/usr/include/eclib/cubic.h is in libec-dev 2013-01-01-1.
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 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 | // cubic.h: integer cubic class for unimodular transforms and reduction.
//////////////////////////////////////////////////////////////////////////
//
// Copyright 1990-2012 John Cremona
//
// This file is part of the mwrank package.
//
// mwrank 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.
//
// mwrank 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 mwrank; if not, write to the Free Software Foundation,
// Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA
//
//////////////////////////////////////////////////////////////////////////
//
// Notation: g(x,z) is replaced by g(m11*x+m12*z,m21*x+m22*z)
//
// Stored as bigint* arrays g of size 4 representing
// g[0]*x^3+g[1]*x^2+g[2]*x+g[3]
class unimod;
class cubic {
friend class unimod;
private:
bigint * coeffs; // will always have length 4
// init just allocates memory
void init();
public:
void set(long a, long b, long c, long d)
{coeffs[0]=a; coeffs[1]=b; coeffs[2]=c; coeffs[3]=d;}
void set(const bigint& a, const bigint& b, const bigint& c, const bigint& d)
{coeffs[0]=a; coeffs[1]=b; coeffs[2]=c; coeffs[3]=d;}
void set(const cubic& q)
{coeffs[0]=q.coeffs[0]; coeffs[1]=q.coeffs[1];
coeffs[2]=q.coeffs[2]; coeffs[3]=q.coeffs[3];}
cubic()
{init(); set(0,0,0,0);}
~cubic();
cubic(const bigint& a, const bigint& b, const bigint& c, const bigint& d)
{init(); set(a,b,c,d);}
cubic(long a, long b, long c, long d)
{init(); set(a,b,c,d);}
cubic(const cubic& q)
{init(); set(q);}
void operator=(const cubic& g) {set(g);}
inline bigint coeff(int i)
{if((i>=0)&&(i<=3)) return coeffs[i]; else return coeffs[0];}
inline bigint operator[](int i) const
{if((i>=0)&&(i<=3)) return coeffs[i]; else return coeffs[0];}
inline bigint a(void) const {return coeffs[0];}
inline bigint b(void) const {return coeffs[1];}
inline bigint c(void) const {return coeffs[2];}
inline bigint d(void) const {return coeffs[3];}
inline void set_coeff(int i, const bigint& a)
{if((i>=0)&&(i<=3)) coeffs[i]=a;}
inline bigint eval(const bigint& x, const bigint& z) const
{ bigint x2=sqr(x), z2=sqr(z);
return a()*x*x2 + b()*x2*z + c()*x*z2 + d()*z*z2;}
inline bigint eval(const bigint& x) const
{ bigint x2=sqr(x);
return a()*x*x2 + b()*x2 + c()*x + d();}
inline bigint disc() const
{ bigint b2=sqr(b()), c2=sqr(c()), ac=a()*c(), bd=b()*d();
return -27*sqr(a()*d()) + 18*ac*bd - 4*ac*c2 -4*bd*b2 + b2*c2;
}
inline void output(ostream& os=cout) const
{
os<<"["<<a()<<","<<b()<<","<<c()<<","<<d()<<"]";
}
friend inline ostream& operator<<(ostream& os, const cubic& g);
void transform(const unimod& m);
// In the next 4 functions, m already holds a unimod and is updated:
void x_shift(const bigint& e, unimod& m);
void y_shift(const bigint& e, unimod& m);
void invert(unimod& m);
void reduce(unimod& m);
// Mathews quantities for use when disc<0:
bigint mat_c1() const
{ return d()*(d()-b())+a()*(c()-a());}
bigint mat_c2() const
{ return a()*d() - (a()+b())*(a()+b()+c());}
bigint mat_c3() const
{ return a()*d() + (a()-b())*(a()-b()+c());}
bigint p_semi() const
{ return sqr(b())-3*a()*c(); }
bigint q_semi() const
{ return b()*c()-9*a()*d(); }
bigint r_semi() const
{ return sqr(c())-3*b()*d(); }
bigint u_semi() const
{ return 2*b()*sqr(b()) + 27*sqr(a())*d() - 9*a()*b()*c();}
bigint j_c1() const;
bigint j_c2() const;
bigint j_c3() const;
bigcomplex hess_root() const;
bigfloat real_root() const; // requires disc<0
void hess_reduce(unimod& m);
void mathews_reduce(unimod& m);
void jc_reduce(unimod& m);
// Just shifts x, returns the shift amount:
bigint shift_reduce();
};
inline ostream& operator<<(ostream& os, const cubic& g)
{
return os<<"["<<g.a()<<","<<g.b()<<","<<g.c() <<","<<g.d()<<"]";
}
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