Opened 4 years ago

Closed 4 years ago

#17693 closed enhancement (fixed)

mutable poset: a data structure for asymptotic expressions

Reported by: dkrenn Owned by:
Priority: major Milestone: sage-6.9
Component: asymptotic expansions Keywords: asymptotics
Cc: behackl, cheuberg, jmantysalo Merged in:
Authors: Daniel Krenn Reviewers: Benjamin Hackl, Clemens Heuberger
Report Upstream: N/A Work issues:
Branch: a0b3d7b (Commits) Commit: a0b3d7bce3325e271e53b0a83047a6f80ac28a22
Dependencies: Stopgaps:

Description

The aim of this ticket is to implement a data structure which is to be used within an asymptotic expression (see Meta-Ticket #17601). This mutable poset stores elements together with its successors and predecessors. Those data is updated when a new element is inserted or an element is removed. It offers a couple of efficient routines for manipulations (all of which will be needed for the asymptotic expression).

Change History (51)

comment:1 Changed 4 years ago by dkrenn

  • Branch set to u/dkrenn/asy/mutable_poset

comment:2 Changed 4 years ago by dkrenn

  • Authors set to Daniel Krenn
  • Commit set to e2f884f56743c7d8780586c4b04b3d2e8242ce73

Last 10 new commits:

67522abadd-method: allow cancellation of elements
91c071bmoved hook from add to __init__
bdc3f16rename: value --> element --> shell
434f4e1write method element
98e20b0improve/extend docstrings
5488f10conditional iterations for shells
f00d323rename element_exists_hook to merge_hook
1dc03d7introduce can_merge and rename merge_hook to merge
960b18ba couple of minor rewritings to make the code and doctests nicer
e2f884fwrite merge-methods

comment:3 follow-up: Changed 4 years ago by ncohen

  • Cc jmantysalo added

A mutable poset class should be stored in sage.combinat.posets.

Nathann

comment:4 Changed 4 years ago by dkrenn

This series of comments are the result of an email discussion. Its aim is to give a better understanding of the needs of the data structure used in an asymptotic expression.

An example of an asymptotic expression in say 2 variables (n->oo, t->oo) is

A = n^3*t^2 + 42*n^2*t^2 + 3*n*t^4 + O(t)

This is stored in the mutable poset in the following way: the elements of the poset are exactly the summands of the expression above. This means

sage: A.data  # or however this may be called
poset(n^3*t^2, 42*n^2*t^2, 3*n*t^4, O(t))

The growth of these summands is partially ordered: a) n^3*t^2 >= n^2*t^2 b) n^3*t^2 >= t c) n^2*t^2 >= t d) n*t^4 >= t The mutable poset stores/caches the direct successors/predecessors, i.e., only the relations a), c), d), but not b), since this follows by transitivity out of a) and c). Thus, for the example above, we have the following information stored

poset
- term O(t)
  successors: n^3*t^2, 42*n^2*t^2, 3*n*t^4
  no predecessors
- term 3*n*t^4
  no successors
  predecessors: O(t)
- term 42*n^2*t^2
  successors: n^3*t^2
  predecessors: O(t)
- term n^3*t^2
  no successors
  predecessors: 42*n^2*t^2

comment:5 Changed 4 years ago by dkrenn

We want to perform arithmetic with asymptotic expressions, in particular we need to do efficiently: 1) addition (and multiplication) 2) merging/absorbing terms, e.g.

n^4 + 2*n^2 + 3*n + O(1) + O(n^2) = n^4 + O(n^2)

or

O(n*t) + n + t = O(n*t)

3) removing elements of the poset, because of 2)

To make them efficent, we store successors and predecessors of each element in the poset. These are updated when inserting/removing elements.

Note that an asymptotic expression can contain several O-terms, e.g.

O(n^3 t^2) + O(n^4 t^1) + O(n^2 t^3)

is a valid expression. In the poset each O-term is a minimal element and they are all pairwise incomparable (thus, the O terms will be an antichain in the poset). Anyhow, non-O-terms be be compareable to other elements, e.g. in

3*n*t + O(n) + O(t)

we have n*t >= n and n*t >= t.

We also need to deal with situations where we want to insert an element of the same growth: E.g. 4n+3n = 7n, 4n+O(n) = O(n), thus, the elements themselves can change during addition. When merging/absorbing and working with O-Terms with explicit O-constants, this also occurrs frequently (even with terms of different growth).

comment:6 Changed 4 years ago by dkrenn

Note that all the terms (individual summands) support one operation, namely these can be multiplied, maybe coercion is used, e.g.

4*n^2*t * O(n) --> O(n^2*t) * O(n) --> O(n^3*t)

Thus we have monoids here. "Addition" of terms is more complicated since not always possible. E.g.

n + O(t) = n + O(t)

But since this is an operation we want to have, the data structure has to take this into consideration.

