Re: [sage-combinat-devel] I want product of the outgoing vertices as product of variables but it gives nonint type erros

[Christian Stump]

Dear Biswajit,

it doesn't hurt opening a question with a friendly sentence.

Anyway, as the output tells you, your graph vertices are labelled by
strings (namely "x0", "x1", ...) which you cannot multiply as the
product of two strings is not defined here.

If you want to use variables instead, you do for example

sage: P. = PolynomialRing(QQ,5)
sage: dia = DiGraph({x0:{x1:(1, -1),y1:(1, -1),x2:(1, -1)},y2:{x0:(1,
-1),x1:(1, -1)}})
sage: diaout = dia.neighbors_out(x0);diaout
[y1, x2, x1]
sage: prod(diaout)
x1*x2*y1

Cheers, Christian

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[sage-combinat-devel] How to set the category of finite Coxeter groups properly?

[Christian Stump]

Hi there,

I need some help with the category framework.

There is a category finite Coxeter group which is
CoxeterGroups().Finite(). I now have implemented a category
ComplexReflectionGroups().Finite().WellGenerated() which is certainly
a super category of CoxeterGroups().Finite().

But if I add a method CoxeterGroups().Finite().super_categories
returning that, I run into trouble:

1. Now, the repr of CoxeterGroups().Finite() is Category of finite
well generated coxeter groups. How do I get rid of the well
generated there?

2. Many doctests in CoxeterGroups().Finite() now fail. I do not
understand how doctests can break there at all since I did only add
some new methods. Or did I also overwrite some -- and if so, how do I
prevent the system doing so?

Thanks,

Christian

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Re: [sage-combinat-devel] How to set the category of finite Coxeter groups properly?

[Christian Stump]

Great, that worked -- thanks Nicolas!

Here is one more issue, is that what I should expect, or should I
change something there? (Should Category of finite groups still be
there?

Thanks again,

Christian

Failed example:
FiniteCoxeterGroups().super_categories()
Expected:
[Category of coxeter groups,
 Category of finite groups,
 Category of finite finitely generated semigroups]
Got:
[Category of coxeter groups,
 Category of finite well generated complex reflection groups,
 Category of finite finitely generated semigroups]

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Re: [sage-combinat-devel] weyl group element of E8 act on a positive root to get some partiular root but the below program shows error

[Christian Stump]

Hi all,

 - Can GAP iterate through the elements of a finite matrix group (at
   this point this is all GAP know about the group) without storing
   them all in memory.

according to the user manual of Chevie
(https://www.imj-prg.fr/~jean.michel/gap3/htm/chap069.htm#SECT024) it
is possible to iterate through a finite Coxeter group there. I haven't
figured out if that is as well possible for permutation groups or
matrix groups in gap3 or gap4 in general though.

Cheers,

Christian

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Re: [sage-combinat-devel] Re: redesign combinatorial statistics

[Christian Stump]

 Does findstat relly on a big database that is enhanced with the new queries? 
 Or does it compute every query from scratch?

I start with answering here since this the crucial point.

We want to use Sage in FindStat only in the background, a user
interacting with FindStat (by searching for statistics, or by
contributing statistics) should not see what's happening in the
background.

By a combinatorial statistic I mean a map from some combinatorial
collection to the integers. FindStat does not store combinatorial
statistics as maps, but only as finite explicit data sets (and finite
should be flexible in the sense that it can be very few or quite some,
say 10-2000).

Reasons:

- this gives anyone the chance to contribute to FindStat: it might
be that you computed some statistic by hand for a few values without
having any written code (think of the dimension some variety attached
to a permutation and not of something you can code super easily), or
it might be that you prefer to work in one of the Ma's and still want
to contribute your statistic.

- it is *impossible* to compute statistics on the fly. Even if you
had code to compute the statistic: what if it takes 13sec to compute
your statistic for the permutation [6,5,4,3,1,2] (just checked with
the number of decompositions into simple transpositions). In a single
database search, there are 1th if not millions of statistics
values tested. These cannot be computed on the fly, even if you store
them temporarily.

 Just to clarify, i wasn't thinking on sage sending a query to findstat

But that will be the only possible way to go. Your question here is as
asking the same for the OEIS, see above.

 but performing the search locally (i.e. having findstat software included in 
 Sage).

I don't know if that's maybe as well what you thought of: it might be
possible to query FindStat for the plain statistics data and do the
remaining computations within Sage. I would actually very much
appreciate if we were doing that at some point simply because I would
expect this to result in strong improvements of the search engine we
have written for FindStat so far.

BUT: this would result in code in Sage that is not useful purely
within Sage. And there are people, loud people, that say there should
not be such code in Sage.

Another problem that would need to be solved would be: Such code would
always need to interact with FindStat and would thus need to follow
predefined specifications for that interaction.

Cheers,

Christian

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Re: [sage-combinat-devel] Re: redesign combinatorial statistics

[Christian Stump]

 Would it be possible to include the findstat functionality in sage? That is,
 i have a bunch of pairs (permutation, number), then call the function
 findtsta on them, and get a list of possible ways that the numbers can me
 computed from the permutations. All inside sage, without need to go to the
 findstat webpage.

I really appreciate that so many people appear to be interested in the
FindStat functionality, being it from within Sage or from the FindStat
webpage!

-- It is almost sure that it will *never* be possible to use FindStat
without a web connection

-- Nevertheless, it is on our ToDo list (which is, as for basically
everyone, very packed -- I don't promise anything for a given time in
the future) to provide a text based query to the database to obtain
machine readable results that can be parsed into Sage. That should go
similarly to the Sage functionality for the OEIS. BUT please see that
querying FindStat is *much more complicated* than the simple query for
the OEIS: (A) the data structure is more complicated, (B) the
following maps is much more complicated.

-- It will not be possible (say within the next two years, except the
unlikely event that I will a lottery without participating, and then
spend some money to hire a professional programmer) to only query the
statistics data, and do the computations within your own Sage. That's
because there is (A) in additional layer of code on top of Sage that
makes that possible and (B) this layer is extra thick because we also
have stuff there that could be part of Sage but is not because there
is a *partial unwelcoming attitute* that prefers to give a that's not
good for Sage over include non-perfect code, even if it would have a
strictly positive influence on the Sage user community in such
instances.

Cheers,

Christian

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Re: [sage-combinat-devel] Re: redesign combinatorial statistics

[Christian Stump]

 Just to make this statement more precise: it will not be possible within the 
 next two years if Mmarco relies on your availability for this (there is no 
 blame in that statement, it's  just a clarification that others might be 
 willing to work on this problem).

It is not a problem -- it's the way we set up our project! Its main
features are designed for users who do not want to do any coding or
even seeing a terminal environment. And that's good about it and one
of the reasons why people like it! I recently talked about the project
with Michelle Wachs -- she was actually asking about it! -- and she
seemed to be really impressed. I think that didn't just come from the
bare functionality, but from the easy possibility for her to interact
with it.

Anyone who is interested in working on more sophisticated features to
be done from within Sage are very welcome to talk to me and/or to
Chris Berg (though he might be a little less responsive these days)
about it to see how we can approach it. But I would not like if I find
out in 18 months from now that someone implemented a much stronger
query machine (which is certainly possible) based on our ideas, but
without collaborating with us!

Cheers, Christian

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Re: [sage-combinat-devel] Re: redesign combinatorial statistics

[Christian Stump]

 It seems that actually nobody read my initial post on that thread... so let 
 me repeat

I did -- but didn't really have any qualified contribution...

 But the semantic has to be implemented at the level of maps not at the level 
 of methods.

could you explain what you mean there (maybe using your example of the
number of descents of a permutation).

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Re: [sage-combinat-devel] Re: redesign combinatorial statistics

[Christian Stump]

 The second step would be to think how to add semantic to the map. Part
 of is already managed by the axioms/categories (for example a Morphism
 between GradedSets preserve the grading). But there is nothing for
 injectivity/surjectivity or more subtle properties.

Thanks for the clarification! I have a few more questions there:

-- Can I turn any method in Sage which mimics a mathematical function
into a map in the above sense? To put it differently: Is it right that
there are always (or almost always) parents available to use as domain
and codomain?

