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Macaulay2 web site
WeylGroups
::
Root
Root -- the class of roots (or, more generally, elements of the root lattice)
Description
a root is represented by the respective weight
Methods that use an object of class Root :
addRoots(RootSystem,Root,Root)
-- the sum of two roots
eval(RootSystem,Weight,Root)
-- evaluate the dual of a root at a Weight
eval(RootSystem,ZZ,Root)
-- evaluate the dual of a root at a fundamental weight
isRoot(RootSystem,Parabolic,Root)
-- check whether a root is in the sub root system of the parabolic
norm(RootSystem,Root)
-- the squared norm of a root
reflect(RootSystem,BasicList,Root)
-- apply to a root several reflections with respect to simple roots
reflect(RootSystem,ZZ,Root)
-- apply to a root the reflection with respect to a simple root
reflection(RootSystem,Root)
-- the reflection with respect to a root
rootCoefficients(RootSystem,Root)
-- the coefficients at the simple roots
WeylGroupElement * Root
-- apply an element of a Weyl group to a root
ZZ * Root
-- multiplication of a root by an integer
For the programmer
The object
Root
is
a
type
, with ancestor classes
Weight
<
Vector
<
BasicList
<
Thing
.