Here an example of the addition of two asymptotic expressions, to see what the poset should do:

B = n^2*t + n + O(1)
C = n*t^2 + O(n)

Steps in computing B + C:

1) calculate: B.poset union C.poset This gives

poset(n^2*t, n, O(1), n*t^2, O(n)).

2) simplify: returns

poset(n^2*t, n*t^2, O(n))

To achieve this, we have to search for what can be "absorbed" by the O-term O(n). These are exactly all the predecessors of O(n) (not only the direct, but also the predecessors of the predecessors...) Thus some kind of caching of predecessors is necessary, but "cache" has to be updated when modifying the poset.

Note that this data structure does a preprocessing of its relations, which is definitely good for nonsmall instances. At the moment this class should provide an interface for the needed routines. A fine tuning (w.r.t. speed optimization for various sizes) can be done later (if the performance is too bad).

To conclude, the data structure needed in an asymptotic expression needs to deal with dynamic changes (mutability) and do some caching to provide efficient methods. And it needs to do more than a poset which is made mutable. In particular, it has to provide the methods for the above mentioned merging and absorbing.

comment:7 in reply to: ↑ 3 ; follow-up: Changed 4 years ago by dkrenn

Replying to ncohen:

A mutable poset class should be stored in sage.combinat.posets.

This class has nothing to do with combinatorics, therefore I am against sage.combinat. And it implements a data structure and we have sage.data_structures, so it seems the right place.

comment:8 in reply to: ↑ 7 ; follow-ups: Changed 4 years ago by ncohen

This class has nothing to do with combinatorics, therefore I am against sage.combinat. And it implements a data structure and we have sage.data_structures, so it seems the right place.

Graphs are a data structure, they are in graphs/. Incidence Structures are data structure, and they are in combinat/designs. Matrices are a data structure, and they are in matrix/. Posets and Hasse Diagrams are a data structure, and they are in combinat/posets/.

Also, you wrote in your branch a 'todo note' to implement in your MutablePoset data structure that 20+ methods from the current Posets should be implemented for your new class: the proper way to do that would be to inherit them from posets.

Could you also explain what "shells" are, and how they differ from the 'facade' boolean argument of Posets ?

Thanks,

Nathann

comment:9 in reply to: ↑ 8 ; follow-up: Changed 4 years ago by cheuberg

Replying to ncohen:

Also, you wrote in your branch a 'todo note' to implement in your MutablePoset data structure that 20+ methods from the current Posets should be implemented for your new class: the proper way to do that would be to inherit them from posets.

A FinitePoset inherits from Parent and my understanding is that parents must be immutable. Thus, IMHO, this mutable poset here should not inherit from FinitePoset.

comment:10 in reply to: ↑ 9 Changed 4 years ago by ncohen

A FinitePoset inherits from Parent and my understanding is that parents must be immutable.

Indeed, but it may actually be time to change that. We are also having problem with this, because apparently the construction of Parent/UniqueRepresentation instances is known to be very slow, and you "should not build too many of them at once" or it will slow code down a lot.

That is what is already preventing us from implementing a proper iterator over all non-isomorphic posets of a given size: this operation creates too many parents and is the bottleneck in the computations.

If it seems that you are bothered by the same thing, it gives all the more reasons to make that change.

Nathann

comment:11 in reply to: ↑ 8 Changed 4 years ago by dkrenn

Replying to ncohen:

Could you also explain what "shells" are, and how they differ from the 'facade' boolean argument of Posets ?

There are similarities between shells and facades, but a facade is something in Sage that represent other things and again uses parents/elements (thus immutable). It has well-defined properties and there is even a category for facade sets. The shells in the mutable poset are more like a container for the elements. Ideally a user of the poset does not need them at all (and only a few MutablePoset?-methods use them). They are only used inside the poset-algorithms. At one point I thought about making shells and the related methods private, but never did this...

comment:12 in reply to: ↑ 8 ; follow-up: Changed 4 years ago by jdemeyer

Replying to ncohen:

Graphs are a data structure

No, graphs are mathematical objects. "a binary symmetric matrix implemented using bitsets" (which could be used for dense graphs) is a data structure.

comment:13 in reply to: ↑ 12 Changed 4 years ago by ncohen

Graphs are a data structure

No, graphs are mathematical objects.

I was not thinking of a graph as it is defined in a book, but of Sage's graphs. I should have said "the Graph class" probably.

