def build_B(cls, n, k=1, **kw):
roots = []
lookup = {}
# long roots
for i in range(n):
for j in range(i + 1, n):
for a in [-1, 1]:
for b in [-1, 1]:
root = [0] * n
root[i] = a
root[j] = b
root = tuple(root)
lookup[root] = len(roots)
roots.append(root)
# short roots
for i in range(n):
for a in [-1, 1]:
root = [0] * n
root[i] = a * k
root = tuple(root)
lookup[root] = len(roots)
roots.append(root)
assert len(lookup) == len(roots)
assert len(roots) == 2 * n**2
gen = []
for i in range(n - 1):
perm = []
for idx, root in enumerate(roots):
_root = list(root)
_root[i], _root[i +
1] = _root[i +
1], _root[i] # swap i, i+1 coords
jdx = lookup[tuple(_root)]
perm.append(jdx)
perm = Perm(perm, roots)
gen.append(perm)
perm = []
for idx, root in enumerate(roots):
_root = list(root)
_root[n - 1] = -_root[n - 1]
jdx = lookup[tuple(_root)]
perm.append(jdx)
perm = Perm(perm, roots)
gen.append(perm)
return Weyl_B(roots, gen, name="B_%d" % n, **kw)
def build_D(cls, n, **kw):
assert n >= 2
roots = []
lookup = {}
for i in range(n):
for j in range(i + 1, n):
for a in [-1, 1]:
for b in [-1, 1]:
root = [0] * n
root[i] = a
root[j] = b
root = tuple(root)
lookup[root] = len(roots)
roots.append(root)
assert len(lookup) == len(roots)
assert len(roots) == 2 * n * (n - 1)
gen = []
for i in range(n - 1):
perm = []
for idx, root in enumerate(roots):
_root = list(root)
_root[i], _root[i +
1] = _root[i +
1], _root[i] # swap i, i+1 coords
jdx = lookup[tuple(_root)]
perm.append(jdx)
perm = Perm(perm, roots)
gen.append(perm)
perm = []
for idx, root in enumerate(roots):
_root = list(root)
_root[n - 1], _root[n - 2] = -_root[n - 2], -_root[
n - 1] # swap & negate last two coords
jdx = lookup[tuple(_root)]
perm.append(jdx)
perm = Perm(perm, roots)
gen.append(perm)
return Weyl_D(roots, gen, name="D_%d" % n, **kw)