The software chooses a basis of the lattice X^*(T). The "roots"
command prints out the list of all the positive roots for the group,
in this basis.
The software picks a basis of the character lattice X^*(T). If G is
defined using the "sc" (respectively "ad") option to be simply
connected (resp. adjoint) this basis is the basis of fundamental
weights (resp. simple roots), plus a copy of Z^n if G is not
semisimple. In general this basis may be fairly arbitrary, and the
information from the roots command is useful in understanding this
basis.
The "roots_rootbasis" command gives all roots in the basis of simple
roots. See also coroots, coroots_rootbasis, posroots,
posroots_rootbasis, poscoroots, poscoroots_rootbasis and rootdatum.
Example: all roots of Sp(4):
main: roots
Name an output file (return for stdout, ? to abandon):
[-2,0]
[0,-1]
[2,-2]
[-2,1]
[2,-1]
[-2,2]
[0,1]
[2,0]
main: roots_rootbasis
Name an output file (return for stdout, ? to abandon):
[-2,-1]
[-1,-1]
[0,-1]
[-1,0]
[1,0]
[0,1]
[1,1]
[2,1]