Centralizers, improved normal closure & applications #1495

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Implemented an algorithm to compute centralizers of groups/subsets/elements within other groups, using a backtrack search .subgroup_search().

Improved the normal closure algorithm with some randomization, and added some applications - the derived and lower central series, nilpotency testing, etc.

Changed the file structure a bit by introducing some new files: sympy/combinatorics/group_constructs.py, which will host functions treating several groups equally, such as DirectProduct, and sympy/combinatorics/testutil.py which will host utility functions used exclusively for testing purposes (such as _verify_bsgs).

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This pull request fails (merged 2ec4d27 into a35203f).

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SymPy Bot Summary: 🔴 There were test failures.

@amakelov: Please fix the test failures.

Test command: setup.py test
master hash: a35203f
branch hash: 2ec4d27

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SymPy Bot Summary: 🔴 There were test failures.

@amakelov: Please fix the test failures.

Test command: setup.py test
master hash: a35203f
branch hash: 2ec4d27

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This pull request passes (merged babfccb into a35203f).

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SymPy Bot Summary: 🔴 There were test failures.

@amakelov: Please fix the test failures.

Test command: setup.py test
master hash: 5569bb2
branch hash: c232fb2

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SymPy Bot Summary: 🔴 There were test failures.

@amakelov: Please fix the test failures.

Test command: setup.py test
master hash: 5569bb2
branch hash: c232fb2

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This pull request passes (merged c97bcf35 into a35203f).

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SymPy Bot Summary: 🔴 There were test failures.

@amakelov: Please fix the test failures.

Test command: setup.py test
master hash: 5569bb2
branch hash: c97bcf355315130989e1c7721ddff4accb2aa795

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SymPy Bot Summary: 🔴 There were test failures.

@amakelov: Please fix the test failures.

Test command: setup.py test
master hash: 5569bb2
branch hash: c97bcf355315130989e1c7721ddff4accb2aa795

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This pull request passes (merged 5dd357c9 into a35203f).

This pull request passes (merged 5dd357c9 into a35203f).

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I downloaded and looked over the new code. This looks good to me.

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wdjoyner commented Aug 19, 2012

I downloaded and looked over the new code. This looks good to me.

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SymPy Bot Summary: ✳️ All tests have passed.

Test command: setup.py test
master hash: 5569bb2
branch hash: 5dd357c9034a205a120f641f397787bd7b9d4ca6

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Test results html report: http://reviews.sympy.org/report/agZzeW1weTNyDAsSBFRhc2sYy8ojDA

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SymPy Bot Summary: ✳️ All tests have passed.

Test command: setup.py test
master hash: 5569bb2
branch hash: 5dd357c9034a205a120f641f397787bd7b9d4ca6

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@amakelov is this ready to be merged?

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asmeurer commented Aug 19, 2012

@amakelov is this ready to be merged?

Aleksandar Makelov added some commits Aug 6, 2012

Aleksandar Makelov
Naive implementation of center, new file structure.
Implemented an algorithm for finding the center of a permutation
group using .centralizer() in a straightforward way.

Moved the DirectProduct() function to a new file,
sympy/combinatorics/group_constructs.py
Aleksandar Makelov
Renamed .commutator() to .derived_subgroup()
The commutator subgroup, also known as the derived subgroup,
is the group generated by all the commutators of the group.

The reason for the namechange is that the name commutator
will be used for a more general procedure.
Aleksandar Makelov
Nilpotency testing, improved solvability testing.
And minor fixes in several docstrings.
Aleksandar Makelov
Tests, new utility functions, triviality testing.
Started writing tests for the new functions (currently, there are
tests for .center() and .centralizer().

Wrote some new utility functions to help in the test process.

Wrote a method to test whether a permutation group is trivial.
Aleksandar Makelov
More tests, new file structure.
Added some more tests for the new functions and created a new file,
sympy/combinatorics/testutil.py that will accomodate utility functions
used specifically in testing functions from the combinatorics module
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amakelov Aug 20, 2012

Yes. I just rebased it over the current master.

Yes. I just rebased it over the current master.

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This pull request passes (merged 0bcb3ac into 5569bb2).

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SymPy Bot Summary: ✳️ All tests have passed.

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master hash: 5569bb2
branch hash: 0bcb3ac

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SymPy Bot Summary: ✳️ All tests have passed.

Test command: setup.py test
master hash: 5569bb2
branch hash: 0bcb3ac

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Ok, merging it now...

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asmeurer commented Aug 20, 2012

Ok, merging it now...

asmeurer added a commit that referenced this pull request Aug 20, 2012

Merge pull request #1495 from amakelov/week10
Centralizers, improved normal closure & applications

@asmeurer asmeurer merged commit 00abb2f into sympy:master Aug 20, 2012

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Thanks! :)

Thanks! :)

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@amakelov , I didn't realize how recently your own work went in. I made a lot of combinatorics changes elsewhere, however, in getting Saptarshi's summer's work ready to merge. I wonder if you could have a look at the changes and see if they look ok to you. I can also help if this breaks some of the things that you are working on this summer if needed. It's at #1498.

