Mathlib Phrasebook

17.2. Properties of root systems and root data🔗

Mathlib contains API for numerous properties of root systems including:

  • Being reduced RootPairing.IsReduced

  • Being irreducible RootPairing.IsIrreducible

  • Being crystallographic RootPairing.IsCrystallographic

In addition the following concepts also all exist:

  • Morphisms RootPairing.Hom

  • Equivalences RootPairing.Equiv

  • The induced bilinear form RootPairing.RootForm

  • The Weyl group RootPairing.weylGroup

  • The concept of a base RootPairing.Base (aka a system of simple roots).