def test_create_psi():
x = psi(x=sg.vector(sg.ZZ, [5, 6, 7]), k=10, prec=20)
assert 1.2247830486256163744e-7 == pytest.approx(x, 1e-10)
x = psi(x=sg.vector(sg.ZZ, [5, 6, 7]), k=300, prec=20)
assert x == sg.Rational(0)
x = psi(x=[], k=200, prec=20)
assert x == sg.Rational(0)
def Psi_matrix(matrix, digits, cutoff=30, extrapolation = 100, prec=None):
# create explicitly the sets S for up to d digits.
S = create_S(matrix.values, digits=digits)
Psi = {k: S.applymap(partial(psi, k=k, prec=prec)) for k in range(1, cutoff)}
# append zero rows...
for k in Psi.keys():
Psi[k] = Psi[k].append(pd.DataFrame(columns=Psi[k].columns, data=sg.Rational(0),
index=list(range(digits, extrapolation)))).values
limit = 10 ** (prec * (-1))
# digits!!!
for i in range(digits, extrapolation):
for k in Psi.keys():
if Psi[k][i - 1, 0] > 0:
for index, www in np.ndenumerate(matrix):
if www > 0:
for w in range(extrapolation - k):
p = Psi[k+w][i-1,index[0]]
if p > limit:
a = a_coeff(k, w, index[1], prec=prec, base=matrix.shape[1])
Psi[k][i, www-1] += a * p
else:
if k+w==2:
print("********************************")
print(limit, i, p)
print("********************************")
break
return Psi
def psi(x, k, prec):
if len(x) == 0 or (x[0]**k) > 10**prec:
return sg.Rational(0.0)
x_power = x.apply_map(lambda y: y**k)
return sg.sum(
x_power.apply_map(lambda y: sg.numerical_approx(1 / y, digits=prec)))
def a_coeff(k, w, m, prec=None, base=10):
#print(k,w,m)
if m + w == 0:
mw = sg.Rational(1)
else:
mw = __power(m, w)
y = __power(1.0 / base, k + w) * mw * __power(-1, w) * __binomial(
k + w - 1, w)
if prec:
y = sg.numerical_approx(y, digits=prec)
return y
def experiment():
rank = 5
level = 4
num_points = 11
client = cbc.CBClient()
liealg = cbd.TypeALieAlgebra(rank, store_fusion=True, exact=True)
rays = []
wts = []
ranks = []
for wt in liealg.get_weights(level):
if wt == tuple([0 for x in range(0, rank)]):
continue
cbb = cbd.SymmetricConformalBlocksBundle(client, liealg, wt,
num_points, level)
if cbb.get_rank() == 0:
continue
divisor = cbb.get_symmetrized_divisor()
if divisor == [
sage.Rational(0) for x in range(0, num_points // 2 - 1)
]:
continue
rays = rays + [divisor]
wts = wts + [wt]
ranks = ranks + [cbb.get_rank()]
#print(wt, cbb.get_rank(), divisor)
p = Polyhedron(rays=rays, base_ring=RationalField(), backend="cdd")
extremal_rays = [list(v.vector()) for v in p.Vrepresentation()]
c = Cone(p)
print("Extremal rays:")
for i in range(0, len(rays)):
ray = rays[i]
wt = wts[i]
rk = ranks[i]
if ray in extremal_rays:
print(rk, wt, ray)
def Fraction(x, y):
try:
return sage.Rational((x, y))
except TypeError:
return x / y
def __power(a, b):
return sg.Rational(a)**b