-- How do you think more semantic should be implemented? As a dict
with some conventions for keys and values?

-- What if I want to give properties that depend on input parameter
like the length of the permutation? Say I look at the map from
Permutations(n) to itself given by composition with the long cycle
(1..n), and now want to add the semantic information that it has order
n?

-- Is there a way to implement your ideas such that the lines of code
I need to touch in order to turn a method into a map is right where
the method is implemented?

Thanks, Christian

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Re: [sage-combinat-devel] Re: redesign combinatorial statistics

[Christian Stump]

 Ceterum censeo: Please do not put too much semantic into an attribute of
 the map. It will be a burden for the map, will cost memory, and will be
 difficult to search.

I would personally really like to get semantic information about maps
implemented in Sage. This starts with automated concatenating maps,
and does not even end with information about a map in the Journal of
Applied Nonsense. I am sure you have reasons to vote for a centralized
system where to store such information. But how am I then convincing
someone knowing that information to add that information there? What I
like about a local system (preferably accompanying the code of the
very method) is that it makes it easy for the person having
information about a specific map to provide that information.

Of course, that information must be organized to be searchable
properly. But I don't see a problem there beside conventional namings.

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Re: [sage-combinat-devel] combinatorial statistics

[Christian Stump]

 well, there was a decorator for statistics before the move to gitI have 
 code that used it.

sorry, Martin, that we removed it again!

But you see that Nathann keeps arguing it is not useful to people (I
am not going to participate in that discussion -- I want to do math
and I don't kill my time *again* in such a discussion), so I am not
going to put it back in. But feel free to use it locally, you can
either just take the old code from an old version of Sage, or I can
send you instructions of how to do it.

Cheers, Christian

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Re: [sage-combinat-devel] combinatorial statistics

[Christian Stump]

 Besides: is it possible to run a more exhaustive FindStat search?  If I 
 understand correctly, FindStat limits itself to 3 maps, right?

No -- you can change the 3 into a 5 at most. And the at most is just a
limit to not run for too long, so if you are willing to wait
overnight, we can also do 6 or maybe 7.

(Am I getting your question right, now?)

Cheers, Christian

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Re: [sage-combinat-devel] combinatorial statistics

[Christian Stump]

 Another question: I would like to search for a statistic (on permutations,
 but the question applies in general) that satisfies addtitional structural
 constraints (eg., it should be invariant under conjugation with the long
 cycle).  Is such a search also possible?

The obvious solution is to take the FindStat output and check if the
given outputted statistic satisfies your constraints. I currently
cannot think of any more sophisticated things to do there, but maybe
you have something in mind...

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Re: [sage-combinat-devel] combinatorial statistics

[Christian Stump]

 Yes!  So, if I want to perform such a query, I should send the code 
 generating the statistic to you, right?

How urgent is it? -- I could try and see if the server explodes if I
increase the 5 to a 7. That way, you can keep playing there.

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Re: [sage-combinat-devel] combinatorial statistics

[Christian Stump]

 I am in need of browsing through all the statistics on permutations and 
 derangements, and wanted to use combinatorial_statistics_in_class, but I 
 can't find it anymore...
 What should I be using?

Hi Martin --

sage: from sage.combinat.combinatorial_map import combinatorial_maps_in_class
sage: combinatorial_maps_in_class(type(Permutation([])))
[Combinatorial map: complement,
 Combinatorial map: permutation poset,
 Combinatorial map: Binary search tree (left to right),
 Combinatorial map: major-index to inversion-number bijection,
 Combinatorial map: Robinson-Schensted tableau shape,
 Combinatorial map: inverse,
 Combinatorial map: Robinson-Schensted recording tableau,
 Combinatorial map: foata_bijection,
 Combinatorial map: descent composition,
 Combinatorial map: Robinson-Schensted insertion tableau,
 Combinatorial map: to alternating sign matrix,
 Combinatorial map: Increasing tree,
 Combinatorial map: Simion-Schmidt map,
 Combinatorial map: reverse,
 Combinatorial map: inversion-number to major-index bijection]

Let me add that I was thinking of opening a ticket to remove
combinatorial maps from Sage again (in the medium time future) simply
because the negative comments about it were louder (and I am currently
not in the position to be able to spend much time on stuff I don't
need for my research). So if you have some use cases for combinatorial
maps, please write about it so such cases are also visible.

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Re: [sage-combinat-devel] combinatorial statistics

[Christian Stump]

 thanks for the fast reply -- but I need statistics, not maps.  I..e, I'd like 
 to have a list of all methods applying to permutations that return a number...

sorry for not properly reading your request! We had, similar to the
@combinatorial_maps decorator, an @combinatorial_statistic decorator
at some point.
But I don't think this semantic information is currently available
since we stopped the use case in FindStat and then also stopped
implementing it in sage.

 Is it correct that findstat implements more statistics and more maps?  Is it 
 possible to use findstat from within sage?

That's correct for maps.

But it is not correct for statistics. Indeed, there is no statistic at
all implemented in FindStat, we only store statistics as their values
(though in a human readable field, there is the option to put (any
sort of) code (most often Sage, but we also have Mathematica code) to
generate that data, see www.findstat.org/St000193/ for a statistic
with code that is not directly in Sage). The reason is that we cannot
generate the data on the fly since that's much too slow (even for
simple statistics) to be usable in FindStat.

So you are very welcome to suggest a way of using the fairly flexible
code field of a statistic to make it machine readable (only if this
is desired for a given statistic), we will then find a way of making
that info available in Sage.

A first naive example could be:

The code field for the above statistic is
{{{
for i in [1..5]:
for a in AlternatingSignMatrices(i):
print [list(row) for row in
a.to_matrix()],=,a.transpose().to_monotone_triangle()[-1][0]
}}}
so we have no chance to actually turn that *automatically* into a
statistic. But if we would introduce a convention like use a
decorator to tell that sth. is code to generate a statistic, we could
have that code starting with @combinatorial_statistic is taken to be
a statistic like
{{{
@combinatorial_statistic
def my_stat(ASM):
return a.to_matrix()],=,a.transpose().to_monotone_triangle()[-1][0]

for i in [1..5]:
for a in AlternatingSignMatrices(i):
print [list(row) for row in a.to_matrix()],=,my_stat(a)
}}}
can be parsed and the statistic would be stored semantically as a statistic.

Finally, we could have a Sage interface that allows to check for all
stats for a combinatorial collection (say Permutations), or to get a
particular statistic to use it in sage.

But that's a lot of work and we would need some volunteer to actually do it.

Cheers,

Christian

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[sage-combinat-devel] Input for skew tableaux

[Christian Stump]

Hi,

Is it on purpose / can I rely on the following behaviour for skew tableaux:

sage: tab =
SkewTableau([[0,1,None],[None,None,1,2],[None,None,0,0,1],[1,None]]); tab
[[0, 1, None], [None, None, 1, 2], [None, None, 0, 0, 1], [1, None]]

As we also had for compositions, it appears that I can even give other
stuff into a skew tableau. Anyway, because of the 0's, methods like
to_word are broken, and because of the not very shapy shape, shape,
inner_shape, and outer_shape are also broken.

I actually thought that such a multi purpose skew tableau might be nice to
implement Le diagrams, but I guess that this is too much of a hack relying
on bad behaviour of skew tableaux...

Is it worth opening a ticket for input tests of skew tableau then?

Cheers, Christian

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Re: [sage-combinat-devel] Le diagrams and permutation tableaux

[Christian Stump]

Thanks for your comments, Darij! My impression is that I also do not quite
answer to your mail:

What I would like to have:

Given a partition \lambda (or something more general, even a BadShape
without knowing what that is), I would like a class of all Le diagrams of
shape \lambda. I.e., a class that mimics the behaviour of all 0/1 fillings
of \lambda satisfying an additional property (if the shape is something
more general than a partition, than I obviously want this property to be
well-defined). Call such a filling of \lambda Le filling.

As a set, such fillings should thus be a subset of BadShapeFilling and
inherit say the drawing, repr, latex methods.

Then, I want a containment test: easy to check, and an iterator: more
difficult, I wouldn't have any non-brute-force idea currently (but I don't
know the literature on Le diagrams...)

