permaviss.spectral_sequence.local_chains_class

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.

Classes

local_chains(*args)

Chains in local forms, references and local coordinates.

class permaviss.spectral_sequence.local_chains_class.local_chains(*args)

Chains in local forms, references and local coordinates.

p

Prime number to be used for computations.

Type:int or None

__add__(B)

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)

Add a references and coordinates at some index.

Checks that the input is correct.

Parameters:

• 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 [].

Raises:

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

copy_seq()

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

minus()

Minus all local coordinates of self.

sums(coord_sums)

Sum chains as indicated by “coord_sums”

Parameters:

• 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.