This module takes care of chains stored on first page of the spectral sequence.

The format will be, for a certain position (n_deg, deg): References on each open cover of intersection degree n_deg Local chain coordinates as rows for each reference.


local_chains(*args) Chains in local forms, references and local coordinates.
class permaviss.spectral_sequence.local_chains_class.local_chains(*args)[source]

Chains in local forms, references and local coordinates.


Prime number to be used for computations.

Type:int or None

Given two local chains, adds then and returns the result.

Assumes that references are the same

Parameters:B (:class:local_chains object) –
add_entry(index, ref, coord)[source]

Add a references and coordinates at some index.

Checks that the input is correct.

  • index (int) – Position in local_chains object.
  • ref (list) – Reference list for current index.
  • coord (Numpy Array or list) – Local coordinates where expressions are indexed by rows. If it is a list it is the empty list [].

ValueError – If the given pair of ref and coord do not respect the format rules.


Given a sequence of local chains, makes a copy and returns it.


Minus all local coordinates of self.


Sum chains as indicated by “coord_sums”

  • chains (local_chains object) – Chains in local_chains format to be added.
  • coord_sums (Numpy Array) – Each sum is given by rows in coord_sums. These store the coefficients that the chain entries need to be added.