/usr/include/eclib/mquartic.h is in libec-dev 20160101-1.
This file is owned by root:root, with mode 0o644.
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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 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 | // mquartic.h: Declaration of class quartic and related 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 _MQUARTIC_H
#define _MQUARTIC_H
#define NEW_EQUIV
#include "compproc.h"
#include "marith.h"
#include "bigrat.h"
#include "points.h"
#include "realroots.h"
inline bigint II(const bigint& a, const bigint& b, const bigint& c,
const bigint& d, const bigint& e)
{
return 12*a*e - 3*b*d + c*c;
}
inline bigint JJ(const bigint& a, const bigint& b, const bigint& c,
const bigint& d, const bigint& e)
{
return (72*a*e + 9*b*d - 2*sqr(c)) * c - 27*(a*sqr(d) + sqr(b)*e);
}
inline bigint H_invariant(const bigint& a, const bigint& b, const bigint& c)
{
return 8*a*c - 3*sqr(b);
}
inline bigint R_invariant(const bigint& a, const bigint& b, const bigint& c,
const bigint& d)
{
return pow(b,3) + 8*d*sqr(a) - 4*a*b*c;
}
class quartic {
public:
// constructors (NOT inline as they all use "new"
quartic();
quartic(const bigint& qa, const bigint& qb, const bigint& qc,
const bigint& qd, const bigint& qe,
bigcomplex* qr, int qt,
const bigint& qi,const bigint& qj,const bigint& qdisc);
quartic(const bigint& qa, const bigint& qb, const bigint& qc,
const bigint& qd, const bigint& qe);
// latter calls set_roots_and_type()
~quartic();
quartic(const quartic& q);
// member functions & operators
void set_roots_and_type();
void assign(const bigint& qa, const bigint& qb, const bigint& qc,
const bigint& qd, const bigint& qe,
bigcomplex *qr, int qt,
const bigint& qi,const bigint& qj,
const bigint& qdisc);
void assign(const bigint& qa, const bigint& qb, const bigint& qc,
const bigint& qd, const bigint& qe);
// latter calls set_roots_and_type()
void operator=(const quartic& q);
bigint geta() const {return a;}
bigint getb() const {return b;}
bigint getcc() const {return c;} //NB "getc" is a standard macro
bigint getd() const {return d;}
bigint gete() const {return e;}
void getcoeffs(bigint& xa, bigint& xb, bigint& xc, bigint& xd, bigint& xe) const {xa=a; xb=b; xc=c; xd=d; xe=e;}
int gettype() const {return type;}
bigint getI() const {return ii;}
bigint getJ() const {return jj;}
bigint getH() const {return H_invariant(a,b,c);}
bigint getdisc() const {return disc;}
bigcomplex* getroots(void) const {return roots;}
void doubleup()
{
b*=2; c*=4; d*=8; e*=16; ii*=16; jj*=64; disc*=4096;
}
vector<bigrational> rational_roots() const; // returns rational roots
int trivial() const; // Checks for a rational root
long nrootsmod(long p) const;
friend ostream& operator<<(ostream& s, const quartic& q);
friend int new_equiv(quartic* q1, quartic* q2, int info);
friend void qc(quartic& g,
const bigint& x0, const bigint& y0, const bigint& z0,
Curvedata * E, Curvedata* IJ_curve,
const bigint& tr_u, const bigint& tr_r,
const bigint& tr_s, const bigint& tr_t,
Point& P, int verbose);
void dump(ostream& s) const
{
s<<"Coeffs: ("<<a<<","<<b<<","<<c<<","<<d<<","<<e<<")\n"
<<"Roots("<<roots<<"): \n"<<roots[0]<<"\n"<<roots[1]<<"\n"
<<roots[2]<<"\n"<<roots[3]<<"\n"
<<"Type = "<<type<<", I="<<ii<<", J="<<jj<<endl;
}
// Implementation
private:
bigint a,b,c,d,e; // coefficients
bigcomplex* roots; // roots, array 0f 4 created in all constructors
int type; // 1, 2 or 3
bigint ii,jj,disc;
// The following are used by new_equiv: (NB p = -H)
bigint p, r, psq, asq;
void make_zpol();
int have_zpol;
unsigned long equiv_code;
public:
unsigned long set_equiv_code(const vector<long>& plist);
};
inline ostream& operator<<(ostream& s, const quartic& q)
{
s<<"("<<q.a<<","<<q.b<<","<<q.c<<","<<q.d<<","<<q.e<<")"<<flush;
return s;
}
quartic make_quartic(const bigint& a, const bigint& b, const bigint& c, const bigint& d, const bigint& e);
#endif
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