalue equation of a square well)
• (eigenvalue equation delta function potential)
  ...
  
• Solve numerically transcendental equations in a region of

The special functions of mathematical physics.

• Again solving odes around branch points
• Use functional relations
• Problem for some functions: new branch points at nonprincipal sheets

Pictures of Riemann surfaces of special functions

Other visualization techniques

• Interactive cuts with projections through 4D --space
• Spheres with ears

Pictures of Riemann surfaces over the Riemann sphere

Animations

Animations of Riemann Surfaces with Movable Branch Points

Introduction | Construction Method | Implementation | Outlook |