Demonstrating Klein's icosahedral solution of the quintic equation
Switch branches/tags
Nothing to show
Clone or download
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Permalink
Failed to load latest commit information.
README.md
bring-jerrard_solution_demo.py
quintic_icosahedral_solution_demo.py

README.md

The icosahedral solution of the quintic in Python

Although the general quintic equation cannot be solved 'in radicals', it can be solved using some additional special functions associated to the icosahedron.

The scripts here implement the icosahedral solution for quintics that take the form:

  • y^5 + y + c = 0 in bring-jerrard_solution_demo.py
  • y^5 + 5ay^2 + 5by + c = 0 in quintic_icosahedral_solution_demo.py

Note that it is possible to reduce a general quintic equation to either of these forms and it requires solving only one auxiliary quadratic equation to reduce it to the latter form.

I waffled on about this in a bit more detail in the notes published here available for free at this link.