State and Prove fundamental theorem of algebra Pdf

We present a formalization of the Fundamental Theorem of Algebra in the Coq proof assistant, by lifting the proof from [Waerden 1949] to the up-to-date language of dependent type theory. We prove that this formalization is free of errors and unnecessary lemmas, and that it preserves all facts about the theorem proved in [Waerden], apart from those that rely on numerical computations.

 

The Fundamental Theorem of Algebra is one of the most important theorems in all of mathematics. Mathematicians regard this theorem as one of the greatest mathematical discoveries ever. Its importance lies in its ability to connect two seemingly unrelated branches of mathematics, algebra and geometry.

 

In the areas of algebra and number theory, a fundamental theorem is a result from which many other results follow. The name “fundamental theorem” may be misleading, however; even though these theorems are important, they are often not considered to be more fundamental than many other theorems (hence their name). Many important theorems in each of these two fields either were found to follow from some fundamental theorem or led to the discovery of such a theorem.