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@dwbump
dwbump committed Jun 16, 2020
1 parent aabbb24 commit 72c2c44
Showing 1 changed file with 12 additions and 108 deletions.
120 changes: 12 additions & 108 deletions src/sage/combinat/root_system/weyl_characters.py
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Expand Up @@ -2389,14 +2389,13 @@ def twists_matrix(self):
sage: B22=FusionRing('B2',2)
sage: B22.twists_matrix()
[ 0 0 0 0 0 0]
[ 0 2 0 0 0 0]
[ 0 0 4/5 0 0 0]
[ 0 0 0 6/5 0 0]
[ 0 0 0 0 1/2 0]
[ 0 0 0 0 0 3/2]
[ 0 4/5 0 0 0 0]
[ 0 0 1/2 0 0 0]
[ 0 0 0 2 0 0]
[ 0 0 0 0 3/2 0]
[ 0 0 0 0 0 6/5]
"""
return diagonal_matrix(self.basis()[x].twist() for x in self.get_order())
# return diagonal_matrix(obj.twist() for obj in self.ordered_basis())

def q_dims(self):
r"""
Expand All @@ -2409,78 +2408,10 @@ def q_dims(self):
[1, -zeta80^24 + zeta80^16 + 1]
sage: B22=FusionRing("B2",2)
sage: B22.q_dims()
[1, 1, 2, 2, -2*zeta40^12 + 2*zeta40^8 + 1, -2*zeta40^12 + 2*zeta40^8 + 1]
[1, 2, -2*zeta40^12 + 2*zeta40^8 + 1, 1, -2*zeta40^12 + 2*zeta40^8 + 1, 2]
"""
b = self.basis()
return [b[x].q_dimension() for x in self.get_order()]
# return [x.q_dimension() for x in self.ordered_basis()]

def ordered_basis(self):
"""
Returns a basis of simple objects ordered according to
[NaiRow2011]_. For type A level 1, the basis is ordered by the
fundamental weights. The order is described in [Fuchs1994]_.
"""
ct = self._cartan_type[0]
k = self._k
r = self.rank()
wts = self.fundamental_weights()
ord_basis = list()
#Order bases for dimension 2 algebras
if self.dimension() == 2:
ord_basis.append(self(wts[1]*0))
for wt in self.basis():
wt = wt.highest_weight()
if wt.inner_product(wt) > 0:
ord_basis.append(self(wt))
if ct == 'A' and k == 1:
ord_basis = [self(wts[1]*0)]
ord_basis += [self(wts[i+1]) for i in range(r)]
if ct == 'A' and k == 2:
#TODO: generalize to higher rank
if r == 1:
ord_basis = [self(wts[1]*0), self(wts[1]), self(wts[1]*2)]
if ct == 'B' and k == 2:
ord_basis = [self(wts[1]*0), self(2*wts[1])]
ord_basis += [self(wts[i]) for i in range(1, r)]
ord_basis += [self(2*wts[r]), self(wts[r]), self(wts[1]+wts[r])]
if ct == 'D' and k == 1:
if r % 2 == 0:
ord_basis = sorted(self.basis().values())
else:
temp = sorted(self.basis().values(), reverse=1)
ord_basis = [temp.pop()]
ord_basis.extend(temp)
if ct == 'D' and k == 2:
ord_basis = [self(wts[1]*0), self(2*wts[1]), self(2*wts[r-1]), self(2*wts[r])]
ord_basis += [self(wts[i]) for i in range(1, r-1)]
ord_basis += [self(wts[r-1] + wts[r]), self(wts[r-1]), self(wts[r])]
ord_basis += [self(wts[1] + wts[r-1]), self(wts[1] + wts[r])]
if ct == 'E' and k == 1:
if r == 6:
ord_basis = [self(wts[1]*0), self(wts[1]), self(wts[6])]
if ct == 'E' and k == 2:
if r == 8:
ord_basis = [self(wts[1]*0), self(wts[8]), self(wts[1])]
if not ord_basis:
raise ValueError("ordered basis not yet available for this FusionRing")
return ord_basis

def s_ij_legacy(self, elt_i, elt_j, fusion_mat_i=[]):
"""
Remove this soon
"""
dims = self.q_dims()
ord_basis = self.ordered_basis()
twists = [x.twist() for x in ord_basis]
rng = range(len(ord_basis))
j = ord_basis.index(elt_j)
fusion_matrix = fusion_mat_i if fusion_mat_i else elt_i.fusion_matrix()
q = self.q_field().gen()
l = self.fusion_l()
s_ij = sum(fusion_matrix[k,j]*q**(2*l*twists[k])*dims[k] for k in rng)
s_ij *= q**(-2*l*(elt_i.twist() + elt_j.twist()))
return s_ij

def s_ij(self, elt_i, elt_j):
"""
Expand All @@ -2493,20 +2424,18 @@ def s_ij(self, elt_i, elt_j):
EXAMPLES::
#TODO: update docstring using next iteration of ordered basis method
sage: G21=FusionRing("G2",1)
sage: b=G21.basis()
sage: [G21.s_ij(x,y) for x in b for y in b]
[1, -zeta60^14 + zeta60^6 + zeta60^4, -zeta60^14 + zeta60^6 + zeta60^4, -1]
"""
l = self.fusion_l()
K = self.q_field()
q = K.gen()
ijtwist = -2*l*(elt_i.twist() + elt_j.twist())
return sum(self(k).q_dimension()*q**(2*l*self(k).twist()+ijtwist) for k in (elt_i.dual()*elt_j).monomial_coefficients())


def s_matrix(self):
b = self.basis()
return matrix([[self.s_ij(b[x],b[y]) for x in self.get_order()] for y in self.get_order()])

def s_matrix_old(self):
r"""
Return the S-matrix of this FusionRing.
Expand All @@ -2526,13 +2455,8 @@ def s_matrix_old(self):
[ 1 -1 1 -1]
[ 1 -1 -1 1]
"""
ord_basis = self.ordered_basis()
rng = range(len(ord_basis))
S = matrix(self.q_field(), len(ord_basis))
for i in rng:
for j in rng:
S[i,j] = self.s_ij(ord_basis[i], ord_basis[j])
return S
b = self.basis()
return matrix([[self.s_ij(b[x],b[y]) for x in self.get_order()] for y in self.get_order()])

def fusion_labels(self, labels=None, key=str):
"""
Expand Down Expand Up @@ -2672,23 +2596,3 @@ def q_dimension(self):
expr = expr.substitute(q=q**2)/q**(expr.degree())
zet = self.parent().q_field().gen()
return expr.substitute(q=zet)

def fusion_matrix(self):
r"""
Return a matrix containing the object's fusion coefficients.
EXAMPLES::
sage: G21=FusionRing('G2',1)
sage: G21.basis()
Finite family {(0, 0, 0): G21(0,0), (1, 0, -1): G21(1,0)}
sage: G21(1,0).fusion_matrix()
[0 1]
[1 1]
"""
if not self.is_simple_object():
raise ValueError("fusion matrix is only available for simple objects of a FusionRing")
ord_basis = self.parent().ordered_basis()
wts = [x.highest_weight() for x in ord_basis]
rows = [[wt in (self*obj).monomial_coefficients() for wt in wts] for obj in ord_basis]
return matrix(rows)

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