Bug in k-bounded symmetric functions #13743

sagetrac-chrisjamesberg · 2012-11-22T14:58:14Z

The indices method of the KBoundedSubspace class is done wrong. The code is:

self.indices = ConstantFunction(Partitions(NonNegativeIntegers(), max_part=k))

Partitions is not meant to take a set. It will usually complain if you input something like NonNegativeIntegers but due to a bug in partitions, it allows it if you have optional arguments.

This creates the following bugs when playing around with k-Schur functions:

sage: ks = SymmetricFunctions(QQ).kBoundedSubspace(3,1).kschur()
sage: f = ks[2,1]
sage: f.coefficient(f.support()[0])
---------------------------------------------------------------------------
AssertionError                            Traceback (most recent call last)

/Users/chrisberg/<ipython console> in <module>()

/Applications/sage/local/lib/python2.7/site-packages/sage/combinat/free_module.pyc in coefficient(self, m)
    479         # that can be turned on or off
    480         C = self.parent()._basis_keys
--> 481         assert m in C, "%s should be an element of %s"%(m, C)
    482         if hasattr(C, "element_class") and not isinstance(m, C.element_class):
    483             m = C(m)

AssertionError: [2, 1] should be an element of Partitions of the integer An example of an infinite enumerated set: the non negative integers satisfying constraints max_part=3

Depends on #13605
Depends on #14228

CC: @anneschilling @zabrocki @tscrim

Component: combinatorics

Author: Travis Scrimshaw

Reviewer: Mike Zabrocki

Merged: sage-5.9.beta0

Issue created by migration from https://trac.sagemath.org/ticket/13743

The text was updated successfully, but these errors were encountered:

nthiery · 2012-11-22T16:15:25Z

comment:1

That Partitions accepts a set is in fact not a bug. Granted, it should be documented, and there certainly are many cases like this one where this is not supported (so I agree with the existence of this ticket). But this is definitely a feature we want (and that is, more or less, implemented in IntegerListsLex).

Cheers,
Nicolas

anneschilling · 2012-11-22T16:25:09Z

comment:2

You can just do

sage: ks = SymmetricFunctions(QQ).kschur(3,1)
sage: f = ks[2,1]
sage: f[Partition([2,1])]
1

Anne

zabrocki · 2012-11-24T16:58:43Z

Dependencies: 13605

zabrocki · 2012-11-24T16:58:43Z

comment:3

As far as I can tell, Travis' changes to Partitions may fix this bug. I am adding him as cc on this ticket. There are currently still conflicts between the symmetric functions and Partitions. Perhaps they are resolved it is possible that they will fix this problem so he can take this into account as he writes his patch. So for instance after I apply Travis' patch trac_13605-partition_options-ts.patch I have:

    sage: ks = SymmetricFunctions(QQ).kBoundedSubspace(3,1).kschur()
    sage: f = ks([2,1])
    sage: f.coefficient(f.support()[0])
    1

However the same patch currently causes a different problem with symmetric functions:


sage: ks[2,1]
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/Applications/sage-5.4.rc2/devel/sage-combinat/<ipython console> in <module>()

/Applications/sage-5.4.rc2/local/lib/python2.7/site-packages/sage/combinat/sf/new_kschur.pyc in __getitem__(self, c, *rest)
    298                 ks3[]
    299             """
--> 300             if isinstance(c, Partition_class):
    301                 assert len(rest) == 0
    302             else:

TypeError: isinstance() arg 2 must be a class, type, or tuple of classes and types

Travis, was it your intention to allow Partitions( NonNegativeIntegers(), max_part=k ) to represent the set of all Partitions with max_part=k?

tscrim · 2012-11-24T17:56:39Z

comment:4

Replying to @zabrocki:

However the [trac_13605-partition_options-ts.patch] currently causes a different problem with symmetric functions:


sage: ks[2,1]
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/Applications/sage-5.4.rc2/devel/sage-combinat/<ipython console> in <module>()

/Applications/sage-5.4.rc2/local/lib/python2.7/site-packages/sage/combinat/sf/new_kschur.pyc in __getitem__(self, c, *rest)
    298                 ks3[]
    299             """
--> 300             if isinstance(c, Partition_class):
    301                 assert len(rest) == 0
    302             else:

TypeError: isinstance() arg 2 must be a class, type, or tuple of classes and types

I'll go through now and scrub all instances of Partition_class from the sage code so you can adequately test to see if the patch (unintentionally) fixes this problem.

Travis, was it your intention to allow Partition( NonNegativeInteger(), max_part=k ) to represent the set of all Partitions with max_part=k?

Do you mean Partitions(NonNegativeIntegers(), max_part=k) with the s's? If so, this has some quirks noted in the wierdness page. However, if you mean exactly what you wrote, then I believe that should raise an exception since Partition() should return a single partition, although maybe with that input, one should get a random partition with max part k...

zabrocki · 2012-11-24T18:02:38Z

comment:5

Do you mean Partitions(NonNegativeIntegers(), max_part=k) with the s's? If so, this has some quirks noted in the wierdness page. However, if you mean exactly what you wrote, then I believe that should raise an exception since Partition() should return a single partition, although maybe with that input, one should get a random partition with max part k...

I meant Partitions(NonNegativeIntegers(), max_part=k). Sorry for the double typos (corrected in comment).

zabrocki · 2012-11-24T18:04:06Z

Changed dependencies from 13605 to #13605

tscrim · 2012-11-24T20:56:43Z

comment:7

In an ideal world, yes, that should be all partitions with max part k.

