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Added Documentation for Polycyclic Groups #17399

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merged 7 commits into from Aug 18, 2019
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Just for now

@@ -90,7 +90,7 @@ few more attributes which are defined below:
>>> Collector.free_group
<free group on the generators (x0, x1)>
>>> Collector.pc_presentation
{x1**3: (), x0**2: (), x0**-1*x1*x0: x1**2}
{x0**2: (), x1**3: (), x0**-1*x1*x0: x1**2}

Computation of Minimal Uncollected Subword
@@ -184,16 +184,19 @@ To get a clear picture, start with an example of SymmetricGroup(4). For S(4) the
generators in pcgs say [x0, x1, x2, x3] and the relative_order vector is [2, 3, 2, 2].
Starting from bottom of this sequence the presentation is computed in order as below.

>>> x3^2 ---|
>>> x2^2 |---> using only [x3] from pcgs and pc_series[1]
>>> x2^{-1}x3x2 ---|
>>> x1^3 ---|
>>> x1^{-1}x3x1 |---> using [x3, x2] from pcgs and pc_series[2]
>>> x1^{-1}x2x1 ---|
>>> x0^2 ---|
>>> x0^{-1}x3x0 |---> using [x3, x2, x1] from pcgs and pc_series[3]
>>> x0^{-1}x2x0 |
>>> x0^{-1}x1x0 ---|
>>> x3^2 # ---|---> using only [x3] from pcgs and pc_series[4]

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@jksuom

jksuom Aug 16, 2019

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It seems that >>> should not be included. Sphinx will try to run the code.

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@divyanshu132

divyanshu132 Aug 16, 2019

Author Member

Okay, If we'll write it directly then, how we can use comments because I tried it without >>> but it generates an error due to the comments(basically due to|-->), or may be we can write those comments directly without using special symbols.

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@jksuom

jksuom Aug 16, 2019

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Maybe it is | that is causing the problems. # will probably not be needed if this is not run.

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@divyanshu132

divyanshu132 Aug 16, 2019

Author Member

It doesn't look good without >>> and keeping the above structure so, I tried removing those symbols and putting the comments up, have a look at the last commit, if it looks good.

>>> x2^2 # ---|---> using only [x3] from pcgs and pc_series[3]
>>> x2^{-1}x3x2 # ---|
>>> x1^3 # ---|
>>> x1^{-1}x3x1 # |---> using [x3, x2] from pcgs and pc_series[2]
>>> x1^{-1}x2x1 # ---|
>>> x0^2 # ---|
>>> x0^{-1}x3x0 # |---> using [x3, x2, x1] from pcgs and pc_series[1]
>>> x0^{-1}x2x0 # |
>>> x0^{-1}x1x0 # ---|
One thing to note is same group can have different pcgs due to variying derived_series which,
results in different polycyclic presentations.
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