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use lazy series for Siegel dimensions #6384

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fchapoton wants to merge 6 commits into from
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use lazy series for Siegel dimensions #6384

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8c53177
use lazy series for Siegel dimensions
fchapoton Jun 9, 2025
3fac972
fix mistake
fchapoton Jun 9, 2025
c4158cc
same in another file
fchapoton Jun 9, 2025
ff5f554
really use lazy ring
fchapoton Jun 9, 2025
b6aeb31
try to use more lazy rings
fchapoton Jun 9, 2025
1ea1b88
re-separate num and denom
fchapoton Jun 9, 2025
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33 changes: 13 additions & 20 deletions lmfdb/siegel_modular_forms/dimensions.py
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Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@
#
# Author: Nils Skoruppa <nils.skoruppa@gmail.com>

from sage.all import ZZ, QQ, FunctionField, PowerSeriesRing
from sage.all import (ZZ, PolynomialRing, LazyPowerSeriesRing)

from lmfdb.utils import flash_error
from lmfdb import db
Expand Down Expand Up @@ -162,8 +162,7 @@ def _dimension_Sp4Z(wt_range):
"""
headers = ['Total', 'Eisenstein', 'Klingen', 'Maass', 'Interesting']

R = PowerSeriesRing(ZZ, default_prec=wt_range[-1] + 1, names=('x',))
(x,) = R._first_ngens(1)
x = LazyPowerSeriesRing(ZZ, 'x').gen()
H_all = 1 / (1 - x ** 4) / (1 - x ** 6) / (1 - x ** 10) / (1 - x ** 12)
H_Kl = x ** 12 / (1 - x ** 4) / (1 - x ** 6)
H_MS = (x ** 10 + x ** 12) / (1 - x ** 4) / (1 - x ** 6)
Expand Down Expand Up @@ -228,8 +227,8 @@ def _dimension_Gamma_2(wt_range, j, group='Gamma(2)'):
if not db_cusp:
raise NotImplementedError(r'Dimensions of \(M_{k,j}\) for \(j=%d\) not implemented' % j)

P = PowerSeriesRing(ZZ, default_prec=wt_range[-1] + 1, names=('t'))
Qt = FunctionField(QQ, names=('t'))
P = LazyPowerSeriesRing(ZZ, 't')
Qt = PolynomialRing(ZZ, 't').fraction_field()
total = {}
cusp = {}
for p in partitions:
Expand Down Expand Up @@ -317,12 +316,11 @@ def __dimension_Sp6Z(wt):
"""
if wt % 2:
return (0, 0, 0, 0)
R = PowerSeriesRing(ZZ, default_prec=wt + 1, names=('x',))
(x,) = R._first_ngens(1)
S = PowerSeriesRing(ZZ, default_prec=max(2 * wt - 1, 1), names=('y',))
(y,) = S._first_ngens(1)
x = LazyPowerSeriesRing(ZZ, 'x').gen()
y = LazyPowerSeriesRing(ZZ, 'y').gen()

H_all = 1 / ((1 - x ** 4) * (1 - x ** 12) ** 2 * (1 - x ** 14) * (1 - x ** 18) *
(1 - x ** 20) * (1 - x ** 30)) * (
(1 - x ** 20) * (1 - x ** 30)) * (
1 + x ** 6 + x ** 10 + x ** 12 + 3 * x ** 16 + 2 * x ** 18 + 2 * x ** 20
+ 5 * x ** 22 + 4 * x ** 24 + 5 * x ** 26 + 7 * x ** 28 + 6 * x ** 30 + 9 * x ** 32
+ 10 * x ** 34 + 10 * x ** 36 + 12 * x ** 38 + 14 * x ** 40 + 15 * x ** 42 + 16 * x ** 44
Expand Down Expand Up @@ -440,8 +438,7 @@ def _dimension_Gamma0_4_half(k):
"""
if k < 1:
raise ValueError("$k$ must be a positive integer")
R = PowerSeriesRing(ZZ, default_prec=k, names=('x',))
(x,) = R._first_ngens(1)
x = LazyPowerSeriesRing(ZZ, 'x').gen()
H_all = 1 / (1 - x) / (1 - x ** 2) ** 2 / (1 - x ** 3)
H_cusp = (2 * x ** 5 + x ** 7 + x ** 9 - 2 * x ** 11 + 4 * x ** 6 - x ** 8 + x ** 10 - 3
* x ** 12 + x ** 14) / (1 - x ** 2) ** 2 / (1 - x ** 6)
Expand Down Expand Up @@ -478,8 +475,7 @@ def _dimension_Gamma0_3_psi_3(wt):