What I'm doing in #13605 won't really affect how input is handled, and if I understand this ticket correctly, it is to port the list input aspect of IntegerListsLex into Partitions. For this, my first thoughts give me one of three possibilities:

Create new classes which act like Partitions_all which just iterates over all of the classes with specified n in the passed in set.
Create DisjointUnionEnumeratedSets with an appropriate Family.
Copy how IntegerListsLex does things

On a slight side note, IntegerListsLex has some finiteness issues that will might also need to be addressed; see #13749.

sagetrac-chrisjamesberg · 2012-11-26T04:28:14Z

comment:8

Two small comments:

First,

Partitions(NonNegativeIntegers())

returns a value error.

Second, your set

Partitions(NonNegativeIntegers(), max_part = 3)

has repr:

Partitions of the integer Non negative integers satisfying constraints max_part=3

which is confusing. I have implemented something similar to Travis' first suggested solution to deal with the k-quotient side of things.

sagetrac-chrisjamesberg · 2012-11-26T05:34:34Z

comment:9

Found another bug which is really related to this one. If we give an input to a kSchur function which isn't k-bounded, then it should return an error:

ks = SymmetricFunctions(QQ).kBoundedSubspace(3,1).kschur()
ks([4,1])
Traceback (click to the left of this block for traceback)
...
TypeError: do not know how to make x (= [4, 1]) an element of self
(=3-bounded Symmetric Functions over Rational Field with t=1 in the
3-Schur basis also with t=1)

But this should also return an error:

ks(Partition([4,1]))
ks3[4, 1]

tscrim · 2013-03-07T22:17:18Z

Changed dependencies from #13605 to #13605 #14228

zabrocki · 2013-03-07T23:16:16Z

comment:11

Replying to @tscrim:

Does this affect at all #14235 (dependency one way or another?)

tscrim · 2013-03-07T23:20:11Z

comment:12

We both end up deleting the NonNegativeIntegers import (which is essentially trivial cleanup for both our patches), but other than that, the patches should^(tm) commute.

zabrocki · 2013-03-11T20:08:05Z

comment:13

Everything looks good. This seems to catch all the issues with having the correct indices in k-Schur functions that I can find. Thanks for coming back to this one.

tscrim · 2013-03-11T20:35:45Z

comment:14

Thank you for doing the review.

jdemeyer · 2013-03-11T21:54:02Z

Reviewer: Mike Zabrocki

zabrocki · 2013-03-11T22:02:20Z

Changed author from Chris Berg to Travis Scrimshaw

jdemeyer · 2013-03-14T08:10:01Z

comment:17

This should be rebased to sage-5.8.rc0.

zabrocki · 2013-03-14T16:52:41Z

comment:18

I've rebased to 5.8.rc0.

Apply: trac_13743-fix_kschur-ts.2.patch

jdemeyer · 2013-03-14T23:25:29Z

comment:19

It still doesn't apply properly, are you sure you have a clean build of sage-5.8.rc0?

applying /release/merger/patches/trac_13743-fix_kschur-ts.2.patch
patching file sage/combinat/partition.py
Hunk #3 succeeded at 304 with fuzz 2 (offset -1 lines).

jdemeyer · 2013-03-15T21:42:46Z

Attachment: trac_13743-fix_kschur-ts.2.patch.gz

zabrocki · 2013-03-16T16:05:00Z

comment:20

I am restoring positive review. I had to recompile sage-5.8.rc0 to ensure that I didn't have a problem. This patch now applies cleanly.

jdemeyer · 2013-03-17T15:32:17Z

Merged: sage-5.9.beta0

sagetrac-chrisjamesberg mannequin added this to the sage-5.8 milestone Nov 22, 2012

sagetrac-chrisjamesberg mannequin added c: combinatorics labels Nov 22, 2012

sagetrac-chrisjamesberg mannequin assigned sagetrac-sage-combinat Nov 22, 2012

tscrim added the s: needs review label Mar 7, 2013

zabrocki mannequin added s: positive review and removed s: needs review labels Mar 11, 2013

jdemeyer modified the milestones: sage-5.8, sage-5.9 Mar 11, 2013

jdemeyer added s: needs work and removed s: positive review labels Mar 14, 2013

zabrocki mannequin added s: positive review and removed s: needs work labels Mar 16, 2013

jdemeyer removed the s: positive review label Mar 17, 2013

jdemeyer closed this as completed Mar 17, 2013

sagetrac-chrisjamesberg mannequin mentioned this issue Jan 23, 2013

Implement k-bounded quotient space #13762

Closed

This was referenced Apr 6, 2013

Cleanup of symmetric function code #14220

Closed

Implements antipode and counit in new_kschur.py #14235

Closed

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Bug in k-bounded symmetric functions #13743

Bug in k-bounded symmetric functions #13743

sagetrac-chrisjamesberg mannequin commented Nov 22, 2012

nthiery commented Nov 22, 2012

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Bug in k-bounded symmetric functions #13743

Bug in k-bounded symmetric functions #13743

Comments

sagetrac-chrisjamesberg mannequin commented Nov 22, 2012

nthiery commented Nov 22, 2012

anneschilling commented Nov 22, 2012

zabrocki mannequin commented Nov 24, 2012

zabrocki mannequin commented Nov 24, 2012

tscrim commented Nov 24, 2012

zabrocki mannequin commented Nov 24, 2012

zabrocki mannequin commented Nov 24, 2012

tscrim commented Nov 24, 2012

sagetrac-chrisjamesberg mannequin commented Nov 26, 2012

sagetrac-chrisjamesberg mannequin commented Nov 26, 2012

tscrim commented Mar 7, 2013

zabrocki mannequin commented Mar 7, 2013

tscrim commented Mar 7, 2013

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tscrim commented Mar 11, 2013

jdemeyer commented Mar 11, 2013

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