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// transform.cc: implementation of quartic transformation 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
//
//////////////////////////////////////////////////////////////////////////
//
// Notation: g(x,z) is replaced by g(m11*x+m12*z,m21*x+m22*z)/m00^2
//
#include <eclib/marith.h>
#include <eclib/unimod.h>
#include <eclib/transform.h>
bigint g_content(const bigint& ga, const bigint& gb, const bigint& gc,
const bigint& gd, const bigint& ge)
// returns largest SQUARE which divides all
{
// first find the content:
bigint ans=abs(ga);
if(ans==1) return ans;
ans=gcd(ans,gb);
if(ans==1) return ans;
ans=gcd(ans,gc);
if(ans==1) return ans;
ans=gcd(ans,gd);
if(ans==1) return ans;
ans=gcd(ans,ge);
if(ans==1) return ans;
// if content non-trivial, get its divisors whose square divides
// (as we alreasy have this function to hand...)
vector<bigint> cdivs = sqdivs(ans);
// and return the last in the list, which is the biggest:
return cdivs[(cdivs.size())-1];
}
void apply_transform(bigint& a, bigint& b, bigint& c, bigint& d, bigint& e,
const unimod& m)
{
bigint m11=m(1,1), m12=m(1,2), m21=m(2,1), m22=m(2,2);
bigint m112=sqr(m11); bigint m113=m112*m11; bigint m114=m113*m11;
bigint m212=sqr(m21); bigint m213=m212*m21; bigint m214=m213*m21;
bigint m222=sqr(m22); bigint m223=m222*m22; bigint m224=m223*m22;
bigint m122=sqr(m12); bigint m123=m122*m12; bigint m124=m123*m12;
bigint newa = m214*e + m11*m213*d + m112*m212*c + m113*m21*b + m114*a;
bigint newe = m224*e + m12*m223*d + m122*m222*c + m123*m22*b + m124*a;
bigint newb = 4*m213*m22*e + (3*m11*m212*m22+m12*m213)*d
+ 2*(m112*m21*m22+m11*m12*m212) * c
+ (3*m112*m12*m21+m113*m22)*b + 4*m113*m12*a;
bigint newd = 4*m21*m223*e + (3*m12*m21*m222+m11*m223)*d
+ 2*(m122*m21*m22+m11*m12*m222)*c
+ (m123*m21+ 3*m11*m122*m22)*b + 4*m11*m123*a;
bigint newc = 6*m212*m222*e + 3*(m12*m212*m22+m11*m21*m222) * d
+ (m122*m212+ 4*m11*m12*m21*m22+m112*m222) * c
+ 3*(m11*m122*m21+m112*m12*m22) * b + 6*m112*m122*a;
a=newa; b=newb; c=newc; d=newd; e=newe;
}
void apply_transform(bigint& a, bigint& b, bigint& c, bigint& d, bigint& e,
const scaled_unimod& m)
{
apply_transform(a,b,c,d,e,(unimod)m);
bigint u2=sqr(m.scale_factor());
if(u2>1)
{
divide_exact(a,u2,a);
divide_exact(b,u2,b);
divide_exact(c,u2,c);
divide_exact(d,u2,d);
divide_exact(e,u2,e);
}
}
void xshift(const bigint& alpha,
bigint& a, bigint& b, bigint& c, bigint& d, bigint& e,
unimod& m)
{
e = e+alpha*(d+alpha*( c+alpha*( b+ alpha*a)));
d = d+alpha*(2*c+alpha*(3*b+4*alpha*a));
c = c+alpha*(3*b+6*alpha*a);
b = b+4*alpha*a;
//a = a;
m.x_shift(alpha);
}
void zshift(const bigint& gamma,
bigint& a, bigint& b, bigint& c, bigint& d, bigint& e,
unimod& m)
{
a = a+gamma*(b+gamma*( c+gamma*( d+ gamma*e)));
b = b+gamma*(2*c+gamma*(3*d+4*gamma*e));
c = c+gamma*(3*d+6*gamma*e);
d = d+4*gamma*e;
//e = e;
m.y_shift(gamma);
}
void m_invert(bigint& a, bigint& b, bigint& c, bigint& d, bigint& e,
unimod& m)
{
swap(a,e); swap(b,d); ::negate(b); ::negate(d);
m.invert();
}
void m_invert(bigint& a, bigint& b, bigint& c, bigint& d, bigint& e,
scaled_unimod& m)
{
swap(a,e); swap(b,d); ::negate(b); ::negate(d);
m.invert();
}
int check_transform(const bigint& a, const bigint& b, const bigint& c,
const bigint& d, const bigint& e,
const unimod& m,
const bigint& xa, const bigint& xb, const bigint& xc,
const bigint& xd, const bigint& xe)
{
bigint aa(a), bb(b), cc(c), dd(d), ee(e);
apply_transform(aa,bb,cc,dd,ee,m);
if(aa!=xa) return 0;
if(bb!=xb) return 0;
if(cc!=xc) return 0;
if(dd!=xd) return 0;
if(ee!=xe) return 0;
return 1;
}
int check_transform(const bigint& a, const bigint& b, const bigint& c,
const bigint& d, const bigint& e,
const scaled_unimod& m,
const bigint& xa, const bigint& xb, const bigint& xc,
const bigint& xd, const bigint& xe)
{
bigint aa(a), bb(b), cc(c), dd(d), ee(e);
apply_transform(aa,bb,cc,dd,ee,m);
if(aa!=xa) return 0;
if(bb!=xb) return 0;
if(cc!=xc) return 0;
if(dd!=xd) return 0;
if(ee!=xe) return 0;
return 1;
}
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