Revision #557 → #1246 · back to history
addedFundamental theorem of algebrad2e0a3d2ea61
addedAlgebraic closure of C (equivalent form)6c9605619761
addedCounting roots with multiplicity29e170d71f14
addedReal-coefficient FTA equivalent3ec35342819f
addedComplex-coefficient FTA equivalent8e028e893590
addedLinear factorization over Cac4b52d183af
addedMultiplicity of a root63df16d20516
addedReal quadratic factor existsfb3b4c6f8297
addedFactorization into linear and quadratic real factorscde5ee81142e
addedGrowth lemma for polynomials9cd8ee1cc56f
addedReal-analytic divisibility by quadraticbb5a756043ab
addedAxler's proof via De Moivre and EVT63d7aa86eca3
addedProof via maximum modulus principleee0533dbe59a
addedProof via Liouville's theorem81509ea9c105
addedProof via argument principle35ec3fbcdb0e
addedEquivalence with eigenvalue existence77749aa0928e
addedProof via Rouché's theorembf6b3ce74e30
addedTopological proof via minimum of |p|018ee2f4b735
addedTopological proof via winding number590551244965
addedAnalytic facts used in algebraic proofse171615e794a
addedReal-closed field extension is algebraically closeda0871dbebf54
addedAlgebraic proof by induction on 2-adic valuation614926f4d74e
addedShipman's improvement (prime degree suffices)bba12d196907
addedGalois-theoretic proof04be9b953191
addedFlat Riemannian surfacea1b1c38aa13f
addedGeometric proof via Gauss-Bonnetf98ff80dcd4a
addedC is the algebraic closure of Rf7234c8512e3
addedComplex linear factorization corollary05a505610efb
addedReal factorization into linear and irreducible quadratic factorsb5ca65fcbf52
addedPartial fraction decomposition over Rc474b79f83fa
addedElementary primitive of rational functions2cb2d305714d
addedAlgebraic extensions of Rc0d1fc43f550
addedA priori modulus bound on zeroseffb7a394b57
addedp-norm bound on zerosa5c9a6441320