It looks like the clients
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morse_matching.cc, morse_matching_critical_faces.cc, morse_matching_n_critical_faces.cc, morse_matching_size.cc
At least, it appears from /usr/local/share/polymake/apps/topaz/rules/morse_matching.rules that these clients should be callable. Saying
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application("topaz");
$cc = cube_complex(1,1,1);
print $cc->MORSE_MATCHING_CRITICAL_FACES;
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polymake: WARNING: Use of inherited AUTOLOAD for non-method Polymake::topaz::SimplicialComplex::client() is deprecated at /usr/local/share/polymake/apps/topaz/rules/morse_matching.rules line 106, <GEN9> line 79.
polymake: WARNING: rule greedy.morse_matching: MORSE_MATCHING, MORSE_MATCHING_SIZE, MORSE_MATCHING_CRITICAL_FACES, MORSE_MATCHING_N_CRITICAL_FACES, MORSE_MATCHING_CRITICAL_FACE_VECTOR : HASSE_DIAGRAM failed: Can't locate object method "type" via package "morse_matching" (perhaps you forgot to load "morse_matching"?) at /usr/local/share/polymake/perllib/Polymake/Core/Object.pm line 1712, <GEN9> line 79.
polymake: WARNING: Use of inherited AUTOLOAD for non-method Polymake::topaz::SimplicialComplex::client() is deprecated at /usr/local/share/polymake/apps/topaz/rules/morse_matching.rules line 111, <GEN9> line 79.
polymake: WARNING: rule cancel.morse_matching: MORSE_MATCHING, MORSE_MATCHING_SIZE, MORSE_MATCHING_CRITICAL_FACES, MORSE_MATCHING_N_CRITICAL_FACES, MORSE_MATCHING_CRITICAL_FACE_VECTOR : HASSE_DIAGRAM failed: Can't locate object method "type" via package "morse_matching" (perhaps you forgot to load "morse_matching"?) at /usr/local/share/polymake/perllib/Polymake/Core/Object.pm line 1712, <GEN9> line 79.
polymake: WARNING: Use of inherited AUTOLOAD for non-method Polymake::topaz::SimplicialComplex::client() is deprecated at /usr/local/share/polymake/apps/topaz/rules/morse_matching.rules line 101, <GEN9> line 79.
polymake: WARNING: rule MORSE_MATCHING, MORSE_MATCHING_SIZE, MORSE_MATCHING_CRITICAL_FACES, MORSE_MATCHING_N_CRITICAL_FACES, MORSE_MATCHING_CRITICAL_FACE_VECTOR : HASSE_DIAGRAM failed: Can't locate object method "type" via package "morse_matching" (perhaps you forgot to load "morse_matching"?) at /usr/local/share/polymake/perllib/Polymake/Core/Object.pm line 1712, <GEN9> line 79.
polymake: ERROR: no more rules available to compute 'MORSE_MATCHING_CRITICAL_FACES'
Best,
Julian