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 = [
R(literal_eval(e[0][1:] + "]")),
R(literal_eval("[" + e[1][0:-1]))
]
else:
e = f.split(",")
f = [R(str(e[0][1:])), R(str(e[1][0:-1]))]
else:
f = R(str(f))
try:
C = magma.HyperellipticCurve(f)
g2 = magma.G2Invariants(C)
except TypeError:
return None
g2 = str([str(i) for i in g2]).replace(" ", "")
for r in db.g2c_curves.search({'g2_inv': g2}):
eqn = literal_eval(r['eqn'])
D = magma.HyperellipticCurve(R(eqn[0]), R(eqn[1]))
# there is recursive bug in sage
if str(magma.IsIsomorphic(C, D)) == 'true':
return r['label']
return None
def genus2_lookup_equation(input_str):
# retuns:
# label, C_str
# None, C_str when it couldn't find it in the DB
# "", input_str when it fails to parse
# 0, C_str when it fails to start magma
R = PolynomialRing(QQ, "x")
y = PolynomialRing(R, "y").gen()
def read_list_coeffs(elt):
if not elt:
return R(0)
else:
return R([int(c) for c in elt.split(",")])
if ZLLIST_RE.fullmatch(input_str):
input_str = input_str.strip('[').strip(']')
fg = [read_list_coeffs(elt) for elt in input_str.split('],[')]
elif ZLIST_RE.fullmatch(input_str):
input_str = input_str.strip('[').strip(']')
fg = [read_list_coeffs(input_str), R(0)]
else:
input_str = input_str.strip('[').strip(']')
fg = [R(list(coeff_to_poly(elt))) for elt in input_str.split(",")]
if len(fg) == 1:
fg.append(R(0))
C_str_latex = fr"\({latex(y**2 + y*fg[1])} = {latex(fg[0])}\)"
try:
C = magma.HyperellipticCurve(fg)
g2 = magma.G2Invariants(C)
except TypeError:
raise ValueError(f'{C_str_latex} invalid genus 2 curve')
g2 = str([str(i) for i in g2]).replace(" ", "")
for r in db.g2c_curves.search({"g2_inv": g2}):
eqn = literal_eval(r["eqn"])
fgD = [R(eqn[0]), R(eqn[1])]
D = magma.HyperellipticCurve(fgD)
# there is recursive bug in sage
if str(magma.IsIsomorphic(C, D)) == "true":
if fgD != fg:
flash_info(f"The requested genus 2 curve {C_str_latex} is isomorphic to the one below, but uses a different defining polynomial.")
return r["label"], ""
return None, C_str_latex
def mHyperellipticCurve(f, h):
return magma.HyperellipticCurve(magma(f), magma(h))