Finally, I want a class PermutationTableaux with parameters n and k
mimicking the set of all Le fillings of shapes of partitions fitting inside
the rectangle k x (n-k), again with easy containment test and probably
harder iterator.

@Darij How would that fit your framework?

Cheers, Christian

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[sage-combinat-devel] Le diagrams and permutation tableaux

[Christian Stump]

Hi there,

I wonder if someone already has code for Postnikov's Le diagrams. These are
fillings of partitions fitting in a box with 0's and 1's with the
additional property that no 0 has a 1 in the same column AND to its left in
the same row.

My aim is to get Le diagrams (or maybe the subclass of permutation
tableaux) into FindStat, since these admit many maps to other combinatorial
objects, and also tons of statistics.

I have seen that Florent played at some point with partitions fitting in a
box, so having a class for these would be a first step.

Thanks, Christian

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Re: [sage-combinat-devel] Russian

[Christian Stump]

Below my office mate's term for lattice polytope:


lattice polytope is
целочисленный многогранник
(by the way, both polytope and polyhedron are translated in Russian by this
single word).

Cheers, Christian

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Re: [sage-combinat-devel] Russian

[Christian Stump]

 Sorry, I don't know Russian either. As a tiny step, I selected links

to the appropriate english wikipedia page to at least clear potential
 ambiguity. Some have translations in other languages which might help.


I am sure Sergey Fomin knows all those terms in case they exist in Russian
- I will also ask my Russian office mate on Monday.

Cheers, Christian

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Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality

[Christian Stump]

 Yes, but it's associative, so it works... (Except I don't expect it to
 have much of a use.)


can you be more specific? How is the product uv defined? I see that you
have a shuffle product defined, but I don't see that you have
concatenation...

Thanks, Christian

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[sage-combinat-devel] Bug in Core

[Christian Stump]

Hi,

do you consider the following a bug?

sage: A = Core([2],4)
sage: B = Core([2],5)
sage: hash(A) == hash(B)
True

The hash of a core only depends on the list and not on the core. Since the
same list considered as an x- and as a y-core are fundamentally different
objects, I would rather suggest to have the hash depending not only on the
list.

If others agree, I will provide a patch fixing that...

Cheers, Christian

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Re: [sage-combinat-devel] Re: Bug in Core

[Christian Stump]

 sage: (Partition([2]).to_core(4)).parent()

5-Cores of length 2


Okay, I get from the documentation of to_core that this returns what it is
supposed to.

But anyway, let me mention that for me as someone not very familiar with
the topic, I would expect that Partition([2]).to_core(k) checks if the
input partition is actually a k-core and then turns it into a k-core if
possible...

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Re: [sage-combinat-devel] Re: Bug in Core

[Christian Stump]

 I wouldn't necessarily call that a bug, as it is necessary since A == B.


four people, two options, five opinions...

Let me ask this, is being a k-core a property of a partition or is it a
 *distinct* combinatorial object?


As mathematical concepts, that doesn't make much of a difference, I'd say.
It is just too easy to think of something written as [4,2,1,1] at the same
time as a partition, a list, a composition, a core, ...

On the other hand, sagewise, if being a k-core is only a property of a
partition, why do their methods differ that much? do some methods even have
different results depending on the type of core? As it seems this is the
case, I do think of a core as a different combinatorial object.

just my 2 cents...

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Re: [sage-combinat-devel] Equality of objects

[Christian Stump]

Hi,

you find the same question here:
https://groups.google.com/d/topic/sage-combinat-devel/1zS_nkfqSSA/discussion

I would very much appreciate if we could get this fixed!

Cheers, Christian
http://www.stump.tv

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[sage-combinat-devel] Usage of the term Composition

[Christian Stump]

crossposting nbruin's comment from
http://trac.sagemath.org/ticket/14862#comment:6 :


The thing that mainly surprises me is that

sage: a=Hom(ZZ,ZZ)(1)
sage: b=Hom(ZZ,ZZ)(1)
sage: Composition(a,b)

fails. Composition is such an overused term in mathematics that I think
it's ill-advised to expose some specialist combinatorial notion of the term
in the global scope.


Cheers, Christian

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[sage-combinat-devel] Maximality for PairwiseCompatibleSubsets

[Christian Stump]

Hi,

I see that there is already an optional argument maximality=False in the
code of PairwiseCompatibleSubsets, but I don't see it used in the code -
and I actually vaguely remember Nicolas saying that this was not yet done.

I wonder if it would be hard to add the maximality feature to
PairwiseCompatibleSubsets, or if someone maybe even have it implemented
already...

Thanks, Christian

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[sage-combinat-devel] hashing only the list

[Christian Stump]

Hi all,

I am sure some of you have been thinking about that before:

sage: a = Permutation([3,2,1])
sage: b = Partition([3,2,1])
sage: c = Composition([3,2,1])
sage: a == b == c
True
sage: hash(a) == hash(b) == hash(c)
True

Is this desired behaviour?

Thanks, Christian

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Re: [sage-combinat-devel] hashing only the list

[Christian Stump]

Hi Nicolas,

 to use the Cythonized class
 ClonableList instead of CombinatorialObject: I just checked and
 ClonableList._hash_ takes the parent into account.

Thanks Nicolas! Is this still planned to happen in the not too far future?

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Re: [sage-combinat-devel] hashing only the list

[Christian Stump]

 That is, if we postpone the optimization of the various methods to take 
 better advantage of clonable lists, but that's ok.

would this eventually also improve the speed to check dict containment
of such elements?

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[sage-combinat-devel] combinatorial map decorators

[Christian Stump]

Hi all,

since Nathann started to hate combinatorial map decorators, I think
we can start yet another discussion if we want them or not here on the
mailing list.

I start with Nathann's comment on #14734:


The function's name is way too vague, and I think that it brings
absolutely nothing to Sage. It is just there to add an output to
find_stat, and has nothing to do in Sage.

I hate this patch.

Oh, and just to keep on being unpleasant : from time to time I write
long graph functions that I move to modules, and never import them to
Graph or DiGraph? class.

I do that because we already have a lot of methods in those objects,
and that they would not be useful to the vast majority of Sage users,
only to specialists. So I store them where they will only be found by
those who look for them.

If at the same time you add empty functions just to add maps to a
third-party project, I do feel like I waste my time when I do that.

But that was just to keep on being unpleasant.

Nathann


And my answer:


I do not agree that the combinatorial_map decorator doesn't have
anything to do with Sage. It organizes mathematical concepts by
providing the possibility to ask for things like:

- which involutions are there on permutations
- which bijections between 132-avoiding permutations and Dyck paths are there,

and so on. The decorator should even be able to carry information
about the maps (though this is not yet there), like injective,
surjective, bijective, ... And these mathematical information are
interesting and useful for Sage users!

Feel free to start a discussion about the decorators on the
sage-combinat mailing list, or to ask for a poll if the community
wants such decorators or not. I will at least copy your comment and my
answer there in order to get a discussion started.

Obviously, the decorator might have downsides. E.g., we have seen that
it not yet works well together with the cached_method decorator.

I will add some further points once we have a discussion started at
sage-combinat-devel.

Cheers, Christian


What do others think about decorating maps between combinatorial
objects by a decorator?

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[sage-combinat-devel] an algorithm generating random young tableaux of given shape

[Christian Stump]

Just for the records, in case we / someone is interested in such an algorithm:

http://mathoverflow.net/questions/128540/generating-random-young-tableaux-a-peculiar-probability-identity

Cheers, Christian

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[sage-combinat-devel] Posets are now upside down

[Christian Stump]

Hi,

Does anyone know if there is an easy way to draw posets from bottom to
top as we had it a while ago?

Cheers, Christian

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Re: [sage-combinat-devel] Posets are now upside down

[Christian Stump]

 latex or plot drawing?

Do you mean something like

sage: H = P.hasse_diagram()
sage: H.set_latex_options(format='dot2tex', prog='dot', layout='acyclic')
sage: view(H)

This gives the poset as well upside down.