Not completely implemented
"""
R = PowerSeriesRing(ZZ, default_prec=wt + 1, names=('x',))
(x,) = R._first_ngens(1)
x = LazyPowerSeriesRing(ZZ, 'x').gen()
B = 1 / (1 - x ** 1) / (1 - x ** 3) / (1 - x ** 4) / (1 - x ** 3)
H_all_odd = B
H_all_even = B * x ** 14
Expand Down Expand Up @@ -523,8 +519,7 @@ def _dimension_Gamma0_4_psi_4(wt):

The formula for odd weights is unknown or not obvious from the paper.
"""
R = PowerSeriesRing(ZZ, default_prec=wt + 1, names=('x',))
(x,) = R._first_ngens(1)
x = LazyPowerSeriesRing(ZZ, 'x').gen()
H_all_even = (x ** 12 + x ** 14) / (1 - x ** 2) ** 3 / (1 - x ** 6)
if not wt % 2:
return (H_all_even[wt],)
Expand Down Expand Up @@ -559,8 +554,7 @@ def _dimension_Gamma0_4(wt):

Not completely implemented
"""
R = PowerSeriesRing(ZZ, 'x')
x = R.gen().O(wt + 1)
x = LazyPowerSeriesRing(ZZ, 'x').gen()
H_all = (1 + x**4) * (1 + x**11) / (1 - x**2)**3 / (1 - x**6)
return (H_all[wt],)

Expand Down Expand Up @@ -593,8 +587,7 @@ def _dimension_Gamma0_3(wt):

Only total dimension implemented.
"""
R = PowerSeriesRing(ZZ, 'x')
x = R.gen().O(wt + 1)
x = LazyPowerSeriesRing(ZZ, 'x').gen()
H_all = (1 + 2 * x**4 + x**6 + x**15 * (1 + 2 * x**2 + x**6)) / (1 - x**2) / (1 - x**4) / (1 - x**6)**2
return (H_all[wt],)

Expand Down
33 changes: 12 additions & 21 deletions lmfdb/siegel_modular_forms/siegel_core.py
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,8 @@
#
# Author: Nils Skoruppa <nils.skoruppa@gmail.com>

from sage.all import QQ, ZZ, PowerSeriesRing, is_even, is_prime
from sage.all import (QQ, ZZ, is_even, is_prime,
LazyPowerSeriesRing)
from lmfdb.utils import integer_divisors

