(a) Language
|
Java
|
C++
|
Java
|
C++
|
C++
|
C++
|
C++
|
C++
|
C++
|
(b) Algorithms for PH
|
standard, dual, zigzag
|
Morse reductions, standard
|
standard (uses javaPlex)
|
standard, dual, zigzag
|
standard, dual, twist, chunk, spectral sequence
|
twist, dual, distributed
|
dual, multifield
|
simplicial map
|
twist, dual
|
(c) Coefficient field
|
\(\mathbb{Q}\), \(\mathbb{F}_{p}\)
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\(\mathbb{F}_{2}\)
|
\(\mathbb{F}_{2}\)
|
\(\mathbb{F}_{2}\) (standard, zigzag), \(\mathbb{F}_{p}\) (dual)
|
\(\mathbb{F}_{2}\)
|
\(\mathbb{F}_{2}\)
|
\(\mathbb{F}_{p}\)
|
\(\mathbb{F}_{2}\)
|
\(\mathbb{F}_{p}\)
|
(d) Homology
|
simplicial, cellular
|
simplicial, cubical
|
simplicial
|
simplicial
|
simplicial, cubical
|
simplicial, cubical
|
simplicial, cubical
|
simplicial
|
simplicial
|
(e) Filtrations computed
|
VR, W, \(\mathrm{W}_{\nu}\)
|
VR, lower star of cubical complex
|
WRCF
|
VR, α, C̆
|
-
|
VR, lower star of cubical complex
|
VR, α, W, lower star of cubical complex
|
-
|
VR
|
(f) Filtrations as input
|
simplicial complex, zigzag, CW
|
simplicial complex, cubical complex
|
-
|
simplicial complex, zigzag
|
boundary matrix of simplicial complex
|
boundary matrix of simplicial complex
|
-
|
map of simplicial complexes
|
-
|
(g) Additional features
|
Computes some homological algebra constructions, homology generators
|
weighted points for VR
|
-
|
vineyards, circle-valued functions, homology generators
|
-
|
-
|
-
|
-
|
-
|
(h) Visualization
|
barcodes
|
persistence diagram
|
-
|
-
|
-
|
persistence diagram
|
-
|
-
|
-
|