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@fchapoton
fchapoton committed Nov 21, 2023
1 parent d13ad4b commit f70bfb2
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Showing 2 changed files with 25 additions and 27 deletions.
50 changes: 24 additions & 26 deletions src/sage/modular/modform_hecketriangle/abstract_ring.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -80,7 +80,7 @@ def __init__(self, group, base_ring, red_hom, n):
"""

# from graded_ring import canonical_parameters
# (group, base_ring, red_hom, n) = canonical_parameters(group, base_ring, red_hom, n)
# group, base_ring, red_hom, n = canonical_parameters(group, base_ring, red_hom, n)

# if not group.is_arithmetic() and base_ring.characteristic()>0:
# raise NotImplementedError
Expand Down Expand Up @@ -140,7 +140,7 @@ def _element_constructor_(self, el):
sage: from sage.modular.modform_hecketriangle.graded_ring import ModularFormsRing
sage: MR = ModularFormsRing()
sage: (x,y,z,d) = MR.pol_ring().gens()
sage: x,y,z,d = MR.pol_ring().gens()
sage: MR(x^3)
f_rho^3
Expand Down Expand Up @@ -494,7 +494,7 @@ def reduce_type(self, analytic_type=None, degree=None):
elif degree is None:
return FormsSpace(analytic_type, group=self.group(), base_ring=self.base_ring(), k=self.weight(), ep=self.ep())
else:
(weight, ep) = degree
weight, ep = degree
if self.is_homogeneous() and (weight != self.weight() or ep != self.ep()):
analytic_type = self._analytic_type.reduce_to([])
return FormsSpace(analytic_type, group=self.group(), base_ring=self.base_ring(), k=weight, ep=ep)
Expand Down Expand Up @@ -808,15 +808,14 @@ def _derivative_op(self):
sage: ModularFormsRing(n=infinity)._derivative_op()
-X*Y*dX + X*Z*dX + 1/2*Y*Z*dY + 1/4*Z^2*dZ - 1/2*X*dY - 1/4*X*dZ
"""
(X, Y, Z, dX, dY, dZ) = self.diff_alg().gens()
X, Y, Z, dX, dY, dZ = self.diff_alg().gens()

if self.hecke_n() == infinity:
return (X*Z-X*Y) * dX\
+ ZZ(1)/ZZ(2) * (Y*Z-X) * dY\
+ ZZ(1)/ZZ(4) * (Z**2-X) * dZ
return (X*Z-X*Y) * dX + ZZ(1) / 2 * (Y*Z-X) * dY \
+ ZZ(1) / 4 * (Z**2-X) * dZ

return 1/self._group.n() * (X*Z-Y) * dX\
+ ZZ(1)/ZZ(2) * (Y*Z-X**(self._group.n()-1)) * dY\
return 1/self._group.n() * (X*Z-Y) * dX \
+ ZZ(1) / 2 * (Y*Z-X**(self._group.n()-1)) * dY \
+ (self._group.n()-2) / (4*self._group.n()) * (Z**2-X**(self._group.n()-2)) * dZ

@cached_method
Expand All @@ -834,15 +833,14 @@ def _serre_derivative_op(self):
sage: ModularFormsRing(n=infinity)._serre_derivative_op()
-X*Y*dX - 1/4*Z^2*dZ - 1/2*X*dY - 1/4*X*dZ
"""
(X, Y, Z, dX, dY, dZ) = self.diff_alg().gens()
X, Y, Z, dX, dY, dZ = self.diff_alg().gens()

if self.hecke_n() == infinity:
return - X * Y * dX\
- ZZ(1)/ZZ(2) * X * dY\
- ZZ(1)/ZZ(4) * (Z**2+X) * dZ
return - X * Y * dX - ZZ(1) / 2 * X * dY \
- ZZ(1) / 4 * (Z**2+X) * dZ

return - 1/self._group.n() * Y*dX\
- ZZ(1)/ZZ(2) * X**(self._group.n()-1) * dY\
return - 1/self._group.n() * Y*dX \
- ZZ(1) / 2 * X**(self._group.n()-1) * dY \
- (self._group.n()-2) / (4*self._group.n()) * (Z**2+X**(self._group.n()-2)) * dZ

@cached_method
Expand Down Expand Up @@ -1091,7 +1089,7 @@ def J_inv(self):
sage: WeakModularForms().J_inv()
1/1728*q^-1 + 31/72 + 1823/16*q + 335840/27*q^2 + 16005555/32*q^3 + 11716352*q^4 + O(q^5)
"""
(x, y, z, d) = self._pol_ring.gens()
x, y, z, d = self._pol_ring.gens()

if self.hecke_n() == infinity:
return self.extend_type("weak", ring=True)(x/(x-y**2)).reduce()
Expand Down Expand Up @@ -1142,7 +1140,7 @@ def j_inv(self):
sage: WeakModularForms().j_inv()
q^-1 + 744 + 196884*q + 21493760*q^2 + 864299970*q^3 + 20245856256*q^4 + O(q^5)
"""
(x, y, z, d) = self._pol_ring.gens()
x, y, z, d = self._pol_ring.gens()

