>
> Andrew, does this mean, that your patch when ready will actually take care
> of the tickets mentioned?
>
>
Not really. What I have been doing provides a different way of displaying
tables from inside sage (rather than specifically from the notebook). What
I am doing provides a different way of solving the problems in these
tickets but it will not solve the actual problems.
There are two components to what I am doing:
1. A LabelledMatrix class which has some overlap with John's patch
#13131, which I have only just learnt about.
2. A new (one way) html interface, HTMLDisplay, which opens a web page -
in the sage documentation style - for the pretty printing of sage objects.
I am writing this mainly so that I can display and work with "large" tables
although I am trying to make the class as general as possible in the hope
that it will be useful to someone else.
Except for the documentation, and hence many minor fixes, the
LabelledMatrix class is basically done (although now I clearly need to talk
with John and work out what he has done...).
I have a working prototype for the HTMLDisplay class but I still need to
throw in the css/html for my application -- tables with fixed row/column
labels and with scrollable entries.
The focus of my LabelledMatrix class seems to be a little different to
John's patch #13131. What I really want/need is a way of labelling and
accessing the entries of a matrix using the combinatorial data that labels
its rows and columns - given the focus on the combinatorics, at one point
my class was called CombinatorialMatrix.
The idea is that virtually any sage object can be used to label the rows
and columns of a matrix, and to access it's entries. It is also possible to
associate CombinatorialFreeModules with the row and column spaces in a
natural way.
As an example, my class lets you do the following (the formatting is a
little mucked up...):
sage: P4=CombinatorialFreeModule(ZZ,Partitions(4),prefix='P')
sage: K4=KleshchevPartitions(3,4) # labels irreducible modules in
characteristic 3
sage: d=LabelledMatrix(rows=P4,columns=K4, unitriangular=True,
default_value=0)
sage: d.display()
[4] |
[3, 1] | 1
[2, 2] | . 1
[2, 1, 1] | . . 1
[1, 1, 1, 1] | . . . 1
sage: d.options(row_label='compact_high'); d.display()
4 |
3,1 | 1
2^2 | . 1
2,1^2 | . . 1
1^4 | . . . 1
sage: d[[1,1,1,1]]
P[[1, 1, 1, 1]]
sage: d[[2,2],[1,1,1,1]]=2
sage: d[[2,2]]
2*P[[1, 1, 1, 1]] + P[[2, 2]]
sage: d[[2,2]] in P4
True
Here is a second example:
sage: d=LabelledMatrix(rows=Partitions(5), columns=['dim S(mu)','dim
D(mu)'],default_value=0)
sage: for mu in d.rows(): d[mu,0]=StandardTableaux(mu).cardinality()
sage: d[:,1]=[0,0,4,6,1,4,1] # a work around until graded Specht
modules are merged
sage: d.options(row_label='compact_high',col_label='repr',
name='Dimensions in characteristic 3')
sage: d.display()
Dimensions in characteristic 3
---------------------------
| dim S(mu) dim D(mu)
------|--------------------
5 | 1 .
4,1 | 4 .
3,2 | 5 4
3,1^2 | 6 6
2^2,1 | 5 1
2,1^3 | 4 4
1^5 | 1 1
sage: d.transpose().display()
Dimensions in characteristic 3
-----------------------------------------------------
| 5 4,1 3,2 3,1^2 2^2,1 2,1^3 1^5
----------|------------------------------------------
dim S(mu) | 1 4 5 6 5 4 1
dim D(mu) | . . 4 6 1 4 1
When the LabelledMatrix is actually a matrix then all of the matrix methods
are available to it -- but without tab-completions, and sometimes with
embellishments as above. For example, the inverse of an invertible labelled
matrix is again a labelled matrix (of course, the default labelling sets
won't always be mathematically correct...).
The LabelledMatrix class is intended to be used as a base class for
building richer classes for working with things like decomposition
matrices, character tables, Cayley tables, homomorphisms of combinatorial
free modules, .... Such classes would set the many (cumbersome) options to
a LabelledMatrix as well as provide new methods. The applications that I am
most interested in are decomposition matrices and homomorphisms, but as a
test case I wrote a rudimentary wrapper for character tables which lets you
do things like:
sage: ct=CharacterTable(G); ct.display()
Character table of Symmetric group of order 5! as a permutation group
-------------------------
| 1a 2a 2b 3a 6a 4a 5a
---|---------------------
X0 | 1 -1 1 1 -1 -1 1
X1 | 4 -2 0 1 1 0 -1
X2 | 5 -1 1 -1 -1 1 0
X3 | 6 0 -2 0 0 0 1
X4 | 5 1 1 -1 1 -1 0
X5 | 4 2 0 1 -1 0 -1
X6 | 1 1 1 1 1 1 1
sage: ct['X3']
[6, 0, -2, 0, 0, 0, 1]
sage: ct[3]
[6, 0, -2, 0, 0, 0, 1]
sage: ct[:,'3a']
[1, 1, -1, 0, -1, 1, 1]
My HTMLDisplay class is still rather rough. It's aim is to display sage
objects in a web browser or, if you like, extreme pretty printing. The
information exchange is one way: sage opens a window/tab in your browser
but the browser cannot communicate with sage. Rather than just displaying a
single sage object, the aim of HTMLDisplay to construct, and crudely edit,
an HTML page which can contain many sage objects. The web pages constructed
by HTMLDisplay are modelled on the sage documentation pages. As one
application (using LabelledMatrices), I would like to be able to display
all of the decomposition matrices of the symmetric groups in characteristic
p for n\le 20, say, and a fixed prime p.
For most sage objects I doubt an HTML interface is necessary, however, for
a large matrix (such as a decomposition matrix) even printing it is not so
useful because it is just too big. My initial goal is simply to be able to
scroll the entries of the table (in the browser) whilst keeping the row and
column labels fixed. Modulo the css specifications, which I have in some
other code, this is almost done too. There are still many sharp corners to
smooth out, however, and I may not be able to work on this for a few more
weeks.
Finally, I guess that there is a third aspect to all of this which I
haven't though about yet: ultimately, I also want to write an interface
between LabelledMatrices and an (SQLite?) database for storing an
retrieving decomposition matrices...
Andrew
Andrew
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