92 lines
2.9 KiB
Python
92 lines
2.9 KiB
Python
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#!/usr/bin/env sage
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proof.all(False) # faster
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from maxorders import p, orders
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from cformat import Ibz, Object, ObjectFormatter
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# Prime of same size than p for random ideal of fixed norm
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bitlength_p = int(p).bit_length()
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prime_cofactor = next_prime((2^(bitlength_p)))
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algobj = [Ibz(p)]
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objs = \
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[
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[
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# basis (columns)
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[
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Ibz(mat.denominator()),
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[[Ibz(v) for v in vs]
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for vs in mat.transpose()*mat.denominator()],
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],
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# sqrt(-q)
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[
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Ibz(mat.denominator()),
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[Ibz(c) for c in ii*mat.denominator()],
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],
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# sqrt(-p)
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[
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Ibz(1),
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[Ibz(c) for c in (0,0,1,0)]
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],
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q
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]
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for q,_,mat,ii,_,_ in orders
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]
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idlobjs = \
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[
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[
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# basis (columns)
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[
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Ibz(idl.denominator()),
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[[Ibz(v) for v in vs]
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for vs in idl.transpose()*idl.denominator()],
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],
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# norm
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Ibz(abs(idl.row_space(ZZ).intersection((ZZ^4).submodule([[1,0,0,0]])).basis()[0][0])),
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# left order
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'&MAXORD_O0',
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]
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for _,_,mat,_,idl,_ in orders
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]
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gammaobjs = \
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[
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[
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Ibz(gamma.denominator()),
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list(map(Ibz, gamma * gamma.denominator())),
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]
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for _,_,_,_,_,gamma in orders
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]
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objs = ObjectFormatter([
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Object('ibz_t', 'QUAT_prime_cofactor', Ibz(prime_cofactor)),
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Object('quat_alg_t', 'QUATALG_PINFTY', algobj),
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Object('quat_p_extremal_maximal_order_t[]', 'EXTREMAL_ORDERS', objs),
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Object('quat_left_ideal_t[]', 'CONNECTING_IDEALS', idlobjs), # ideal corresponding to an isogeny from E0 which acts as identity w.r.t. the basis_even
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Object('quat_alg_elem_t[]', 'CONJUGATING_ELEMENTS', gammaobjs), # elements γ such that each I has right order γ O₁ γ^-1
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])
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with open('include/quaternion_data.h','w') as hfile:
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with open('quaternion_data.c','w') as cfile:
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print(f'#include <quaternion.h>', file=hfile)
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print(f'#include <stddef.h>', file=cfile)
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print(f'#include <stdint.h>', file=cfile)
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print(f'#include <quaternion_data.h>', file=cfile)
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#FIXME this should eventually go away?
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print(f'#define MAXORD_O0 (EXTREMAL_ORDERS->order)', file=hfile)
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print(f'#define STANDARD_EXTREMAL_ORDER (EXTREMAL_ORDERS[0])', file=hfile)
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print(f'#define NUM_ALTERNATE_EXTREMAL_ORDERS {len(orders)-1}', file=hfile)
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print(f'#define ALTERNATE_EXTREMAL_ORDERS (EXTREMAL_ORDERS+1)', file=hfile)
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print(f'#define ALTERNATE_CONNECTING_IDEALS (CONNECTING_IDEALS+1)', file=hfile)
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print(f'#define ALTERNATE_CONJUGATING_ELEMENTS (CONJUGATING_ELEMENTS+1)', file=hfile)
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objs.header(file=hfile)
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objs.implementation(file=cfile)
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