Libraries

A collection of libraries written in order to facilitate mathematical computations.

frontals.lib (Singular)

Compute invariants of frontal hypersurfaces. Download it here!

Note: Requires presmatrix.lib.

Procedures

invariants(map f)

• Number of swallowtails, cuspidal double points, triple points and folded Whitney umbrellas in the frontal disentanglement of f.
• Cuspidal edge and double point sets of f, along with their Milnor numbers.
• Frontal Milnor number of f.

is_frontal(map f)

• Check if f is frontal, using a procedure by G. Ishikawa.

wfinvariants(poly g, z)

• Number of swallowtails, cuspidal double points and triple points in the discriminant of the map G(x,y,z)=(x, y, g(x,y,z)), using a Theorem by W.L. Marar, J. Montaldi and M.A.S. Ruas.

You can use cURL to download these libraries! Simply type curl <link> --output <libname> on your terminal of choice.