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[sage-combinat-devel] Where to add a new road map

[Christian Stump]

Hi,

I wonder if we have a place to provide a road map for particular
projects (here: cluster algebras and quivers) where is more space than
on the road map on trac.

I thought, http://wiki.sagemath.org/combinat might be the right place,
but since there is nothing like that so far, I thought, I first ask
here...

Thanks, Christian

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Re: [sage-combinat-devel] Where to add a new road map

[Christian Stump]

 http://trac.sagemath.org/sage_trac/wiki/SageCombinatRoadMap


Thanks Anne, I added a link here, and created the new page on
http://sagemath.org/combinat/clusteralgebras

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[sage-combinat-devel] Canonical form for permutation groups

[Christian Stump]

Hi,

I wonder if there is a way to get a canonical form of a subgroup of a
permutation group (or, even better, any group). This would be
something like a method canonical_labeling for permutation groups
that returns an isomorphic permutation group, and such that two groups
are isomorphic if and only if their canonical labellings coincide.

I don't think anything like that is currently implemented, right?

A natural implementation would be to compute the multiplication
table of the group, apply the canonical form algorithm from graphs (by
simultaneous row and column permutations of the multiplication table),
obtain a canoncial form of the multiplication table, and turn this
data into a canonical form of a permutation group.

@Nathann et al.: would this be doable without too much effort from the
current algorithm for graphs? How far is the current implementation
from the possibility to take any n*n array (or square matrix, but with
no/less restrictions on the entries) and get it into a canonical form
by simultaneous row and column permutations?

Cheers, Christian

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Re: [sage-combinat-devel] Canonical form for permutation groups

[Christian Stump]

 In GAP one would just IdGroup() to get a unique label.

Is this given for any finite group in GAP, or is this depending on
http://www.gap-system.org/Packages/sgl.html ? It looks like there is
not much to do beyond these IdGroup in Sage since I guess they would
have gone beyond n=22 in Gap otherwise). On sage-devel, John Cremona
was basically suggesting the same as a unique labelling for small
groups.

   -  (1,2) 
   -  (2,3) 
   -  (1,2)(3,4) 
   - the multiplicative group ({-1,1}, *).

That is right, these should all result in the same group... and yes, I
forgot to add the action on the entries of the multiplication table.
So some canonical generating system on a particular subgroup of a
finite permutation group would not be enough.

Cheers, Christian

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Re: [sage-combinat-devel] Re: Adding data in patch

[Christian Stump]

 Make a database_foobar.spkg for your tables.

Thanks!

I did that, and everything seems to work (I can install the package
using sage -f cluster_seed-1.0.spkg). Could maybe someone have a look
at it 
(http://trac.sagemath.org/sage_trac/raw-attachment/ticket/13425/cluster_seed-1.0.spkg)
since I am not quite sure if I did everything right:

- I initialized the hg repo and added src to the .hgignore. But the
documentation doesn't say what to do then with it, so this repo is
still not tracking anything.

- In spkg-install, I basically only copy the raw files from src/ into
$SAGE_LOCAL/share/cluster_algebra_quiver. Is that what I should do? Or
do I have patch this?

- The documentation says that if I want to make the package standard,
I have to add it in the file SAGE_ROOT/spkg/install. But how do I get
this change into sage?

Thanks for your help! Christian

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[sage-combinat-devel] Adding data in patch

[Christian Stump]

Hi there,

I wonder if it is reasonable to add files containing precomputed data
to a patch. In our case, we are talking about 0.5mb of exceptional
mutation classes of clusters of Kac-Moody type. What would then be the
way to get these files into some subfolder of the data folder, or
where should such data be stored?

Thanks for your replies, Christian

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[sage-combinat-devel] Plotting a (multi-)graph

[Christian Stump]

Hi graph plotting people!

I have the following graph with loops and multiple edges:

sage: G = DiGraph()
sage: G.allow_loops(True)
sage: G.allow_multiple_edges(True)
sage: G.add_edges(
[('Binary trees', 'Binary trees', 'Left border symmetry'),
 ('Binary trees', 'Binary trees', 'Left-right symmetry'),
 ('Binary trees', 'Dyck paths', recursive map '1 L 0 R'),
 ('Binary trees', 'Dyck paths', recursive map 'L 1 R 0' (Tamari)),
 ('Dyck paths', 'Binary trees', recursive map '1 L 0 R'),
 ('Dyck paths', 'Integer partitions', 'to partition'),
 ('Dyck paths', 'Permutations', 'to 132 avoiding permutation'),
 ('Dyck paths', 'Permutations', 'to 312 avoiding permutation'),
 ('Dyck paths', 'Permutations', 'to 321 avoiding permutation'),
 ('Dyck paths', 'Permutations', 'to non-crossing permutation'),
 ('Integer partitions', 'Integer partitions', 'conjugate'),
 ('Integer partitions', 'Standard tableaux', 'initial_tableau'),
 ('Perfect Matchings', 'Permutations', 'to permutation'),
 ('Permutations', 'Binary trees', 'Binary search tree (left to right)'),
 ('Permutations', 'Binary trees', 'Increasing tree'),
 ('Permutations', 'Integer compositions', 'descent composition'),
 ('Permutations', 'Integer partitions', 'Robinson-Schensted tableau shape'),
 ('Permutations', 'Permutations', 'complement'),
 ('Permutations', 'Permutations', 'inverse'),
 ('Permutations', 'Permutations', 'reverse'),
 ('Set partitions', 'Integer partitions', 'shape'),
 ('Set partitions', 'Permutations', 'to permutation'),
 ('Standard tableaux', 'Integer partitions', 'shape'),
 ('Standard tableaux', 'Permutations', 'reading word permutation')]
)

Can someone (maybe you Nathann), tell me how to get a nice tikz
plot of this (using Sage, of course)? If there is no change to get
multiple edges, I could as well take the edge and provide a long
string (drawn maybe along the edge) to replace the multiple edge.

Help highly appreciated!

If I do something like

sage: G.remove_multiple_edges()
sage: opts = G.latex_options()
sage: view(LatexExpr(opts.tkz_picture()))

I always get latex errors. I will provide it if this might solve the problem.

Thanks, Christian

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Re: [sage-combinat-devel] Plotting a (multi-)graph

[Christian Stump]

 Can someone (maybe you Nathann), tell me how to get a nice tikz
 plot of this (using Sage, of course)? If there is no change to get
 multiple edges, I could as well take the edge and provide a long
 string (drawn maybe along the edge) to replace the multiple edge.

Thanks Nicolas, that worked!

Btw: to you happen to know how to draw edge labels along the edge (I
do get a lot of vertical edges with very long labels...).

Cheers, Christian

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Re: [sage-combinat-devel] Plotting a (multi-)graph

[Christian Stump]

 Not exactly an answer to your question, but you could maybe ask for a
 left-to-right layout instead of top to bottom?

thanks for the suggestion, but this is not really an option since I
get edges in all directions, however I turn it, I will have quite some
edges going north-south...

Cheers, Christian

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Re: [sage-combinat-devel] Re: Longest element in a Coxeter Group - name decision

[Christian Stump]

 Of
 course this would only be after it has been broken up into connected
 components. Perhaps I'm over simplifying things...

If I understand it right, Nicolas suggested to move that stuff the the
CoxeterGroups category. In this generality, this approach of checking
finite types doesn't work, but the other way round should be possible
by checking if the Cartan matrix is a finite type Cartan matrix.

Cheers, Christian

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[sage-combinat-devel] Permutation constructor bug

[Christian Stump]

Isn't that nice:

sage: Permutation(12)
ValueErrorTraceback (most recent call last)
...
ValueError: invalid literal for int() with base 10: ''

sage: Permutation(123)
[1, 2]

sage: Permutation(1234)
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
20, 21, 22, 23]

sage: Permutation(X14Y)
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]

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Re: [sage-combinat-devel] how do you tell what branch you are in?

[Christian Stump]

 When I start up sage-5.7.beta3 it doesn't tell me what branch I am using.
 Is there a way to tell?
 If there is a command in sage like 'branch()' it would be helpful.  How do I
 find it?

It usually tells you when starting sage (nothing for main, or current
brench is: ... otherwise). You can also go to the order devel and
check which brench the symbolic link sage points to.

