Class Function Partitions

[tekaysquared]

The current output of SymmetricGroup(n).irreducible_characters() is a list of ClassFunction_libgap objects. It would be nice to take one of those class functions and instead of passing in a SymmetricGroup element, pass in a Partition of n since those represent the conjugacy classes.

This could be done by checking if the input to ClassFunction_libgap objects are Partitions, and if so using the default_representative of the partition.

CC: @slel

Component: group theory

Keywords: partition, symmetric group, character

Author: Trevor K. Karn

Branch/Commit: u/tkarn/class_funcion_partitions @ 0493345

Issue created by migration from https://trac.sagemath.org/ticket/30897

[tekaysquared]

Changed keywords from partition, symmetric group, charachter to partition, symmetric group, character

[trevorkarn]

Changed branch from u/gh-tekaysquared/partn-class-fn-libgap to u/tkarn/partn-class-fn-libgap

[trevorkarn]

Changed branch from u/tkarn/partn-class-fn-libgap to none

[trevorkarn]

New commits:

3894d03	Add ability of class function to take in a partition when G is the symmetric group
71d19b2	Merge branch 'develop' into partition-libgap-class-fcn
05bb0a7	Re order import statements so they make sense

[trevorkarn]

Branch: u/tkarn/class_funcion_partitions

[trevorkarn]

Commit: 05bb0a7

[embray]

comment:8

Thanks for the patch. Hopefully someone with the necessary subject-matter background will be along to review it soon.

[darijgr]

comment:9

Please fix the spacing in the doctest:

+            sage: h.cycle_type()
+            [2,1]
+			sage: triv(h.cycle_type())
+			1

It looks like a space/tab mismatch that might be invisible in your editor.

[darijgr]

comment:10

Also, please check the empty partition [] and [3] too, just in case (ducktyping can often be fickle around such cases).

If this works: LGTM!

[darijgr]

comment:11

Oh, and one more thing: I'm not sure any more, but there might be different implementations of symmetric groups in Sage. Does your code work with all of them? I think Permutations(n) is one thing worth trying, as is the Coxeter group of type A (don't remember how it is created).

EDIT: Not saying that it should work with all of them; probably best to document rather than fix.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

0a7675d	Merge branch 'develop' into partitions
0745497	Fix whitespace errors, add tests, and add assertion on size of group/size of partition. Also include disclaimer about CoxeterMatrixGroups and Permutations.

[sagetrac-git]

Changed commit from 05bb0a7 to 0745497

[trevorkarn]

comment:13

It turns out that the CoxeterMatrixGroup and Permutations classes don't have .irreducible_characters() method. It might be good to implement it eventually, but for now I just want to start by supporting the SymmetricGroup class.

[tscrim]

comment:14

Welcome to Sage development. So I have a few other additional comments for you to address:

• Add your (real) name to the author field.

• Instead of using an assert statement to check for valid input, you should instead raise a ValueError (or more generally whichever type of error is appropriate). This is a general convention we have taken across Sage (there is still some legacy code that does not do this).

• I think the error message would be better as f"the size of the partition {g.size()} must equal {len(self._group.domain())}" as it is more concise and direct about what is needed.

• It would be better to move the if isinstance(self._group, SymmetricGroup): first. This makes the code more clean and slightly faster for other groups.

• These changes:

               sage: chi([2,1])
  -            <BLANKLINE>
               Traceback (most recent call last):
  -                ...
  +            ...
               TypeError: Cyclic group of order 3 as a permutation group is not a SymmetricGroup. Give an element of Cyclic group of order 3 as a permutation group.

[trevorkarn]

Author: Trevor K. Karn

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

02cb2a2	Change assertion to ValueError
e3f9cc2	Reorder check for self._group being symmetric group. Change message on TypeError. Remove blankline so error tests pass.

[sagetrac-git]

Changed commit from 0745497 to e3f9cc2

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

0493345

Reorder check for self._group being symmetric group. Change message on TypeError. Remove blankline so error tests pass.

[sagetrac-git]

Changed commit from e3f9cc2 to 0493345

[mkoeppe]

comment:18

Sage development has entered the release candidate phase for 9.3. Setting a new milestone for this ticket based on a cursory review of ticket status, priority, and last modification date.

[mkoeppe]

comment:20

Setting a new milestone for this ticket based on a cursory review.