Install capdRedHom package in Mathematica

To use Mathematica bindings you need to have compiled library. We recomend to use precompiled binaries (see Download). The bindings are located in <INSTALL_PATH>/usr/local/libexec/capdredhom/capdRedHomM-<VERSION>.zip. You can find source code of the bindings in capdRedHom/programs/apiRedHom-mathematica.
To install the bindings into Mathematica you can use our installator install.m:

(** Insert bellow a correct path to bindings or call from command line
    MathematicaScript -script install.m capdRedHomM.zip **)
capdRedHomPKG=$ScriptCommandLine[[2]];

appsDir = FileNameJoin[{$UserBaseDirectory, "Applications"}];
pkgDir = FileNameJoin[{appsDir, "capdRedHom"}]

If[FileExistsQ[pkgDir],
 DeleteDirectory[pkgDir, DeleteContents -> True]]

(** ExtractArchive[capdRedHomPKG, appsDir] does not work with symlinks !**)

Run["tar xzf", capdRedHomPKG,  "-C", appsDir];


Print["Installed " <> capdRedHomPKG <> " into " <> appsDir];
Print["Restart Mathematica!"];

You can call the installator from command line as follow: MathematicaScript -script install.m <INSTALL_PATH>/usr/local/libexec/capdredhom/capdRedHomM-<VERSION>.zip

To check if all run-time dependencies are satisfied you can load a shared library in Python using following snippet:

python -c "import sys; from ctypes import *; lib = cdll.LoadLibrary(sys.argv[1]);" PATH_TO_LIBRARY

where PATH_TO_LIBRARY is like

# on Linux
~/.Mathematica/Applications/capdRedHom/LibraryResources/Linux-x86-64/libcapdapiRedHom_mathematica.so

# on macOS
~/Library/Mathematica/Applications/capdRedHom/LibraryResources/MacOSX-x86-64/libcapdapiRedHom_mathematica.dylib

In case of error your system will show you a message.

Compute Homology in Mathematica

MathematicaScript -script simplicial_1.m

<< capdRedHom`

(** Complex from list of simplices **)
simplices = {{0, 1, 2}, {0, 1, 3}, {0, 4}, {1, 4}};
Print[RedHomSimplicialBettiNumbersOverZ[simplices]];
Print[RedHomSimplicialBettiNumbersOverZ2[simplices]];
Print[RedHomSimplicialBettiNumbersOverZp[simplices, 3]];

Print[RedHomSimplicialHomologyOverZ[simplices]];
Print[RedHomSimplicialHomologyOverZ2[simplices]];
Print[RedHomSimplicialHomologyOverZp[simplices, 3]];






(**Topological sphere.Points coordinates.**)
simplices = {{2, 3, 4}, {1, 2, 3}, {1, 3, 4}, {1, 2, 4}};
Print[RedHomSimplicialBettiNumbersOverZ[simplices]];

(**Visualization.We need to have points and create a simplex from an \
abstract simplex.**)

points = {{0, 0, 0}, {1, 0, 0}, {0, 2, 0}, {0, 0, 3}};
SimplexCoordinate[simplex_] :=
  Map[Function[p, points[[p]]], simplex];
Graphics3D[Polygon[Map[SimplexCoordinate, simplices]]]

MathematicaScript -script cubical_1.m

Point Cloud Persistent Homology in Mathematica

MathematicaScript -script point_cloud_persistence.m

<< capdRedHom`

(** Compute persistence homology from a point cloud. Arguments:
- a list of points in n-dimensional euclidean space
- max complex dimension
- max distance
 **)

Print[RedHomPointCloudPersistentHomology[{{.1, .2, .3}, {.0, .0, .0}}, 1, .1]];





(** Random points example with visualization **)
Needs["HierarchicalClustering`"];


numberOfPoints = 100;
points = Table[{RandomReal[1], RandomReal[1], RandomReal[1]}, {i, numberOfPoints}];
distanceMatrix = DistanceMatrix[points];
Distance[p_, q_] := distanceMatrix[[p]][[q]];
SimplexCoordinate[simplex_] := Map[Function[p, points[[p]]], simplex];

maxDistance = 0.3;
maxDimension = 2;
(** compute persistence intervals **)
persistenceIntervals =
  RedHomPointCloudPersistentHomology[points, maxDimension,
   maxDistance];
(** compute simplicial Rips complex, only for visualization **)
complex =  RipsComplex[Distance, Length[points], maxDistance, maxDimension];


distance = 0.1;
dimension = maxDimension;
(** create filtration based on the precomputed Rips complex **)
filteredSimplices =
  ComplexFiltration[Distance, complex, distance, dimension];
(** For the filtration we can compute regular homology **)
filteredComplex = RedHomCreateSimplicialComplex[Union @@ filteredSimplices];
betti = RedHomBettiNumbers[filteredComplex];
Print[betti];

plotDimension = 2;
plot = PlotSimplicialComplex[filteredSimplices, plotDimension,  SimplexCoordinate];
Show[plot]