To build the example, run in a Terminal:

cd /path-to-example/
cmake .
make

***********************************************************************************************************************
Example of use of RIPS:

Computation of the persistent homology with Z/2Z coefficients of the Rips complex on points 
sampling a Klein bottle:

./rips_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 2

output:
2  0 0 inf 
2  1 0.0983494 inf 
2  1 0.104347 inf 
2  2 0.138335 inf 


Every line is of this format: p1*...*pr   dim b d
where
 	p1*...*pr is the product of prime numbers pi such that the homology feature exists in homology with Z/piZ coefficients. 
	dim is the dimension of the homological feature,
    b and d are respectively the birth and death of the feature and
   


with Z/3Z coefficients:

./rips_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 3

output:
3  0 0 inf 
3  1 0.0983494 inf 
3  1 0.104347 inf 
3  2 0.138335 inf 

and the computation with Z/2Z and Z/3Z coefficients simultaneously:

./rips_multifield_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.12 -d 3 -p 2 -q 3

output:
6  0 0 inf 
6  1 0.0983494 inf 
6  1 0.104347 inf 
6  2 0.138335 inf 
6  0 0 0.122545 
6  0 0 0.121171 
6  0 0 0.120964 
6  0 0 0.12057 
6  0 0 0.12047 
6  0 0 0.120414 

and finally the computation with all Z/pZ for 2 <= p <= 71 (20 first prime numbers):

 ./rips_multifield_persistence ../../data/points/Kl.off -r 0.25 -m 0.5 -d 3 -p 2 -q 71

output:
557940830126698960967415390  0 0 inf 
557940830126698960967415390  1 0.0983494 inf 
557940830126698960967415390  1 0.104347 inf 
557940830126698960967415390  2 0.138335 inf 
557940830126698960967415390  0 0 0.122545 
557940830126698960967415390  0 0 0.121171 
557940830126698960967415390  0 0 0.120964 
557940830126698960967415390  0 0 0.12057 
557940830126698960967415390  0 0 0.12047 
557940830126698960967415390  0 0 0.120414 

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Example of use of ALPHA:

For a more verbose mode, please run cmake with option "DEBUG_TRACES=TRUE" and recompile the programs.

1) 3D special case
------------------
Computation of the persistent homology with Z/2Z coefficients of the alpha complex on points 
sampling a torus 3D:

./alpha_complex_3d_persistence ../../data/points/tore3D_300.off 2 0.45

output:
Simplex_tree dim: 3
2  0 0 inf 
2  1 0.0682162 1.0001 
2  1 0.0934117 1.00003 
2  2 0.56444 1.03938 

Here we retrieve expected Betti numbers on a tore 3D:
Betti numbers[0] = 1
Betti numbers[1] = 2
Betti numbers[2] = 1

N.B.: - alpha_complex_3d_persistence accepts only OFF files in 3D dimension.
      - filtration values are alpha square values

2) d-Dimension case
-------------------
Computation of the persistent homology with Z/2Z coefficients of the alpha complex on points 
sampling a torus 3D:

./alpha_complex_persistence -r 32 -p 2 -m 0.45 ../../data/points/tore3D_300.off

output:
Alpha complex is of dimension 3 - 9273 simplices - 300 vertices.
Simplex_tree dim: 3
2  0 0 inf 
2  1 0.0682162 1.0001 
2  1 0.0934117 1.00003 
2  2 0.56444 1.03938 

Here we retrieve expected Betti numbers on a tore 3D:
Betti numbers[0] = 1
Betti numbers[1] = 2
Betti numbers[2] = 1

N.B.: - alpha_complex_persistence accepts OFF files in d-Dimension.
      - filtration values are alpha square values

3) 3D periodic special case
---------------------------
./periodic_alpha_complex_3d_persistence ../../data/points/grid_10_10_10_in_0_1.off ../../data/points/iso_cuboid_3_in_0_1.txt 3 1.0

output:
Periodic Delaunay computed.
Simplex_tree dim: 3
3  0 0 inf 
3  1 0.0025 inf 
3  1 0.0025 inf 
3  1 0.0025 inf 
3  2 0.005 inf 
3  2 0.005 inf 
3  2 0.005 inf 
3  3 0.0075 inf 

Here we retrieve expected Betti numbers on a tore 3D:
Betti numbers[0] = 1
Betti numbers[1] = 3
Betti numbers[2] = 3
Betti numbers[3] = 1

N.B.: - periodic_alpha_complex_3d_persistence accepts only OFF files in 3D dimension. In this example, the periodic cube
is hard coded to { x = [0,1]; y = [0,1]; z = [0,1] }
      - filtration values are alpha square values

***********************************************************************************************************************
Example of use of PLAIN HOMOLOGY:

This example computes the plain homology of the following simplicial complex without filtration values:
  /* Complex to build. */
  /*    1   3          */
  /*    o---o          */
  /*   /X\ /           */
  /*  o---o   o        */
  /*  2   0   4        */

./plain_homology 

output:
2  0 0 inf 
2  0 0 inf 
2  1 0 inf 

Here we retrieve the 2 entities {0,1,2,3} and {4} (Betti numbers[0] = 2) and the hole in {0,1,3} (Betti numbers[1] = 1)