Table 2 Overview of existing software for the computation of PH that have an accompanying peer-reviewed publication (and also [ 68 ], because of its performance)

(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

\(\mathbb{Q}\), \(\mathbb{F}_{p}\)

\(\mathbb{F}_{2}\)

\(\mathbb{F}_{2}\)

\(\mathbb{F}_{2}\) (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

-

-

-