Cheers, Christian

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[sage-combinat-devel] Re: The queue on 5.6.beta2

[Christian Stump]

Hi,

I wasn't able to get the queue running on 5.6.beta2 here - but I hope
I didn't introduce too many new problems trying...

@Travis: did you introduce #+5_6_beta1, 10193_rebase ? This way, one
cannot install the combinat queue anymore since sage -combinat
qselect doesn't understand this guard...

Sorry for possible mistakes, Christian

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[sage-combinat-devel] Re: The queue on 5.6.beta2

[Christian Stump]

Hi --

 Below are the results of my attempt to apply the queue on 5.6.beta2.

thanks for investigating!

 Christian: trac_8327_universal_cyclotomic_field-cs.patch needs to be rebased
 over your patches #13727 and #13728, which also need to be added into the
 queue.  (Unless I'm mistaken, the rebase just amounts to deleting the
 corresponding hunks from trac_8327.)

I just removed the UCF from the combinat queue; no one used it anyway
beside me... and I REALLY hope that it finally gets its final final
FINAL positive review soon!

Best, Christian

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[sage-combinat-devel] Lattice paths in Sage

[Christian Stump]

Hi,

I see that there is quite some stuff implemented for WordPaths. I
now wonder if someone already has code (or how much work would it be)
to provide the possibility of constructing WordPaths from a given
start point A to a given end point B that are contained in a region
given by linear (or polynomial, or other) inequalities. I do assume a
priori (since this is almost impossible to check in general, if I
recall correctly) that there are only finitely many paths from A to B.

This seems to be fairly easy to implement:

- if A and B coincide, use the empty path,
- otherwise check for every point A+S for a given step S if all given
inequalities are satisfied, and append S to all paths from A+S to B.

Similarly, one can obtain all paths within the region starting at A of
a given length. A more general question: what about finding by breadth
first search all finite length paths from A to B, even if there exist
paths of arbitrary length ? This must certainly be a known problem...

Such an implementation could be used to define all kinds of relatives
of Dyck and Schröder like paths (and also tons of others)...

Thanks, Christian

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[sage-combinat-devel] maximality condition for PairwiseCompatibleSubsets

[Christian Stump]

Hi --

I just got back to the problem that I would like to have the maximal
elements in what is currently called PairwiseCompatibleSubsets (and
this is at least the n-th time I am getting back to this). So I wonder
if anyone is going to look at this within finite time, or if I should
find a solution myself (which seems a little tricky since the iterator
comes from SearchForest, for which maximality doesn't necessarily make
sense).

Thanks, Christian

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Re: [sage-combinat-devel] Re: state of the queue: 5.4, 5.5.beta0

[Christian Stump]

Hi Travis,

 I've upgraded, so feel free to push your changes and I'll rebase #13605 as 
 needed.

I don't have anything to push, I am fine with the queue as is...

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Re: [sage-combinat-devel] Re: state of the queue: 5.4, 5.5.beta0

[Christian Stump]

Hi,

 The queue applies fine for me on plain 5.5.rc0.  Maybe your guards are not
 set correctly?  This is what is usually the problem for me when the queue
 seems to have suddenly gone wonky.

Thanks, Hugh, for rechecking! My mistake this time was that I was
reviewing Travis patch in the main sage branch (since sage-combinat
wasn't yet ready for 5.5.rc0). So installing sage-combinat first
cloned this branch, and then tried to push the patch again...

Best, Christian

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Re: [sage-combinat-devel] Re: state of the queue: 5.4, 5.5.beta0

[Christian Stump]

Hi,

 Thanks for doing this for me Travis and Nicolas! I've just synced and 
 everything is fine.

I now have again a reliable connection to test the queue.
Unfortunately, it still didn't work for me to install sage combinat on
a plain 5.5.rc0. I had to disable Travis' 12587 due to tons of
conflicts and to update my new version of the universal cyclotomics
(which hopefully make it into main sage soon, thanks to Frédéric!),
and then it worked again.

Since others didn't have this problem, I don't update the queue as
long as Travis doesn't ask me to do so (I also tent to make mistakes
in the process, so it might me my fault)...

Best, Christian

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Re: [sage-combinat-devel] Re: state of the queue: 5.4, 5.5.beta0

[Christian Stump]

 Thanks Travis. I just pulled your rebase off the queue and now #12876 is the
 only patch which does not apply for 5.5.rc0.

 As before, guarding out the #12876 patches let everything else in the queue
 apply, but sage won't build.

I would really appreciate if we could make the queue apply on 5.5.rc0,
if possible (or has this happened already without me noticing?).

Thanks, Christian

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Re: [sage-combinat-devel] Re: sage-combinat repo is still down

[Christian Stump]

 A sysadmin rebooted combinat.math.  He reports that Fyi, the status
 indicator on the front was displaying a multibit error on DIMM C7.
 After power cycling, the display came up blue (no errors).   It may be
 nothing, it may be the problem.   Just sharing in case it helps.

Thanks a lot for getting it running again - I was as well waiting with
my upgrade to 5.4!

Christian

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[sage-combinat-devel] Rebase of non_decreasing_parking_function.py touching patches

[Christian Stump]

Hi Nicolas and Frederic,

in patch

trac_13550_dyck_wordsdinv-addition-cs.patch

I had to modiffy non_decreasing_parking_function.py. This caused problems
in the two patches

finite_semigroup-nt.patch
catalan_quasi_symmetric-fc.patch

I added a rebase patch for each of the two afterwards. Please take over
these patches and fold into yours. (btw: I have seen that the
finite_semigroup patch make tons of doc tests fail in non_dec...)

Best, Christian

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Re: [sage-combinat-devel] revisions to dyck_word.py - suggestions for how to handle maps?

[Christian Stump]

 Christian had one way of handling this that I thought was OK, but I thought 
 not ideal.
 D.to_permutation(Bandlow-Kilpatrick)
 which is now
 D.to_312_avoiding_permutation()

 and

 D.to_permutation(Krattenthaler)
 which is now
 D.to_132_avoiding_permutation()

I do still prefer this approach since it really tells the user which
map is used (and as Nicolas pointed out some time ago, we might
eventually even get

D.to_permutation(tab

or

D.to_permutation(bijection=tab

to get a tab completion for optional arguments -- which would be
really cool, not only here but in general! )

 Christian may have more to add, because he has thought about this more than 
 I have and he is also motivated by the combinatorial statistics patch.

if I read

D.to_XYZ()

I generally think of a method that uses a somehow canonical map,
like D.to_partition, D.associated_parenthesis, D.to_area_sequence.
While I find it wired to say D.to_XYZ_avoiding_permutation, since
there is no canonical way to obtain it.

That's why I do prefer D.to_permutation (or any other to_XYZ) with an
obligatory argument specifying the desired map.

Second, the reason why I prefer not to specify the particular
permutation is that the user then must know in advance which subset of
permutations his desired map hits.

Since we now have two different opinions, we need at least a third
opinion to proceed :-)

Best, Christian

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Re: [sage-combinat-devel] trac_11187-finite_reflection_groups-cs.patch

[Christian Stump]

Hi Florent,

 +__len__ = None
 +

I removed it from my patch

 Do you think you will beat me

certainly not. The main problem is that we didn't get the universal
cyclotomics into Sage yet (hint, hint, hint for anyone), and this is
needed for the reflection group patch... And when this is done there
is still quite some work for the reflection group patch left.

Best, Christian

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Re: [sage-combinat-devel] queue broken for sage 5.3

[Christian Stump]

 I'm rather desperate (I didn't update because I needed a stable
 environment, but now it seems that the operating system was updated
 :-())

if you just want a working version old of the queue, the following might work

cd SAGE_ROOT/devel/sage-combinat
sage -hg update -r XXX
sage -hg qpop -a
sage -hg qpush -a

Here, XXX is a version of the queue that was still working on your
version of sage (if I don't make a mistake, for me XXX=7527 was
working for 5.3.rc1). Please report if this helps since others might
want to do the same if the queue is broken.

Best, Christian

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[sage-combinat-devel] lazily importing the cluster stuff?

