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Diffstat (limited to 'src/Cech_complex/utilities/cechcomplex.md')
-rw-r--r-- | src/Cech_complex/utilities/cechcomplex.md | 17 |
1 files changed, 11 insertions, 6 deletions
diff --git a/src/Cech_complex/utilities/cechcomplex.md b/src/Cech_complex/utilities/cechcomplex.md index 6330727a..f7817dbb 100644 --- a/src/Cech_complex/utilities/cechcomplex.md +++ b/src/Cech_complex/utilities/cechcomplex.md @@ -1,13 +1,18 @@ -# Cech complex # +# Čech complex # ## cech_persistence ## -This program computes the persistent homology with coefficient field *Z/pZ* of a Cech complex defined on a set of input points, using Euclidean distance. The output diagram contains one bar per line, written with the convention: +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). +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** @@ -17,9 +22,9 @@ where `dim` is the dimension of the homological feature, `birth` and `death` are * `-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 Cech complex construction. -* `-d [ --cpx-dimension ]` (default = 1) Maximal dimension of the Cech complex we want to compute. -* `-p [ --field-charac ]` (default = 11) Characteristic p of the coefficient field Z/pZ for computing homology. +* `-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. |