if self.hecke_n() == infinity:
return self.extend_type("weak", ring=True)(1/d*x/(x-y**2)).reduce()
Expand Down Expand Up @@ -1217,7 +1215,7 @@ def f_rho(self):
sage: ModularForms(k=4).f_rho()
1 + 240*q + 2160*q^2 + 6720*q^3 + 17520*q^4 + O(q^5)
"""
(x, y, z, d) = self._pol_ring.gens()
x, y, z, d = self._pol_ring.gens()

if self.hecke_n() == infinity:
return self.extend_type("holo", ring=True)(1).reduce()
Expand Down Expand Up @@ -1283,7 +1281,7 @@ def f_i(self):
sage: ModularForms(k=6).f_i()
1 - 504*q - 16632*q^2 - 122976*q^3 - 532728*q^4 + O(q^5)
"""
(x, y, z, d) = self._pol_ring.gens()
x, y, z, d = self._pol_ring.gens()

return self.extend_type("holo", ring=True)(y).reduce()

Expand Down Expand Up @@ -1352,7 +1350,7 @@ def f_inf(self):
sage: CuspForms(k=12).f_inf()
q - 24*q^2 + 252*q^3 - 1472*q^4 + O(q^5)
"""
(x, y, z, d) = self._pol_ring.gens()
x, y, z, d = self._pol_ring.gens()

if self.hecke_n() == infinity:
return self.extend_type("holo", ring=True)(d*(x-y**2)).reduce()
Expand Down Expand Up @@ -1428,7 +1426,7 @@ def G_inv(self):
...
ArithmeticError: G_inv doesn't exist for odd n(=9).
"""
(x, y, z, d) = self._pol_ring.gens()
x, y, z, d = self._pol_ring.gens()

if self.hecke_n() == infinity:
raise ArithmeticError("G_inv doesn't exist for n={} (it is not meromorphic at -1).".format(self._group.n()))
Expand Down Expand Up @@ -1503,7 +1501,7 @@ def g_inv(self):
if self.hecke_n() == infinity:
raise ArithmeticError("g_inv doesn't exist for n={} (it is not meromorphic at -1).".format(self._group.n()))
if ZZ(2).divides(self._group.n()):
(x, y, z, d) = self._pol_ring.gens()
x, y, z, d = self._pol_ring.gens()
return self.extend_type("weak", ring=True)(1/d*y*x**(self._group.n()/ZZ(2))/(x**self._group.n()-y**2)).reduce()
else:
raise ArithmeticError("g_inv doesn't exist for odd n(={}).".format(self._group.n()))
Expand Down Expand Up @@ -1575,7 +1573,7 @@ def E4(self):
sage: ModularForms(k=4).E4()
1 + 240*q + 2160*q^2 + 6720*q^3 + 17520*q^4 + O(q^5)
"""
(x, y, z, d) = self._pol_ring.gens()
x, y, z, d = self._pol_ring.gens()

if self.hecke_n() == infinity:
return self.extend_type("holo", ring=True)(x).reduce()
Expand Down Expand Up @@ -1640,7 +1638,7 @@ def E6(self):
sage: ModularForms(k=6).E6()
1 - 504*q - 16632*q^2 - 122976*q^3 - 532728*q^4 + O(q^5)
"""
(x, y, z, d) = self._pol_ring.gens()
x, y, z, d = self._pol_ring.gens()

if self.hecke_n() == infinity:
return self.extend_type("holo", ring=True)(x*y).reduce()
Expand Down Expand Up @@ -1711,7 +1709,7 @@ def Delta(self):
sage: CuspForms(k=12).Delta()
q - 24*q^2 + 252*q^3 - 1472*q^4 + O(q^5)
"""
(x, y, z, d) = self._pol_ring.gens()
x, y, z, d = self._pol_ring.gens()

if self.hecke_n() == infinity:
return self.extend_type("cusp", ring=True)(d*x**2*(x-y**2)).reduce()
Expand Down Expand Up @@ -1780,7 +1778,7 @@ def E2(self):
sage: QuasiModularForms(k=2).E2()
1 - 24*q - 72*q^2 - 96*q^3 - 168*q^4 + O(q^5)
"""
(x, y, z, d) = self._pol_ring.gens()
x, y, z, d = self._pol_ring.gens()
return self.extend_type(["holo", "quasi"], ring=True)(z).reduce()

@cached_method
Expand Down
2 changes: 1 addition & 1 deletion src/sage/modular/modform_hecketriangle/graded_ring.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -56,7 +56,7 @@ def canonical_parameters(group, base_ring, red_hom, n=None):
return (group, base_ring, red_hom, n)


class QuasiMeromorphicModularFormsRing(FormsRing_abstract, Parent, UniqueRepresentation):
class QuasiMeromorphicModularFormsRing(FormsRing_abstract, UniqueRepresentation):
r"""
Graded ring of (Hecke) quasi meromorphic modular forms
for the given group and base ring.
Expand Down

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