Weight -- the class of weights

Types of Weight:

• Root -- the class of roots (or, more generally, elements of the root lattice)

Methods that use an object of class Weight:

• - Weight -- the negative of a weight
• eval(RootSystem,Weight,Root) -- evaluate the dual of a root at a Weight
• eval(RootSystem,Weight,ZZ) -- evaluate the dual of a simple root at a Weight
• isPositiveRoot(RootSystem,Weight) -- check whether a weight is a positive root
• isRoot(RootSystem,Weight) -- check whether a weight is a positive root
• reflect(RootSystem,BasicList,Weight) -- apply to a weight several reflections with respect to roots
• reflect(RootSystem,ZZ,Weight) -- apply to a weight the reflection with respect to a root
• rootCoefficients(RootSystem,Weight) -- the coefficients at the simple roots
• scalarProduct(RootSystem,Weight,Weight) -- the scalar product of two weights
• scalarProduct(RootSystem,ZZ,Weight) -- the scalar product of a fundamental weight and a weight
• Weight + Weight -- the sum of two weights
• Weight - Weight -- the difference of two weights
• WeylGroupElement * Weight -- apply an element of a Weyl group to a weight
• ZZ * Weight -- the multiple of a weight

For the programmer

The object Weight is a type, with ancestor classes Vector < BasicList < Thing.

The source of this document is in /__w/M2/M2/macaulay2-1.26.05+ds/M2/Macaulay2/packages/WeylGroups.m2:1871:0.