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Fix bug with pari interface in classical_modular_polynomial #37094

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Merged
vbraun merged 2 commits into from
Jan 22, 2024
Merged

Fix bug with pari interface in classical_modular_polynomial #37094

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2c761b1
Fix bug in classical_modular_polynomial; PR #37094
drago-96 Jan 18, 2024
b372660
Update tests for efficiency and coverage
drago-96 Jan 19, 2024
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25 changes: 22 additions & 3 deletions src/sage/schemes/elliptic_curves/mod_poly.py
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Original file line number Diff line number Diff line change
Expand Up @@ -85,7 +85,24 @@ def classical_modular_polynomial(l, j=None):
sage: j = GF(q).random_element()
sage: l = random_prime(50)
sage: Y = polygen(parent(j), 'Y')
sage: classical_modular_polynomial(l,j) == classical_modular_polynomial(l)(j,Y)
sage: classical_modular_polynomial(l, j) == classical_modular_polynomial(l)(j, Y)
True
sage: p = 2^216 * 3^137 - 1
sage: F.<i> = GF((p,2), modulus=[1,0,1])
sage: l = random_prime(50)
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@fchapoton fchapoton Jan 18, 2024

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you could use the syntax GF((p,2),...) to avoid factoring.

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@drago-96 drago-96 Jan 19, 2024

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Thanks, I didn't know this constructor!

sage: j = F.random_element()
sage: Y = polygen(parent(j), 'Y')
sage: classical_modular_polynomial(l, j) == classical_modular_polynomial(l)(j, Y)
True
sage: E = EllipticCurve(F, [0, 6, 0, 1, 0])
sage: j = E.j_invariant()
sage: l = random_prime(50)
sage: classical_modular_polynomial(l, j) == classical_modular_polynomial(l)(j, Y)
True
sage: R.<Y> = QQ['Y']
sage: j = QQ(1/2)
sage: l = random_prime(50)
sage: classical_modular_polynomial(l, j) == classical_modular_polynomial(l)(j, Y)
True
"""
l = ZZ(l)
Expand Down Expand Up @@ -133,12 +150,14 @@ def classical_modular_polynomial(l, j=None):
# Now try to get the instantiated modular polynomial directly from PARI.
# This should be slightly more efficient (in particular regarding memory
# usage) than computing and evaluating the generic modular polynomial.
# This currently only works if we are over Z/nZ.
try:
pari_Phi = pari.polmodular(l, 0, j)
return R(pari_Phi)
except PariError:
pass
else:
return R(pari_Phi)
except TypeError:
return R(ZZ['Y'](pari_Phi))

# Nothing worked. Fall back to computing the generic modular polynomial
# and simply evaluating it.
Expand Down