Homology

gpresent.spad line 1580 [edit on github]

Intended to hold homology which is calculated using SmithNormalForm: http://www.euclideanspace.com/prog/scratchpad/mycode/topology/homology/ Date Created: June 2016 Basic Operations: Related packages: Related categories: Related Domains: FreeModule, FiniteSimplicialComplex Also See: AMS Classifications:

= : (%, %) -> Boolean

from BasicType

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

dispGenerators : % -> OutputForm

more detailed output with generators

homology : (List(List(Integer)), List(Integer), List(List(Integer))) -> %

construct from lists

homology0 : () -> %

construct empty homology, useful in validation code

homologyGroup : (Matrix(Integer), Matrix(Integer)) -> %

construct from differential over integers uses method described by Waldek Hebisch here: https://groups.google.com/forum/?hl=en#!topic/fricas-devel/mLOdQ-fwbO0

homologyc2 : () -> %

construct C2 homology, useful in validation code

homologyz : () -> %

construct Z homology, useful in validation code

homologyzc2 : () -> %

construct Z+C2 homology, useful in validation code

homologyzz : () -> %

construct Z*Z homology, useful in validation code

latex : % -> String

from SetCategory

~= : (%, %) -> Boolean

from BasicType

CoercibleTo(OutputForm)

SetCategory

BasicType