GSoC 2019 - Week 10 - Induced Pcgs for polycyclic subgroups

The tenth week of coding period has ended and a new PRsympy/sympy#17317 has been introduced. The PR implements induced Pcgs and exponent vector for polycyclic subgroups with respect to the original pcgs of the group. Below is an example to show the functionality.

>>> from sympy.combinatorics import *
>>> S = SymmetricGroup(8)
>>> G = S.sylow_subgroup(2)
>>> gens = [G[0], G[1]]
>>> PcGroup = G.polycyclic_group()
>>> collector = PcGroup.collector
>>> ipcgs = collector.induced_pcgs(gens)
>>> [gen.order() for gen in ipcgs]
[2, 2, 2]

Further it can also be used to implement Canonical polycyclic sequence which can be used to check if two subgroups of polycyclic presented group G are equal or not.

For the next week I’ll try to complete the documentation work on polycyclic groups and open a PR for the same.

Till then, good byee..