Intermediate commit while converting to the new architecture
* Converted Filtration into StaticPersistence and DynamicPersistenceTrails
(both right now work with the underlying std::vector rather than std::list order)
* Filtration is now just an auxilliary glue (a map between Complex and Persistence)
* Whether chains are vectors or lists can be interchanged
* Added PersistenceDiagram with a simple bottleneck_distance() function
* Converted triangle, alphashapes3d, and cech-complex examples
* Lots of organizational changes
(factoring utilities out into containers.h, indirect.h, property-maps.h)
* Trying to document along the way with NaturalDocs-type comments
#include "geometry/linalg.h"
#include <iostream>
#include <synaps/upol.h>
#include <synaps/upol/gcd.h>
#include "geometry/rational-function.h"
typedef UPolDse<double> Polynomial;
typedef RationalFunction<Polynomial> RationalF;
//typedef LinearAlgebra<double> LinAlg;
//typedef LinearAlgebra<Polynomial> LinAlg;
typedef LinearAlgebra<RationalF> LinAlg;
int main()
{
LinAlg::MatrixType a(2,2);
a(0,0) = Polynomial("3*x"); a(1,0) = Polynomial(4); a(0,1) = Polynomial(0); a(1,1) = Polynomial(7);
std::cout << a << std::endl;
std::cout << LinAlg::determinant(a) << std::endl;
std::cout << Polynomial("3*x^2 + 4*x") / Polynomial("3*x^2") << std::endl;
LinAlg::VectorType b(2), x;
b(0) = Polynomial(4); b(1) = Polynomial(3);
LinAlg::solve(a, b, x);
std::cout << x << std::endl;
x(0).normalize(); x(1).normalize();
std::cout << x << std::endl;
}