Solving Cubic and Quartic Equations

René Thiemann 🌐

September 3, 2021

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.


We formalize Cardano's formula to solve a cubic equation $$ax^3 + bx^2 + cx + d = 0,$$ as well as Ferrari's formula to solve a quartic equation. We further turn both formulas into executable algorithms based on the algebraic number implementation in the AFP. To this end we also slightly extended this library, namely by making the minimal polynomial of an algebraic number executable, and by defining and implementing $n$-th roots of complex numbers.


BSD License


Session Cubic_Quartic_Equations