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smichr commented Aug 31, 2012

@amakelov , I didn't realize how recently your own work went in. I made a lot of combinatorics changes elsewhere, however, in getting Saptarshi's summer's work ready to merge. I wonder if you could have a look at the changes and see if they look ok to you. I can also help if this breaks some of the things that you are working on this summer if needed. It's at #1498.

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amakelov Aug 31, 2012

Ok, I'll take a look as soon as possible; the fall term starts in a couple
of days though, so don't count on me for doing a long review until next
weekend or so. The only things I use from sympy.combinatorics.permutations,
are _new_from_array_form, mul, .size, invert.

Cheers,

Alex

On Fri, Aug 31, 2012 at 7:14 PM, Christopher Smith <notifications@github.com

wrote:

@amakelov https://github.com/amakelov , I didn't realize how recently
your own work went in. I made a lot of combinatorics changes elsewhere,
however, in getting Saptarshi's summer's work ready to merge. I wonder if
you could have a look at the changes and see if they look ok to you. I can
also help if this breaks some of the things that you are working on this
summer if needed. It's at #1498#1498
.


Reply to this email directly or view it on GitHubhttps://github.com/sympy/sympy/pull/1495#issuecomment-8197097.

Ok, I'll take a look as soon as possible; the fall term starts in a couple
of days though, so don't count on me for doing a long review until next
weekend or so. The only things I use from sympy.combinatorics.permutations,
are _new_from_array_form, mul, .size, invert.

Cheers,

Alex

On Fri, Aug 31, 2012 at 7:14 PM, Christopher Smith <notifications@github.com

wrote:

@amakelov https://github.com/amakelov , I didn't realize how recently
your own work went in. I made a lot of combinatorics changes elsewhere,
however, in getting Saptarshi's summer's work ready to merge. I wonder if
you could have a look at the changes and see if they look ok to you. I can
also help if this breaks some of the things that you are working on this
summer if needed. It's at #1498#1498
.


Reply to this email directly or view it on GitHubhttps://github.com/sympy/sympy/pull/1495#issuecomment-8197097.

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On Fri, Aug 31, 2012 at 10:03 PM, Aleksandar Makelov <
notifications@github.com> wrote:

Ok, I'll take a look as soon as possible; the fall term starts in a couple
of days though, so don't count on me for doing a long review until next
weekend or so. The only things I use from
sympy.combinatorics.permutations,
are _new_from_array_form, mul, .size, invert.

it's now _af_new ; the others are the same except that __mul__ now
works from R to Left, so you should probably (if it seems ok to you) use
lmul(P, other) to do the multiplication or else continue to use _af_mul (if
you use that). There has been quite a bit of discussion at the now-closed
#1505 and under the discussion thread "permutation groups for cube and
dodecahedron".

I don't think I need a line by line review as much as a look at the overall
changes -- in dropping some methods and changing how others work. I've
added tests and lots of documentation which only need a read and not a lot
of digestion.

Thanks for whatever you can do.

Member

smichr commented Aug 31, 2012

On Fri, Aug 31, 2012 at 10:03 PM, Aleksandar Makelov <
notifications@github.com> wrote:

Ok, I'll take a look as soon as possible; the fall term starts in a couple
of days though, so don't count on me for doing a long review until next
weekend or so. The only things I use from
sympy.combinatorics.permutations,
are _new_from_array_form, mul, .size, invert.

it's now _af_new ; the others are the same except that __mul__ now
works from R to Left, so you should probably (if it seems ok to you) use
lmul(P, other) to do the multiplication or else continue to use _af_mul (if
you use that). There has been quite a bit of discussion at the now-closed
#1505 and under the discussion thread "permutation groups for cube and
dodecahedron".

I don't think I need a line by line review as much as a look at the overall
changes -- in dropping some methods and changing how others work. I've
added tests and lots of documentation which only need a read and not a lot
of digestion.

Thanks for whatever you can do.

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I pulled your branch and rebased it on top of #1498 -- we were heading the same direction. Now only the array_form is stored and a size is always stored. In cyclic notation one has the option of specifying size but I think it's fine to do as you have done and just keep whatever ints they have given. A check for duplicates and a check for all integers being present for perms given in array form is good to keep. As David said, it's nice to know if you accidentally double entered something or mistyped a digit. But the allowing of auto-adjustment during multiplication is a nice addition. I added your week12 to my other work...if you could look at that other branch I think that would be a great "week 12's" work :-) But if you just want to keep the week12 branch separate, that's fine, too.

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smichr commented Aug 31, 2012

I pulled your branch and rebased it on top of #1498 -- we were heading the same direction. Now only the array_form is stored and a size is always stored. In cyclic notation one has the option of specifying size but I think it's fine to do as you have done and just keep whatever ints they have given. A check for duplicates and a check for all integers being present for perms given in array form is good to keep. As David said, it's nice to know if you accidentally double entered something or mistyped a digit. But the allowing of auto-adjustment during multiplication is a nice addition. I added your week12 to my other work...if you could look at that other branch I think that would be a great "week 12's" work :-) But if you just want to keep the week12 branch separate, that's fine, too.

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Coverage Status

Changes Unknown when pulling 0bcb3ac on amakelov:week10 into * on sympy:master*.

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