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Macaulay2 web site
WeylGroups
::
Weight
Weight -- the class of weights
Description
a weight is represented by an element of ZZ
n
, the basis consisting in the fundamental 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
For the programmer
The object
Weight
is
a
type
, with ancestor classes
Vector
<
BasicList
<
Thing
.