Mutability of tableaux part I: lists of tuples instead of lists of lists

[darijgr]

Tableaux in Sage used to be implemented as lists of lists. The outer list was wrapped in a CombinatorialObject, which made it immutable (at least without accessing underscored attributes). The inner lists, however, could be easily mutated; for example:

sage: T = Tableau([[1,2],[2]])
sage: t0 = T[0]
sage: t0[1] = 3 
sage: T
[[1, 3], [2]]

This kind of mutability was likely not intended. I, personally, have only ever triggered it by accident.

The present branch replaces the inner lists in the implementation of tableaux and skew tableaux by tuples. As a consequence, tableaux become completely (rather than just shallowly) immutable (unless their entries themselves are mutable, which can be blamed on the user). They are still printed as lists of lists, but this is just a _repr_ issue.

The branch also makes some optimizations and corrections.

---

Old description:

Tableaux in Sage are mutable objects, at least indirectly:

sage: T = Tableau([[1,2],[2]])
sage: t0 = T[0]
sage: t0[1] = 3 
sage: T
[[1, 3], [2]]

This in itself is probably not a bug, although not the kind of behavior I like either (what exactly is sped up by mutability of tableaux?). But there are things which probably are bugs given this behavior:

1. Tableaux are hashed by reference:

sage: T = Tableau([[1,2],[2]])
sage: hash(T)
-7723024261707595164
sage: T[0][1] = 4
sage: hash(T)
-7723024261707595164

2. Line 311 of sage/combinat/tableau.py says:

            # Since we are (suppose to be) immutable, we can share the underlying data

But we are not immutable. This comment line is supposed to provide justification for initializing the tableau as a CombinatorialObject, but the docstring of CombinatorialObject says that "CombinatorialObjects are shallowly immutable, and the intention is that they are semantically immutable". The latter is not satisfied for tableaux.

If we want tableaux to be mutable, why wrap them inside such a class? If we want them to be immutable, wouldn't it be right to encode them as CombinatorialObjects of CombinatorialObjects? Or is the speed cost for this too steep? And, finally, what is it that CombinatorialObject does that tuple does not?

And, on a related note, does Sage provide a class for immutable dictionaries? (I'm still hell-bent on implementing arbitrary-shaped tableaux.)

3. Mutating tableaux poisons type judgments (or what passes for type judgments in Sage):

sage: T = StandardTableau([[1,2],[3]])
sage: T[0][1] = 5
sage: isinstance(T, StandardTableau)
True

4. There is some action at a distance (although fortunately rare):

sage: T = SkewTableau([[1,2],[3]])
sage: S = T.to_tableau()  # Tableau(S) doesn't work, wondering if it should?
sage: S
[[1, 2], [3]]
sage: T
[[1, 2], [3]]
sage: T[0][1] = 5
sage: S
[[1, 5], [3]]
sage: T
[[1, 5], [3]]

5. How would I define Loday's Hopf algebra of tableaux if tableaux are mutable?

CC: @anneschilling @tscrim @nthiery @stumpc5 @AndrewAtLarge @zabrocki @sagetrac-sage-combinat @hivert @sagetrac-jpswanson

Component: combinatorics

Keywords: tableaux, sage-combinat, mutability, days64

Stopgaps: #17997

Author: Josh Swanson, Jan Keitel, Darij Grinberg

Branch/Commit: 430003d

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/15862

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

9ce201e

one less to_word

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from b68a79b to 9ce201e

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 9ce201e to 81d3af3

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

93c6448	an even more hands-off approach to testing iterability
81d3af3	Merge branch 'public/15862' of git://trac.sagemath.org/sage into tableau_verynew

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

fcf411c

last edits

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 81d3af3 to fcf411c

[darijgr]

comment:40

This is ready for review.

There are minor slowdowns in skew_tableau.py left, relating to the tuple-cast in its initialization. I don't know if they are avoidable.

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from fcf411c to 4520047

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

4520047

put checking into `__init__` and normalization into __classcall_private__

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

8c19ad3

so normalizaton is necessary in the init too

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 4520047 to 8c19ad3

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 8c19ad3 to 430003d

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

430003d

actually, probably no need for normalization in __classcall_private__

[darijgr]

Author: Josh Swanson, Jan Keitel, Darij Grinberg

[darijgr]

Changed work issues from see if skew tableaux have gotten slower to none

[darijgr]

Description changed:

--- 
+++ 
@@ -1,3 +1,22 @@
+Tableaux in Sage used to be implemented as lists of lists. The outer list was wrapped in a `CombinatorialObject`, which made it immutable (at least without accessing underscored attributes). The inner lists, however, could be easily mutated; for example:
+
+```
+sage: T = Tableau([[1,2],[2]])
+sage: t0 = T[0]
+sage: t0[1] = 3 
+sage: T
+[[1, 3], [2]]
+```
+This kind of mutability was likely not intended. I, personally, have only ever triggered it by accident.
+
+The present branch replaces the inner lists in the implementation of tableaux and skew tableaux by tuples. As a consequence, tableaux become completely (rather than just shallowly) immutable (unless their entries themselves are mutable, which can be blamed on the user). They are still printed as lists of lists, but this is just a `_repr_` issue.
+
+The branch also makes some optimizations and corrections.
+
+---
+
+Old description:
+
 Tableaux in Sage are mutable objects, at least indirectly:

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:47

LGTM.

[darijgr]

comment:48

Thank you, Travis!

[vbraun]

Changed branch from public/15862 to 430003d