/usr/include/eclib/descent.h is in libec-dev 20160720-2.
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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 | // descent.h: declaration of classes rank12 and two_descent
//////////////////////////////////////////////////////////////////////////
//
// 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
//
//////////////////////////////////////////////////////////////////////////
#include "bigrat.h"
#include "curve.h"
#include "mwprocs.h"
// rank12 is a common base for separate classes rank1 and rank2 (for
// computing rank via general 2-descent and descent via 2-isogeny
// repectively); class two_descent is a user interface to these
// rank12 must be given a minimal (integral) model. two_descent can
// be given a non-minimal (integral) model, and will work with the
// minimal model; any points returned will be transferred back to the
// original model
class rank1;
class rank2;
class two_descent;
class rank12 {
protected:
Curvedata* the_curve;
int verbose, certain, success, selmer_only, do_second_descent;
long num_aux;
long rank, rank_bound, selmer_rank;
Curvedata IJ_curve; // [0,0,0,-27*I,-27*J]
bigint tr_u,tr_r,tr_s,tr_t; // transformation from latter to minimal curve
long lim1, lim2;
public:
// Constructor:
//
// sel is selmer_only switch
// firstlim is bound on |x|+|z|
// secondlim is bound on log max {|x|,|z| }, i.e. logarithmic
// n_aux only relevant for general 2-descent when 2-torsion trivial
// n_aux=-1 causes default to be used (depends on method)
// second_descent only relevant for descent via 2-isogeny
rank12(){;}
rank12(Curvedata* ec,
int verb=0, int sel=0,
long firstlim=20, long secondlim=5,
long n_aux=-1, int second_descent=1)
:the_curve(ec), verbose(verb), selmer_only(sel),
do_second_descent(second_descent),
num_aux(n_aux), lim1(firstlim), lim2(secondlim) {;}
virtual ~rank12() {;}
long getrank() const {return rank;}
long getrankbound() const {return rank_bound;}
long getselmer() const {return selmer_rank;}
long getcertain() const {return certain;}
int ok() const {return success;}
//
virtual long getselmerprime() const=0;
virtual Curvedata getEprime() const=0;
virtual long getselmerphi() const=0;
virtual long getselmerphiprime() const=0;
//
virtual void listpoints()=0;
virtual void listpoints(Curvedata* CD_orig,
const bigint& u, const bigint& r,
const bigint& s, const bigint& t)=0;
virtual vector<Point> getgens() const =0;
virtual vector<Point> getpoints() =0;
};
class two_descent {
private: rank12 * r12; // does all the work
int verbose, two_torsion_exists, selmer_only;
int success, certain, fullmw;
long rank, rank_bound, selmer_rank, sat_bound;
mw* mwbasis;
vector<bigrational> qai; // Coefficients of initial curve
Curvedata e_orig, e_min;
bigint u,r,s,t; // transform between e_orig and e_min
bigint v; // scaling factor needed to make input curve integral
void do_the_descent(long firstlim, long secondlim, long n_aux,
int second_descent); // (called by constructors)
public:
// Constructor:
//
// sel is selmer_only switch
// firstlim is bound on |x|+|z|
// secondlim is bound on log max {|x|,|z| }, i.e. logarithmic
// n_aux only relevant for general 2-descent when 2-torsion trivial
// n_aux=-1 causes default to be used (depends on method)
// second_descent only relevant for descent via 2-isogeny
two_descent(Curvedata* ec,
int verb=0, int sel=0,
long firstlim=20, long secondlim=5,
long n_aux=-1, int second_descent=1);
// Version which takes a vector [a1,a2,a3,a4,a6] of *rationals*
two_descent(vector<bigrational> ai,
int verb=0, int sel=0,
long firstlim=20, long secondlim=5,
long n_aux=-1, int second_descent=1);
~two_descent() {delete r12; delete mwbasis;}
long getrank() const {return rank;}
long getrankbound() const {return rank_bound;}
long getselmer() const {return selmer_rank;}
long getselmerprime() const {return r12->getselmerprime();}
Curvedata getEprime() const {return r12->getEprime();}
long getselmerphi() const {return r12->getselmerphi();}
long getselmerphiprime() const {return r12->getselmerphiprime();}
long getcertain() const {return certain;}
int ok() const {return success;}
int get2t() const {return two_torsion_exists;}
int getfullmw() const {return fullmw;}
bigfloat regulator() {return mwbasis->regulator();}
vector<P2Point> getbasis(); // returns points on original model
vector<Point> getpbasis(); // returns points on integral model
void report_rank() const;
void saturate(long sat_bd); // =0 for none
void show_gens(); // display points on original model
void show_result_status();
void pari_output();
};
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