[Christian Stump]

Hi,

Robert Bradshaw asked if we could lazily import all the cluster stuff,
and I somewhat agree (without really knowing all deeper implications).
Do we already have some standard procedure to do that with the
combinat stuff?

I was about to replace

from cluster_algebra_quiver.all import *

by

lazy_import(cluster_algebra_quiver, *, overwrite=False)

but since no one else did that before in there I first wanted to ask...

Thanks, Christian

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Re: [sage-combinat-devel] queue broken

[Christian Stump]

Hi Anne,

 sage -hg qselect
 sage -hg qpush -a

I don't know why I constantly forget to do so. Thanks for the reminder...

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[sage-combinat-devel] Macdonald polynomials for root systems

[Christian Stump]

This is something we should certainly have earlier or later (or maybe
someone has code already?):

http://mathoverflow.net/questions/105685/explicit-method-to-compute-macdonald-koornwinder-functions

Christian

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[sage-combinat-devel] queue broken

[Christian Stump]

Hi,

trac_13403-bijection_KR_crystals_tableaux-ts.patch doesn't apply on
5.2 . Since it is the newest version, we might want the queue to apply
there (even if most people updated to 5.3.??? already - I am now doing
so with 5.3.rc0).

Christian

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Re: [sage-combinat-devel] Re: Names for the bases of symmetric functions

[Christian Stump]

Quick and from the phone (since we are currently biking at the Baltic see):
I vote with Anne and Mike for homogeneous or complete homogeneous. Best,
Christian

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[sage-combinat-devel] images on the notebook at sage.lacim.uqam.ca

[Christian Stump]

Hi,

for the record: I updated sage.lacim.uqam.ca and now, the notebook
shows images again properly. I will give a presentation tomorrow at
the ICRA computer algebra session
(http://www.math.uni-bielefeld.de/icra2012/conference_tuesday.php), so
I am glad this issue was solved in 5.2!

Best, Chrstian

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[sage-combinat-devel] building sage 5.2 and higher

[Christian Stump]

Since there were still people having problems to install sage 5.2 (or
higher), here is a discussion on sage-support

https://groups.google.com/d/topic/sage-support/p4VfY9nxsyE/discussion

For Travis an me, it worked after instaling libssl-dev as described there.

Best, Christian

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Re: [sage-combinat-devel] Re: Trac 9265: Remove `CombinatorialClass` from sage.combinat.tableau

[Christian Stump]

 It should apply cleanly to 5.2. Assuming you fix that and repost it,

unfortunately, 9265 does not apply anymore on 5.1...

Best, Christian

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Re: [sage-combinat-devel] Re: how to rebase a patch ?

[Christian Stump]

 what I usually do is:

this is a very nice and detailed description -- thanks! maybe you
wanna add it to wiki?

  * hg qrefresh followed by hg export qtip  foo.patch

is there, in this situation, a difference between hg export qtip 
foo.patch and hg qrefresh (that's what I usually do here) ?

Thanks, Christian

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Re: [sage-combinat-devel] Sage Days 40: Anne, Nicolas, and Daniel

[Christian Stump]

 P.S. Can you/someone please review my massive coxeter patch,
 which has been languishing for months?

I will look at it some day in Japan in the next two weeks...

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Re: [sage-combinat-devel] combinatorial statistics

[Christian Stump]

 sage -combinat qselect 


Thanks, I accidentally did sage -qselect instead...

I pushed the changes.

Best, Christian

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Re: [sage-combinat-devel] combinatorial statistics

[Christian Stump]

Hi Martin,

 one patch per class?

that's completely up to you, I guess

 Another question: is it important to keep the number of statistics
 small?  I.e., if a statistic can be constructed via a map, is it better
 *not* to implement it?  (Eg., saliances and right-to-left-minima.)

I usually do implement them, and add it then to the black list of the
combinatorial map. Otherwise we would even not have maj or inv since
the bijection sending maj to inv is also implemented.

 How about aliases?  (I would like to have right-to-left-maxima be an
 alternative name to saliances...)

we already use them some times. only the decorated one will appear,
not the alias.

best, christian

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Re: [sage-combinat-devel] combinatorial statistics

[Christian Stump]

 I just pushed a change to composition.py which breaks your patch.

I rebased the patch and also enabled Mike's patch again. But now, I
get the following error message after applying the queue, so I don't
push the changed...

Any idea (I am using 5.0)?

--
sage: Building and installing modified Sage library files.


Installing c_lib
scons: `install' is up to date.
Updating Cython code
Building modified file sage/categories/action.pyx.
Building modified file sage/categories/category_singleton.pyx.
Building modified file sage/categories/morphism.pyx.
Building modified file sage/categories/examples/semigroups_cython.pyx.
Building modified file sage/structure/list_clone.pyx.
Building modified file sage/structure/list_clone_demo.pyx.
Building sage/structure/list_clone_timings_cy.pyx because it depends
on sage/structure/list_clone.pxd.
Building modified file sage/sets/finite_set_map_cy.pyx.
Building modified file sage/combinat/dict_addition.pyx.
Traceback (most recent call last):
  File setup.py, line 830, in module
queue = compile_command_list(ext_modules, deps)
  File setup.py, line 790, in compile_command_list
dep_file, dep_time = deps.newest_dep(f,m)
  File setup.py, line 697, in newest_dep
for f in self.all_deps(filename, ext_module):
  File setup.py, line 678, in all_deps
for f in self.immediate_deps(filename, ext_module):
  File setup.py, line 660, in immediate_deps
self._deps[filename] = self.parse_deps(filename, ext_module)
  File setup.py, line 648, in parse_deps
raise IOError, msg
IOError: could not find dependency
sage/combinat/enumeration_mod_permgroup.pxd included in
sage/combinat/invariant_ring_perm_gps/invariant_cython.pyx.
Error installing modified sage library code.

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Re: [sage-combinat-devel] combinatorial statistics

[Christian Stump]

Hi Martin.

 Eg., for personal enjoyment, I just added decorators to
 number_of_crossings and number_of_nestings in perfect matchings.
 (Christian: it works now, I made a stupid mistake)

good - any comments are welcome.

 I see that there is a patch
 concrete_combinatorial_statisics_and_maps_cs.  Should I send patches of
 this patch to Christian, should I create a new one (if so, one for each
 class?), or should I keep this for personal enjoyment?

The decorator is implemented in
combinatorial_statistics_and_maps_decorator-cs.patch, the concrete
examples in the one right after. Please don't modify the later
(concrete_combinatorial_statisics_and_maps_cs.patch) since I am again
and again changing it. But you cad add another patch whereever you
want after the first patch and use the decorators.

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Re: [sage-combinat-devel] Re: Sage install party FPSAC

[Christian Stump]

Hello,

(sorry for my late reply!)

I will also be there and can help with a sage session.

But the candidate of the time of the session is 
 the same time of the poster session on Monday, 
 the same time of the poster session on Tuesday, or 
 the time after all talks on Thursday before the banquet. 


Those 3 candidates are certainly no good options though. I definitely want 
to go to the poster sessions (and I guess most if not all others wanna go 
as well).

Btw: Chris Berg also asked for a software demo of our web-based statistic 
finder www.findstat.org, but I don't know the current status of when and 
were we are going to do it...

Best, Christian

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[sage-combinat-devel] Re: namings for eulerian and mahonian statistics

[Christian Stump]

Hi --

Thanks for your replies!

 really be returning
         return self._parent

(I just made the same change after copying your code...)

here is a disadvantage of this solution:

sage: d = DyckWord([])
sage: d.maps._parent.maps._parent.maps._parent.maps.map1()
[]

which seems to be strange (what I find strange about it is that it is
possible that A and B can be attributes of each other - but it seems
even be possible that A has itself as an attribute...).

Nevertheless, I also prefer this solution for now.

Other thoughts?

Christian

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[sage-combinat-devel] Re: namings for eulerian and mahonian statistics

[Christian Stump]

 My problem here is that on my computer maps? or maps?? is slow, while
 maps.tab is fast.  I don't know if others have this problem (maybe thats
 what happens if you drop your computer and spill wine on it :)

 The other disadvantage is that (short of a copy/paste) you still have to
 type out the full name accessing the function rather than the first few
 characters + keystroke.

same here.

