32 lines
945 B
Python
32 lines
945 B
Python
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#!/usr/bin/env python3
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from sage.all import *
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proof.all(False) # faster
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import re
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for l in open('sqisign_parameters.txt'):
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for k in ('lvl', 'p', 'B'):
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m = re.search(rf'^\s*{k}\s*=\s*([x0-9a-f]+)', l)
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if m:
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v = ZZ(m.groups()[0], 0)
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globals()[k] = v
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L = {l for l,_ in (p**2 - 1).factor(limit=B+5) if l <= B}
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assert 2 in L
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L.remove(2)
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f = (p+1).valuation(2)
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if (p-1).valuation(2) > f:
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raise NotImplementedError('2-power torsion is on twist')
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Lpls = {l for l in L if (p+1).valuation(l) >= (p-1).valuation(l)}
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Lmin = L - Lpls
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Lpls, Lmin = map(sorted, (Lpls, Lmin))
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Epls = [(p+1).valuation(l) for l in Lpls]
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Emin = [(p-1).valuation(l) for l in Lmin]
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Tpls = prod(l**e for l,e in zip(Lpls,Epls))
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Tmin = prod(l**e for l,e in zip(Lmin,Emin))
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Dcom = (Tpls*Tmin).prime_to_m_part(2*3)
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Dchall = prod(l**(p+1).valuation(l) for l in (2,3))
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__all__ = ['lvl', 'p', 'B', 'f', 'Tpls', 'Tmin', 'Dcom', 'Dchall']
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