tbi = 't.b.i.'
Expand All @@ -18,8 +19,7 @@ def _dimension_Sp4Z(wt):
OUTPUT
("Total", "Eisenstein", "Klingen", "Maass", "Interesting")
"""
R = PowerSeriesRing(ZZ, default_prec=wt + 1, names=('x',))
(x,) = R._first_ngens(1)
x = LazyPowerSeriesRing(ZZ, 'x').gen()
H_all = 1 / (1 - x ** 4) / (1 - x ** 6) / (1 - x ** 10) / (1 - x ** 12)
H_Kl = x ** 12 / (1 - x ** 4) / (1 - x ** 6)
H_MS = (x ** 10 + x ** 12) / (1 - x ** 4) / (1 - x ** 6)
Expand All @@ -44,8 +44,7 @@ def _dimension_Sp4Z_2(wt):
"""
if not is_even(wt):
return (uk, uk, uk)
R = PowerSeriesRing(ZZ, default_prec=wt + 1, names=('x',))
(x,) = R._first_ngens(1)
x = LazyPowerSeriesRing(ZZ, 'x').gen()
H = 1 / (1 - x ** 4) / (1 - x ** 6) / (1 - x ** 10) / (1 - x ** 12)
V = 1 / (1 - x ** 6) / (1 - x ** 10) / (1 - x ** 12)
# W = 1 / (1 - x ** 10) / (1 - x ** 12)
Expand All @@ -63,10 +62,8 @@ def _dimension_Sp6Z(wt):
"""
if not is_even(wt):
return (0, 0, 0, 0)
R = PowerSeriesRing(ZZ, default_prec=wt + 1, names=('x',))
(x,) = R._first_ngens(1)
R = PowerSeriesRing(ZZ, default_prec=2 * wt - 1, names=('y',))
(y,) = R._first_ngens(1)
x = LazyPowerSeriesRing(ZZ, 'x').gen()
y = LazyPowerSeriesRing(ZZ, 'y').gen()
H_all = 1 / ((1 - x ** 4) * (1 - x ** 12) ** 2 * (1 - x ** 14) * (1 - x ** 18) *
(1 - x ** 20) * (1 - x ** 30)) * (
1 + x ** 6 + x ** 10 + x ** 12 + 3 * x ** 16 + 2 * x ** 18 + 2 * x ** 20
Expand Down Expand Up @@ -179,8 +176,7 @@ def _dimension_Gamma0_2(wt):
REMARK
Only total dimension implemented.
"""
R = PowerSeriesRing(ZZ, default_prec=wt + 1, names=('x',))
(x,) = R._first_ngens(1)
x = LazyPowerSeriesRing(ZZ, 'x').gen()
H_all = 1 / (1 - x ** 2) / (1 - x ** 4) / (1 - x ** 4) / (1 - x ** 6)
# H_cusp = ??
# H_Kl = ??
Expand All @@ -203,8 +199,7 @@ def _dimension_Gamma0_3(wt):
REMARK
Only total dimension implemented.
"""
R = PowerSeriesRing(ZZ, default_prec=wt + 1, names=('x',))
(x,) = R._first_ngens(1)
x = LazyPowerSeriesRing(ZZ, 'x').gen()
H_all = (1 + 2 * x ** 4 + x ** 6 + x ** 15 * (1 + 2 * x ** 2 + x ** 6)) / (1 - x ** 2) / (1
- x ** 4) / (1 - x ** 6) ** 2
# H_cusp = ??
Expand All @@ -229,8 +224,7 @@ def _dimension_Gamma0_3_psi_3(wt):
REMARK
Not completely implemented
"""
R = PowerSeriesRing(ZZ, default_prec=wt + 1, names=('x',))
(x,) = R._first_ngens(1)
x = LazyPowerSeriesRing(ZZ, 'x').gen()
B = 1 / (1 - x ** 1) / (1 - x ** 3) / (1 - x ** 4) / (1 - x ** 3)
H_all_odd = B
H_all_even = B * x ** 14
Expand All @@ -255,8 +249,7 @@ def _dimension_Gamma0_4(wt):
REMARK
Not completely implemented
"""
R = PowerSeriesRing(ZZ, default_prec=wt + 1, names=('x',))
(x,) = R._first_ngens(1)
x = LazyPowerSeriesRing(ZZ, 'x').gen()
H_all = (1 + x ** 4)(1 + x ** 11) / (1 - x ** 2) ** 3 / (1 - x ** 6)
# H_cusp = ??
# H_Kl = ??
Expand All @@ -280,8 +273,7 @@ def _dimension_Gamma0_4_psi_4(wt):
REMARK
The formula for odd weights is unknown or not obvious from the paper.
"""
R = PowerSeriesRing(ZZ, default_prec=wt + 1, names=('x',))
(x,) = R._first_ngens(1)
x = LazyPowerSeriesRing(ZZ, 'x').gen()
H_all_even = (x ** 12 + x ** 14) / (1 - x ** 2) ** 3 / (1 - x ** 6)
# H_cusp = ??
# H_Kl = ??
Expand All @@ -308,8 +300,7 @@ def _dimension_Gamma0_4_half(k):
Note that formula from Hayashida's and Ibukiyama's paper has formula
that coefficient of x^w is for weight (w+1/2). So here w=k-1.
"""
R = PowerSeriesRing(ZZ, default_prec=k, names=('x',))
(x,) = R._first_ngens(1)
x = LazyPowerSeriesRing(ZZ, 'x').gen()
H_all = 1 / (1 - x) / (1 - x ** 2) ** 2 / (1 - x ** 3)
H_cusp = (2 * x ** 5 + x ** 7 + x ** 9 - 2 * x ** 11 + 4 * x ** 6 - x ** 8 + x ** 10 - 3
* x ** 12 + x ** 14) / (1 - x ** 2) ** 2 / (1 - x ** 6)
Expand Down
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