- Introduction
- Constructing Root Systems
- Operators on Root Systems
- Properties of Root Systems
- Roots and Coroots
- Accessing Roots and Coroots
- Reflections
- Operations and Properties for Roots and Coroot Indices
- Sum(R, r, s) : RootSys, RngIntElt, RngIntElt -> RngIntElt
- IsPositive(R, r) : RootSys, RngIntElt -> BoolElt
- IsNegative(R, r) : RootSys, RngIntElt -> BoolElt
- Negative(R, r) : RootSys, RngIntElt -> RngIntElt
- Example RootSys_RootArithmetic (H103E13)
- RootHeight(R, r) : RootSys, RngIntElt -> RngIntElt
- RootNorms(R) : RootSys -> [RngIntElt]
- RootNorm(R, r) : RootSys, RngIntElt -> RngIntElt
- IsLongRoot(R, r) : RootSys, RngIntElt -> BoolElt
- IsShortRoot(R, r) : RootSys, RngIntElt -> BoolElt
- IsIndivisibleRoot(R, r) : RootSys, RngIntElt -> BoolElt
- LeftString(R, r, s) : RootSys, RngIntElt, RngIntElt -> RngIntElt
- RightString(R, r, s) : RootSys, RngIntElt, RngIntElt -> RngIntElt
- LeftStringLength(R, r, s) : RootSys, RngIntElt, RngIntElt -> RngIntElt
- RightStringLength(R, r, s) : RootSys, RngIntElt, RngIntElt -> RngIntElt
- Example RootSys_RootOperations (H103E14)
- AdditiveOrder(R) : RootSys -> SeqEnum
- IsAdditiveOrder(R, Q) : RootSys, [RngIntElt] -> BoolElt
- Example RootSys_AdditiveOrder (H103E15)
- Building Root Systems
- Related Structures
- Bibliography
V2.28, 13 July 2023