# GSoC 2019 - Week 4 - Phase-I Completion

24 Jun 2019The fourth week of coding period has ended and now it’s time for phase-I evaluations. Below, is a brief progress report of the project.

The tasks that were proposed in the proposal for phase-I consists of:

- Implementation of Abelian Invariants
- Implementation of Composition Series
- Computation with Polycyclic groups

**Abelian Invariants**

Implemented a function to compute the abelian invariants for a given permutation or free group. These are given as a list of prime-powers and describe the stucture of `G/G'`

as a direct product of cyclic groups of prime power order.

**Composition Series**

Implemented a function to compute the composition series. It provides a way to break up a group into simple pieces. Composition series of a group `G`

is defined as the maximal subnormal series `G = H_0 > H_1 > H_2 ... > H_k = 1`

where every factor group `H(i+1)/H(i)`

is simple.

**Polycyclic Groups**

The work on polycyclic group is in progress. For now, collection algorithm has been implemented which needs to be tested and a lot of discussions were made on the polycyclic generating sequence and its presentation and may be in a week we’ll be ready with the stucture of polycyclic groups and collection of words.

- PR link Added Polycyclic Group Class

**Documentation**

Some documentation is done to increase the sphinx coverage of SymPy.

To follow the discussion on above topics and the further progress of the project one can check Gitter room sympy/GroupTheory

Follow @divyanshu132