Opened 10 years ago

Closed 10 years ago

# Bug in k-bounded symmetric functions

Reported by: Owned by: Chris Berg Sage Combinat CC user major sage-5.9 combinatorics Anne Schilling, Mike Zabrocki, Travis Scrimshaw, sage-5.9.beta0 Travis Scrimshaw Mike Zabrocki N/A #13605 #14228

### Description

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
```

### comment:1 follow-up:  2 Changed 10 years ago by Nicolas M. Thiéry

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

### comment:2 in reply to:  1 Changed 10 years ago by Anne Schilling

You can just do

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

Anne

### comment:3 follow-up:  4 Changed 10 years ago by Mike Zabrocki

Cc: Travis Scrimshaw added → 13605

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?

Last edited 10 years ago by Mike Zabrocki (previous) (diff)

### comment:4 in reply to:  3 ; follow-up:  5 Changed 10 years ago by Travis Scrimshaw

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`...

### comment:5 in reply to:  4 Changed 10 years ago by Mike Zabrocki

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).

### comment:6 Changed 10 years ago by Mike Zabrocki

Dependencies: 13605 → #13605

### comment:7 Changed 10 years ago by Travis Scrimshaw

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:

1. Create new classes which act like `Partitions_all` which just iterates over all of the classes with specified `n` in the passed in set.
2. Create `DisjointUnionEnumeratedSets` with an appropriate `Family`.
3. 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.

### comment:8 Changed 10 years ago by Chris Berg

First,

```Partitions(NonNegativeIntegers())
```

returns a value error.

```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.

Last edited 10 years ago by Chris Berg (previous) (diff)

### comment:9 Changed 10 years ago by Chris Berg

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]
```

### comment:10 follow-up:  11 Changed 10 years ago by Travis Scrimshaw

Dependencies: #13605 → #13605 #14228 new → needs_review

### comment:11 in reply to:  10 Changed 10 years ago by Mike Zabrocki

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

### comment:12 Changed 10 years ago by Travis Scrimshaw

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.

### comment:13 Changed 10 years ago by Mike Zabrocki

Status: needs_review → positive_review

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.

### comment:14 Changed 10 years ago by Travis Scrimshaw

Thank you for doing the review.

### comment:15 Changed 10 years ago by Jeroen Demeyer

Milestone: sage-5.8 → sage-5.9 → Mike Zabrocki

### comment:16 Changed 10 years ago by Mike Zabrocki

Authors: Chris Berg → Travis Scrimshaw

### comment:17 Changed 10 years ago by Jeroen Demeyer

Status: positive_review → needs_work

This should be rebased to sage-5.8.rc0.

### comment:18 Changed 10 years ago by Mike Zabrocki

I've rebased to 5.8.rc0.

Apply: trac_13743-fix_kschur-ts.2.patch

### comment:19 Changed 10 years ago by Jeroen Demeyer

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).
```