/usr/include/eclib/hilbert.h is in libec-dev 20160720-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 | // hilbert.h: declarations of Hilbert symbol functions
//////////////////////////////////////////////////////////////////////////
//
// Copyright 1990-2012 John Cremona
//
// This file is part of the eclib package.
//
// eclib is free software; you can redistribute it and/or modify it
// under the terms of the GNU General Public License as published by the
// Free Software Foundation; either version 2 of the License, or (at your
// option) any later version.
//
// eclib is distributed in the hope that it will be useful, but WITHOUT
// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
// for more details.
//
// You should have received a copy of the GNU General Public License
// along with eclib; if not, write to the Free Software Foundation,
// Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA
//
//////////////////////////////////////////////////////////////////////////
#ifndef _HILBERT_H
#define _HILBERT_H 1
//flags that this file has been included
// In all the functions below, the value of the Hilbert symbol is 0 or
// 1 (as an int) rather than +1 or -1, for efficiency;
inline int eps4(const bigint& u) // u must be odd; m1pow(eps4(u))=chi4(u)
{
return (u+1)%4==0; // so 1 mod 4 gives 0,
// 3 mod 4 gives 1
}
inline int omega8(const bigint& u) // u must be odd; m1pow(omega8(u))=chi2(u)
{
return ((u-3)%8==0)||((u+3)%8==0); // so 1,7 mod 8 give 0,
// 3,5 mod 8 give 1
}
// Use p=0 for the infinite prime
int local_hilbert(const bigint& a, const bigint& b, const bigint& p);
inline int local_hilbert(const bigint& a, const bigint& b, const long& p)
{
return local_hilbert(a,b,BIGINT(p));
}
// Returns 0 if soluble at all primes in list (or all dividing a*b, or
// all dividing disc(q)*d) and at infinity; otherwise returns 1 and
// puts the first insoluble prime into badp
int global_hilbert(const bigint& a, const bigint& b, const vector<bigint>& plist, bigint& badp);
int global_hilbert(const bigint& a, const bigint& b, bigint& badp);
int global_hilbert(const quadratic& q, const bigint& d, const vector<bigint>& plist, bigint& badp);
int global_hilbert(const quadratic& q, const bigint& d, bigint& badp);
#endif
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