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+
+
+# Čech complex #
+
+## cech_persistence ##
+This program computes the persistent homology with coefficient field *Z/pZ* of
+a Čech complex defined on a set of input points, using Euclidean distance. The
+output diagram contains one bar per line, written with the convention:
+
+`p dim birth death`
+
+where `dim` is the dimension of the homological feature, `birth` and `death`
+are respectively the birth and death of the feature, and `p` is the
+characteristic of the field *Z/pZ* used for homology coefficients (`p` must be
+a prime number).
+
+**Usage**
+
+`cech_persistence [options] <OFF input file>`
+
+**Allowed options**
+
+* `-h [ --help ]` Produce help message
+* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output.
+* `-r [ --max-edge-length ]` (default = inf) Maximal length of an edge for the Čech complex construction.
+* `-d [ --cpx-dimension ]` (default = 1) Maximal dimension of the Čech complex we want to compute.
+* `-p [ --field-charac ]` (default = 11) Characteristic p of the coefficient field Z/pZ for computing homology.
+* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.
+
+Beware: this program may use a lot of RAM and take a lot of time if `max-edge-length` is set to a large value.
+
+**Example 1 with Z/2Z coefficients**
+
+`cech_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 2`
+
+**Example 2 with Z/3Z coefficients**
+
+`cech_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 3`