 I know that the 'name_.' is not standard, but it will require new notation
 to organize the namespace and I was thinking of examples like:

I don't (yet) see an advantage of using name_. rather than name. .
I have the feeling that a user seeing .statistics in tab completion
understands that this is not unique and that he will get more when
hitting .statistics.tab . So using

statistics? would give the doc string containing an explanation of the
concept of combinatorial maps together with some example, and hitting

statistics.area? would give the description of this particular statistic.

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Re: [sage-combinat-devel] Re: namings for eulerian and mahonian statistics

[Christian Stump]

 I also like that.  One further (?) idea:

 .maps(codomain)

 could be a way to access all maps with the given codomain.  (I don't
 know how one could specify the codomain however.)

 In particular,

 .maps(ZZ)

 would yield all integer valued statistics.

The problem I see here is that whenever a method returns the same kind
of object, it is a map somehow. To organize the code, I would rather
restrict to (the obviously not strictly defined concepts of)
combinatorial maps and combinatorial statistics. And having an
optional argument has the problem that 1. the user must know the
codomain already and cannot easily search all maps to other
combinatorial objects and 2. that it is then a method and we have the
tab completion problem as Mike explained for the situation as for
symmetric functions.

Or did you think of some other way to reach this?

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Re: [sage-combinat-devel] Re: namings for eulerian and mahonian statistics

[Christian Stump]

Hi --

I already asked this, but no one seemed to have an opinion on that...

I have now implemented 5 or 6 bijections between Dyck paths and
subsets of permutations (pattern-avoiding or noncrossing). I think
that it is not practical to have a name for each of them since they 1.
do not necessarily have names in the literature and 2. the list of
methods for Dyck paths (and actually many other objects) becomes more
and more confusing in tab completion which I find not very user
friendly.

I currently have

DyckWord.to_permutation(bijection=None)

and then the optional argument bijection is used to differ between the
bijections. But another solution would actually be to have

sage: d = DyckWord([])
sage: d.to_permutation.tab

yields a list of all possible maps

and even more

sage: d.statistics.tab

yields a list of all combinatorial statistics (Anne actually requested
such a use case some time ago). Using this behavior would make the
statistics not appear directly when typing

sage: d.tab

Only statistics would appear here. The same maybe for maps, then we
would not have

sage: d.to_permutation.tab

but

sage: d.maps.tab

would give a list of maps and

sage: d.maps.to_permutation.tab

then the list of maps to permutations. This way, we would have a
better organization of the combinatorial maps and statistics (which
would be very helpful, I guess, if we keep implementing more and more
of these), and the tab completion becomes arranged in a user readable
way.

a. what do you think about such a design?

b. it seems to be not standard in object-oriented programming. what
are the down-sides?

c. i would have no idea how to reach such an implementation.

Best, Christian

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[sage-combinat-devel] namings for eulerian and mahonian statistics

[Christian Stump]

Hi,

I am currently implementing some (simple to implement and not yet very
well studied) statistics for permutations. The main problem I have is
that they don't come with (or even have any) descriptive names, so I
wonder what to do, as an example, see
http://www-irma.u-strasbg.fr/~guoniu/papers/p17maf.pdf Section 3 A
new mahonian statistic 'maf' . (Yes, I do that for the findstat
project, and yes, I hope that this will lead to new ways to find out
things about not well-studied permutation statistics).

I think of using them like

sage: pi = Permutation([2,3,1])
sage: pi.mahonian_statistics.maf_index()
2

but also

sage: pi.statistics.maf_index()

So the same method could appear in different places (like major_index
would appear in both collections above, but also as a plain method
for permutations.

Q1. Do you think this would help organizing the methods for permutations?
Q2. Does anyone know how to do such an implementation?
Q3. Any other / better ideas?

Best, Christian

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Re: [sage-combinat-devel] Re: namings for eulerian and mahonian statistics

[Christian Stump]

Hi Mike,

 Add http://arxiv.org/pdf/math.CO/0310301.pdf to the list of
 permutation statistics.

I will - in return I should ask to contribute something (whatever you
like) to the wiki at www.findstat.org ;-). I am currently trying to
add content to the page for permutations
www.findstat.org/Permutations/ and associated statistics... any kind
of contribution is very appreciated!

Best, Christian

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Re: [sage-combinat-devel] Re: namings for eulerian and mahonian statistics

[Christian Stump]

Hi Mike,

your statistic made its way already.

 I have a few things to say about dinv/area on Dyck paths that you don't 
already have there.

:-) cool, go for it! If you have questions or remarks on the wiki
(like adding references, see any other page or
www.findstat.org/How%20to%20contribute#References for examples), let
me know...

Thanks, Christian

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Re: [sage-combinat-devel] Re: namings for eulerian and mahonian statistics

[Christian Stump]

Hi Mike,

 your statistic made its way already.

some dependency the finder tells you: did you know that pi.baj_index()
+ pi.reverse().baj_index() == \binom{n+2}{3} ?

Best, Christian

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Re: [sage-combinat-devel] Re: namings for eulerian and mahonian statistics

[Christian Stump]

Hi --

does anyone have an idea why this might be true:

n * pi.inverse().number_of_descents() ==
pi.insertion_tableau().major_index() +
pi.insertion_tableau().cocharge()

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[sage-combinat-devel] Drawing intervals in Weyl groups

[Christian Stump]

Hi --

someone is asking for software to draw intervals in Weyl groups, see
http://mathoverflow.net/questions/98477/software-for-drawing-intervals-in-weyl-groups
.

Maybe someone can get him a satisfactory answer (and point him to
sage.lacim.uqam.ca to get all sage-combinat features).

Moreover, I just tried to show some simple examples, and see the
following annoying things from a user perspective:

- I want to show a Bruhat interval with vertices being reduced words,
then I must first define a vertex labelling by w:w.reduced_word() but
since this is a list, we also need to turn it into a tuple,
w:tuple(w.reduced_word()). Not very nice for a first-time user.

- I want to change the size of the vertex labels, but that doesn't work.

- I want to change the color of the vertex labels, but that doesn't work.

I won't have time today to fix that, but what do you think about
turning reduced expressions into tuples (they should immutable
anyway). What about the other things?

I have to leave my train... christian

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Re: [sage-combinat-devel] constructing the same poset twice

[Christian Stump]

 sage: P = lambda n : Poset([range(n), [(i,i+1) for i in range(0,n,2)]])
 sage: time p = P(1); p
 Time: CPU 2.24 s, Wall: 2.60 s
 Finite poset containing 1 elements
 sage: time p = P(1); p
 ...takes much, much, much longer then 2s...still hasn't finished...

same here -- do you already know where that comes from?

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Re: [sage-combinat-devel] queue broken

[Christian Stump]

Hi!

 There is a break in sage between patch

 trac_12895-subcategory-methods-nt.patch
 trac_8327_universal_cyclotomic_field-cs.patch

fixed -- it was actually Mark closing the last link for the import
loop by importing

from sage.graphs.digraph import DiGraph

in categories/weyl_groups. I updated his patch accordingly (Mark,
please pull my changes before changing your patch!).

I still don't know how to properly do the importing. E.g., here we have

...
-- 243 from sage.combinat.free_module import CombinatorialFreeModule
...
--- 28 from sage.categories.all import ModulesWithBasis
...
-- 126 from weyl_groups import WeylGroups
127 from finite_weyl_groups import FiniteWeylGroups
128 from affine_weyl_groups import AffineWeylGroups

why does something low level like combinatorial free module or
modules with basis import weyl groups ? Or are categories always
considered to be lower ?

Best, Christian

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Re: [sage-combinat-devel] queue broken

[Christian Stump]

Hi,

unfortunately, the queue is still broken at
trac_12940_affine_permutations-td.patch.

Christian

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Re: [sage-combinat-devel] queue broken

[Christian Stump]

 Fixed. See other thread (NCSF/trac_12940_affine_permutations-td.patch)

thx, but don't forget to push, please!

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Re: [sage-combinat-devel] bug in poset

[Christian Stump]

 The definition of grading is that all maximal chains of every interval
 have the same length. This is given in the above poset, but sage says
 it is not graded.

