/usr/include/eclib/conic.h is in libec-dev 20160101-1.
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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 | // conic.h: declarations of functions for solving conics (see also legendre.h)
//////////////////////////////////////////////////////////////////////////
//
// 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 _CONIC_H
#define _CONIC_H 1 //flags that this file has been included
#include "quadratic.h"
bigint cancel1(bigint& x, bigint& y, bigint& z);
// cancels common factors only, return gcd
void cancel(bigint& x, bigint& y, bigint& z);
// cancels common factors and leaves z>=0 or z=0 and x>=0
int solve_conic(const bigint& a, const bigint& b, const bigint& c, const bigint& d,
const vector<bigint>& factorbase,
bigint& x, bigint& y, bigint& z, int method=4);
int solve_conic(const bigint& a, const bigint& b, const bigint& c, const bigint& d,
bigint& x, bigint& y, bigint& z, int method=4);
// Solves axx+bxz+czz=dyy for (x,y,z) not (0,0,0) and returns 1
// or returns 0 if not possible
// Should have a, c, d, bb-4ac non-zero
int solve_conic(const quadratic& q, const bigint& d,
bigint& x, bigint& y, bigint& z, int method=4);
int solve_conic(const quadratic& q, const bigint& d,
const vector<bigint>& factorbase,
bigint& x, bigint& y, bigint& z, int method=4);
int solve_conic_diag(const bigint& a, const vector<bigint>& aplist,
const bigint& b, const vector<bigint>& bplist,
bigint& x, bigint& y, bigint& z, int method);
// Solves xx-azz=byy for (x,y,z) not (0,0,0) and returns 1
// or returns 0 if not possible
// Should have a, b non-zero square-free, their prime divisors in aplist, bplist
void conic_mordell_reduce(const bigint& a, const bigint& b, const bigint& c, bigint& x0, bigint& y0, bigint& z0, int verb=0);
// Given a>0, b>0, c<0, abc square-free and ax^2+by^2+cz^2=0
// reduces x, y, z in place using Mordell's method (page 48)
// to achieve Holzer's bounds |z|<=sqrt(ab) etc.
void conic_diag_reduce(const bigint& a, const bigint& b, bigint& x, bigint& y, bigint& z, int verb=0);
// As above but with a,b square-free only, calls conic_mordell_reduce
int solve_conic_param(const bigint& a, const bigint& b, const bigint& c, const bigint& d,
const vector<bigint>& factorbase,
quadratic& qx, quadratic& qy, quadratic& qz, int method=4, int verb=0);
int solve_conic_param(const bigint& a, const bigint& b, const bigint& c, const bigint& d,
quadratic& qx, quadratic& qy, quadratic& qz, int method=4, int verb=0);
// Solves axx+bxz+czz=dyy for (x,y,z) not (0,0,0) and returns 1
// or returns 0 if not possible
// Should have a, c, d, bb-4ac non-zero
// qx,qy,qz are arrays of coeffs of parametrizing quadratics
// with leading coeffs qx[0],qy[0],qz[0] one solution
int solve_conic_param(const quadratic& q, const bigint& d,
const vector<bigint>& factorbase,
quadratic& qx, quadratic& qy, quadratic& qz,
int method=4, int verb=0);
int solve_conic_param(const quadratic& q, const bigint& d,
quadratic& qx, quadratic& qy, quadratic& qz,
int method=4, int verb=0);
int testsol(const bigint& a, const bigint& b, const bigint& c, const bigint& d,
const bigint& x, const bigint& y, const bigint& z, int verb=0);
// Tests to see if a given solution is a non-trivial solution
int testsol(const quadratic& q, const bigint& d,
const bigint& x, const bigint& y, const bigint& z,
int verb=0);
int testlocsol(const bigint& a,
const bigint& b,
const bigint& c);
// tests if ax^2+by^2+cz^2=0 is soluble, where a, b, c are pairwise
// coprime and square-free
int testlocsol(const bigint& a, const vector<bigint>& alist,
const bigint& b, const vector<bigint>& blist,
const bigint& c, const vector<bigint>& clist);
// tests if ax^2+by^2+cz^2=0 is soluble, where a, b, c are pairwise
// coprime and square-free, their prime factors being in alist etc.
int testlocsol(const bigint& a, const vector<bigint>& alist,
const bigint& b, const vector<bigint>& blist);
// tests if ax^2+by^2=z^2 is soluble, where a, b are
// square-free, their prime factors being in alist and blist.
int testparamsol(const bigint& a, const bigint& b, const bigint& c, const bigint& d,
const quadratic& qx, const quadratic& qy, const quadratic& qz, int verb=0);
// Tests to see if a given parametrization is a solution
int testparamsol(const quadratic& q, const bigint& d,
const quadratic& qx, const quadratic& qy, const quadratic& qz,
int verb=0);
//miscellaneous test functions:
void testmodsqrt();
void testsqf();
void testcancel();
// Output utilities:
void show_xyz(const bigint& x, const bigint& y, const bigint& z);
void show_cert(const bigint& p, const bigint& q, const bigint& r);
void show_eqn(const bigint& a, const bigint& b, const bigint& c);
void show_eqn_cert(const bigint& a, const bigint& b, const bigint& c,
const bigint& p, const bigint& q, const bigint& r);
void show_all(const bigint& a, const bigint& b, const bigint& c,
const bigint& p, const bigint& q, const bigint& r,
bigint& x, bigint& y, bigint& z);
#endif
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