def DiscriminantSurfaceP3_init():
global __magma_DiscriminantSurfaceP3_init__
if not __magma_DiscriminantSurfaceP3_init__:
magma.eval("""
R4<sage0, sage1, sage2, sage3> := PolynomialRing(IntegerRing(), 4);
DiscriminantSurfaceP3 := function(f)
P<x, y, z, w> := PolynomialRing(IntegerRing(), 4);
D := 1;
for j := 1 to 4 do
B := ideal<P | [ Derivative(P!f, i) : i in [1..4] ] cat [P.j - 1]>;
G := GroebnerBasis(B);
D := LCM(G[#G],D);
end for;
return D;
end function;
""")
__magma_DiscriminantSurfaceP3_init__ = True
def assert_if_magma(self, expected, magma_code, mode='equal'):
"""Helper method for running test_download_magma test. Checks
equality only if magma is installed; if it isn't, then the test
passes."""
from sage.all import magma
try:
if mode == 'equal':
assert expected == magma.eval(magma_code)
elif mode == 'in':
assert expected in magma.eval(magma_code)
else:
raise ValueError("mode must be either 'equal' or 'in")
except RuntimeError as the_error:
if str(the_error).startswith("unable to start magma"):
pass
else:
raise
def test_download_magma(self):
L = self.tc.get(
'/ModularForm/GL2/TotallyReal/4.4.725.1/holomorphic/4.4.725.1-31.1-a/download/magma'
)
assert 'NN := ideal<ZF | {31, 31, w^3 - 4*w + 1}>;' in L.data
assert '[89, 89, 3*w^3 - 2*w^2 - 7*w],' in L.data
assert 'heckeEigenvaluesArray := [4, -4,' in L.data
page = self.tc.get(
'ModularForm/GL2/TotallyReal/3.3.837.1/holomorphic/3.3.837.1-48.3-z/download/magma'
)
assert 'No such form' in page.data
# These tests take too long to use magma_free, so we run magma when it is installed
from sage.all import magma
import sys
for field, label, expected in [
[
'2.2.28.1', '2.2.28.1-531.1-m',
'heckeEigenvaluesArray := [e, -1, -1, e^7 - 1/2*e^6 - 10*e^5 + 11/2*e^4 + 27*e^3 - 15*e^2 - 15*e + 4'
],
[
'3.3.837.1', '3.3.837.1-2.1-b',
'heckeEigenvaluesArray := [1, e, e^2 - e - 7, -e^2 + 6, -e + 2, 2*e + 2, -e^2 + 2*e + 8, 2*e^2 - 4*e - 16'
],
[
'4.4.725.1', '4.4.725.1-31.1-a',
'heckeEigenvaluesArray := [4, -4, -7, -4, 4, 2, -2, -1, -8, 2, 10'
]
]:
sys.stdout.write("{}...".format(label))
sys.stdout.flush()
page = self.tc.get(
'/ModularForm/GL2/TotallyReal/{}/holomorphic/{}/download/magma'
.format(field, label))
assert expected in page.data
assert 'make_newform' in page.data
try:
magma_code = page.data + '\n'
magma_code += 'f, iso := Explode(make_newform());\n'
magma_code += 'assert(&and([iso(heckeEigenvalues[P]) eq HeckeEigenvalue(f,P): P in primes[1..10]]));\n'
magma_code += 'f;\n'
assert 'success' in magma.eval(magma_code)
except RuntimeError:
pass
def DiscriminantSurfaceP3(F):
"""
INPUT:
- ``F`` -- a polynomial in 4 variables
OUTPUT:
an integer D such that F mod p is smooth <=> p \ndivides D
EXAMPLES:
sage: R4.<x,y,z,w> = ZZ[];
sage: F = x^4 - 3*x^2*y^2 - 3*x^2*z^2 - 3*x^2*w^2 - 2*x*y*z*w + y^4 - 3*y^2*z^2 - 3*y^2*w^2 + z^4 - 3*z^2*w^2 + w^4;
sage: DiscriminantSurfaceP3(F)
188160
"""
assert len(F.variables()) == 4
assert F.base_ring() == ZZ
DiscriminantSurfaceP3_init()
x, y, z, w = var('sage0 sage1 sage2 sage3')
D = ZZ(magma.eval("DiscriminantSurfaceP3(%s);" % F(x, y, z, w)))
return D
def test_download_magma(self):
# A dimension 1 example
L = self.tc.get(
'/ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/88.5/a/download/magma'
).get_data(as_text=True)
assert 'NN := ideal<ZF | {44, 2*a + 30}>;' in L
assert '[263,a+123],' in L
page = self.tc.get(
'ModularForm/GL2/ImaginaryQuadratic/159.0.7.1/30.5/a/download/magma'
).get_data(as_text=True)
assert 'Bianchi newform not found' in page
# These tests take too long to use magma_free, so we run magma when it is installed
from sage.all import magma
import sys
for label, expected in [[
'2.0.4.1/100.2/a', 'ALEigenvalues[ideal<ZF | {i + 1}>] := -1;'
], ['2.0.11.1/933.1/a', 'ideal<ZF | {a + 30, 933}>;']]:
sys.stdout.write("{}...".format(label))
sys.stdout.flush()
page = self.tc.get(
'/ModularForm/GL2/ImaginaryQuadratic/{}/download/magma'.format(
label)).get_data(as_text=True)
assert expected in page
assert 'make_newform' in page
magma_code = page + '\n'
magma_code += 'f, iso := Explode(make_newform());\n'
magma_code += 'for P in primes[1..15] do;\n if Valuation(NN,P) eq 0 then;\n assert iso(heckeEigenvalues[P]) eq HeckeEigenvalue(f,P);\n end if;\nend for;\n'
magma_code += 'f;\n'
try:
assert 'success' in magma.eval(magma_code)
except RuntimeError as the_error:
if str(the_error).startswith("unable to start magma"):
pass
else:
raise
def has_magma():
try:
magma.eval('2')
return True
except (TypeError, RuntimeError):
return False
def url_for_isogeny_class_label(label):
slabel = label.split(".")
return url_for(".by_url_isogeny_class_label",
cond=slabel[0],
alpha=slabel[1])
def class_from_curve_label(label):
return ".".join(label.split(".")[:2])
################################################################################
# Searching
################################################################################
try:
magma.eval('2')
has_magma = True
except (TypeError, RuntimeError):
has_magma = False
def genus2_lookup_equation(f):
if not has_magma:
return None
f.replace(" ", "")
# TODO allow other variables, if so, fix the error message accordingly
R = PolynomialRing(QQ, "x")
if ("x" in f and "," in f) or "],[" in f:
if "],[" in f:
e = f.split("],[")
f = [