The problem here is what people consider a rank function on a poset.
Do we want that all minimal elements have value 0 ? Then your poset is
indeed not graded. Or do we only want that some element has value 0 ?
Then your poset is graded. But if we take the later, what are then the
levels of a poset? Are all minimal elements in level 0 (which seems
to me like a good choice), or are the levels given by your grading?

I think you're right since the existence of a rank function seems to
be common sense as the definition
(http://en.wikipedia.org/wiki/Graded_poset) (this is equivalent to
your definition for locally finite posets). But then, we have to make
a choice for the levels of a poset.

My 2 cents, Christian

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Re: [sage-combinat-devel] root lattice realizations and Weyl groups

[Christian Stump]

Hi,

 How much are you altering root systems right now?
 I was planning to put a small amount of new stuff in my coxeter-ms patch
 but don't want it to break whatever you are doing.

go ahead, I am not doing any major things in there currently. if you
happen to break some of my stuff, let me know - I will then (try to)
fix it.

Best, Christian

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[sage-combinat-devel] on DyckWords

[Christian Stump]

Hi,

I am currently working on filling the wiki at www.findstat.org with
more data, since Chris Berg and I are going to present it at the FPSAC
this summer.

I would like to make the following changes to Dyck words:

1. changing a-statistic, b-statistic, d-statistic to area, bounce,
dinv (and leaving the old with a warning).
2. changing the to_partition to return the partition when cutting out
the path above the diagonal (currently, the transposed is returned).

Is that okay with everyone?

Christian

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Re: [sage-combinat-devel] on DyckWords

[Christian Stump]

Hi Florent,

 What so you mean by changing them ? Do you mean changing the name ?

yes.

 ok with area

 but I'd rather have number_of_bounce

but number of bounces is the the number of bounce points, while bounce
(being the sum of the heights of the bounce points, equal distributed
with area and dinv) is the statistic introduced by Jim Haglund [1] and
further studied in several papers by Garsia/Haglund/Haiman. So I would
vote for bounce.

 and spelling explicitely inversion in dinv

dinv stands for diagonal inverse introduced by Mark Haiman in [2].
dinv or diagonal_inverse would both be fine for me. Or do you
think of number_of_diagonal_inverses ?

 Do you have a reason for that ? I wrote this one because we needed it for
 k-shape and the convention I took seemed at that time more natural to me. I
 don't mind changing the convention and patching my code if there is a good
 reason for that.

Basically, because I usually think of a Dyck path being above the
diagonal, then cutting out the Dyck path from the staircase shape
gives the partition I proposed. This is also the partition considered
in the sequence of papers mentioned above.

Best, Christian

[1] Haglund - Conjectured statistics for the (q,t)-Catalan numbers
[2] Haiman - some paper, I can find the name if needed (:-))

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Re: [sage-combinat-devel] Re: queue broken

[Christian Stump]

Hi all --

I just see that finally (!!!) 5.0 is out:
ftp://ftp.fu-berlin.de/unix/misc/sage/devel/index.html (you might want
to choose a different mirror though). I am currently compiling it on
Ubuntu 12.04 and OSX Lion with XCode 3.2 (?). Since nothing changed
since 5.0.rc1, I would propose to make the queue apply properly here,
and drop queue support for everything before. So many things changed
and some people (Nicolas and Florent, thanks again!) spent tons of
time getting the queue applying on older versions, including
5.0.beta??'s -- I guess it is worth that everyone working on the queue
should run 5.0...

Christian

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[sage-combinat-devel] docstring in CartanType and CartanTypeFactory

[Christian Stump]

Hi --

I have a question on proper documentation:

Hugh and I are currently finalizing the QuiverMutationType and have
the following problem: the file is organized similarly to CartanType,
so we have a factory delegating the work to reducible or irreducible
classes, or giving samples. In CartanType, we have a long docstring
for the file and a shorter for the call method saying in the end SEE
ALSO: func:`~sage.combinat.root_system.cartan_type.CartanType`.

But when I do

sage: sage.combinat.root_system.cartan_type.CartanType??

I get back exactly this docstring.

1. In which case do I actually see the docstring for the file itself?

2. Is it a bug that the CartanTypeFactory.call docstring is short and
is again obtained when looking at the see also of itself?

3. What would be a proper way of organizing the documentation here?

Thanks! Christian

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Re: [sage-combinat-devel] Posets nightmares

[Christian Stump]

 But come on Just look at that !!!

 sage: P = Poset( (range(len(p)), comparison) )

What happens if you add facade=True ?

 sage: P = Poset( (range(len(p)), comparison), facade=True )

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Re: [sage-combinat-devel] Broken queue

[Christian Stump]

 There was still an issue upon running Sage. Travis: I temporarily
 disabled your patch altogether, because it was conflicting with
 another one.

you guys are still working? Pas mal!

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Re: [sage-combinat-devel] Default basis ring for ambient space

[Christian Stump]

Salut --

I just got up, and would push the base ring change for root / weigth /
ambient spaces.

But somehow, my patch has tons of doctest failures due to

sage: ct = CartanType(A1)
sage: P = ct.root_system().root_space()
sage: X = TestSuite(P)
sage: X.run()
Failure in _test_root_lattice_realization:
tester.assert_(self.coerce_map_from(root_space  ) is not None)
AssertionError: False is not true

The following tests failed: _test_root_lattice_realization

But I don't understand why self.coerce_map_from(root_space) is None
now..., I will have a look later.

Best, Christian

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Fwd: [sage-combinat-devel] Default basis ring for ambient space

[Christian Stump]

Hi Viviane,

 This type of thing just broke my entire patch on multivariate
 polynomials. I had to fix it by changing the field to ZZ or QQ but I
 wonder why the default field has been changed...

sorry for that!

the reason is that I implemented non-crystallographic root systems and
reflection groups. That's why I changed the default ring to be the
universal cyclotomics (which is the smallest field containing the
integers and all roots of unity). But I agree that in the
crystallographic types (where everything works over the integers), we
still should have things working over ZZ.

This patch is still very much under construction, so I expect myself
to make tons of further changes. I will hopefully find some time tod

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[sage-combinat-devel] Re: TransitiveIdeal - TransitiveIdealGraded in RootLatticeRealization ?

[Christian Stump]

here is an example (I think, it looks quite nice, doesn't it?)

sage: RS = CartanType(['A',2,1]).root_system().root_space()
sage: X = iter(TransitiveIdealGraded(attrcall(pred),RS.simple_roots()))
sage: i = 0
sage: while i  25:^Jx = X.next()^Jprint i,x^Ji += 1
: 
0 alpha[0]
1 alpha[1]
2 alpha[2]
3 alpha[0] + alpha[1]
4 alpha[0] + alpha[2]
5 alpha[1] + alpha[2]
6 2*alpha[0] + alpha[1] + alpha[2]
7 alpha[0] + 2*alpha[1] + alpha[2]
8 alpha[0] + alpha[1] + 2*alpha[2]
9 2*alpha[0] + 2*alpha[1] + alpha[2]
10 alpha[0] + 2*alpha[1] + 2*alpha[2]
11 2*alpha[0] + alpha[1] + 2*alpha[2]
12 3*alpha[0] + 2*alpha[1] + 2*alpha[2]
13 2*alpha[0] + 2*alpha[1] + 3*alpha[2]
14 2*alpha[0] + 3*alpha[1] + 2*alpha[2]
15 2*alpha[0] + 3*alpha[1] + 3*alpha[2]
16 3*alpha[0] + 3*alpha[1] + 2*alpha[2]
17 3*alpha[0] + 2*alpha[1] + 3*alpha[2]
18 3*alpha[0] + 3*alpha[1] + 4*alpha[2]
19 4*alpha[0] + 3*alpha[1] + 3*alpha[2]
20 3*alpha[0] + 4*alpha[1] + 3*alpha[2]
21 4*alpha[0] + 4*alpha[1] + 3*alpha[2]
22 4*alpha[0] + 3*alpha[1] + 4*alpha[2]
23 3*alpha[0] + 4*alpha[1] + 4*alpha[2]
24 4*alpha[0] + 5*alpha[1] + 4*alpha[2]

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