Cancellation

Longer description to come.

Documentation

kFilteredMorphisms :: Int -> Morphisms -> Morphisms

Compute all morphisms which change the k-grading by less than k.

whoHasPsi :: AlgGen -> Morphisms -> Set AlgGen

Compute all Generators which map to psi'.

kWhoHasPsi :: Int -> AlgGen -> Morphisms -> Set AlgGen

Compute all Generators which map to psi' with kDrop less than k. (I've tried to stick to this pattern throughout: the k-version of a function just filters by kDrop.)

psiKillers :: AlgGen -> Morphisms -> Set AlgGen

Determine which generators have single arrows to psi'.

kPsiKillers :: Int -> AlgGen -> Morphisms -> Set AlgGen

Same as psiKillers but only checks for arrows which shift the filtration by k or less.

cancelKey :: AlgGen -> Morphisms -> AlgGen -> Morphisms

Cancel g in mors while dodging psi'.

kSimplify :: Int -> AlgGen -> Morphisms -> Morphisms

Simplify the complex at filtration k while dodging psi' Uses the Writer monad to keep track of what's canceled (but that information isn't used, presently)

kSimplifyComplex :: Int -> AlgGen -> Morphisms -> Morphisms

Simplify the complex up to filtration k while dodging psi'.

kDoesPsiVanish :: Int -> AlgGen -> Morphisms -> Bool

Test whether psi' dies at filtration k.