Nathann

comment:14 Changed 4 years ago by dkrenn

  • Branch changed from u/dkrenn/asy/mutable_poset to u/dkrenn/asy/mutable-poset
  • Commit changed from e2f884f56743c7d8780586c4b04b3d2e8242ce73 to 1c6b196bac8386f97bb6234a8442040dd52e8b2d

Last 10 new commits:

143dfeawrite method element
b348d14improve/extend docstrings
520bb00conditional iterations for shells
e443f7erename element_exists_hook to merge_hook
b79f1bcintroduce can_merge and rename merge_hook to merge
82ed0f3a couple of minor rewritings to make the code and doctests nicer
13d4a36write merge-methods
8584f57write __len__
a1678edremove TODO-list of methods (list is now in separat branch)
1c6b196write methods for maximal/minimal elements

comment:15 follow-up: Changed 4 years ago by jmantysalo

If union() does same thing as disjoint_union() in posets and in graphs, please change name accordingly. It seems unnecessary to have INPUT-part at all, if the function has no arguments at all.

Just my two cents. I would give three, if I would have more time.

comment:16 in reply to: ↑ 15 ; follow-up: Changed 4 years ago by dkrenn

Replying to jmantysalo:

If union() does same thing as disjoint_union() in posets and in graphs, please change name accordingly.

No, it does not do the same. Union takes only one instance of equal elements, whereas disjoint_union makes each one of the equal elements distinct.

It seems unnecessary to have INPUT-part at all, if the function has no arguments at all.

The developer guide

http://doc.sagemath.org/html/en/developer/coding_basics.html#documentation-strings

says

An INPUT and an OUTPUT block describing the input/output of the function. This is not optional.

Therefore skipping one of these blocks seems to be against the rules (and hopefully helps avoiding the confusion of a missing input block).

Just my two cents. I would give three, if I would have more time.

Many thanks for all your cents.

Best, Daniel

comment:17 Changed 4 years ago by git

  • Commit changed from 1c6b196bac8386f97bb6234a8442040dd52e8b2d to 19fd1556a56a6d250ca464c385e7960ac715b2ae

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

19fd155allow merge to go over all elements

comment:18 in reply to: ↑ 16 ; follow-up: Changed 4 years ago by jmantysalo

Replying to dkrenn:

Replying to jmantysalo:

If union() does same thing as disjoint_union() in posets and in graphs - -

No, it does not do the same.

OK.

It seems unnecessary to have INPUT-part at all, if the function has no arguments at all.

The developer guide says

An INPUT and an OUTPUT block describing the input/output of the function. This is not optional.

True. But I don't think if it has been thinked that "no input" must be documented. Is it in other places? Or should this part of developer guide be changed?

And should for example docstring of .cardinality() really contain OUTPUT-block saying that output type is sage's Integer?

comment:19 Changed 4 years ago by dkrenn

  • Status changed from new to needs_review

comment:20 in reply to: ↑ 18 ; follow-up: Changed 4 years ago by dkrenn

Replying to jmantysalo:

The developer guide says

An INPUT and an OUTPUT block describing the input/output of the function. This is not optional.

True. But I don't think if it has been thinked that "no input" must be documented. Is it in other places? Or should this part of developer guide be changed?

I would keep it. (At the moment) the developer guide says to include it and I find it very nice to have constistent docstrings starting with one-liner, INPUT, OUTPUT, more details, EXAMPLES, ...

(And: there are other places.)

And should for example docstring of .cardinality() really contain OUTPUT-block saying that output type is sage's Integer?

What do you suggest?

Last edited 4 years ago by dkrenn (previous) (diff)

comment:21 in reply to: ↑ 20 Changed 4 years ago by jmantysalo

Replying to dkrenn:

Replying to jmantysalo:

The developer guide says

An INPUT and an OUTPUT block describing the input/output of the function. This is not optional.

True. But I don't think if it has been thinked that "no input" must be documented. Is it in other places? Or should this part of developer guide be changed?

I would keep it. (At the moment) the developer guide says to include it and I find it very nice to have constistent docstrings starting with one-liner, INPUT, OUTPUT, more details, EXAMPLES, ...

This is discussed at #19041. But don't let this stop coding -- Sage will propably never get finished so that questions like this would have The Final Answer.

And should for example docstring of .cardinality() really contain OUTPUT-block saying that output type is sage's Integer?

What do you suggest?

Every cardinality() should return Integer. For other integer-valued functions there were discussion about int vs. Integer without consensus.

I don't know. For input it is explicitly said that the docstring can say "x in integer", not "x must be Integer or int". These are hard questions, as what is "clear" varies from one person to other.

comment:22 Changed 4 years ago by git

  • Commit changed from 19fd1556a56a6d250ca464c385e7960ac715b2ae to ceb0b37bc7640f4300962a89eabefe5abc7263d1

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

2863321allow merge to go over all elements
9391c78derive MutablePoset from object (instead of SageObject)
70859d7cleanup: delete toset since not yet implemented
d647d95write map and mapped
e64cbd8mapping argument for .copy()
c28749cbring map and mapped back to work and use new copy-construction
ceb0b37fix bug in merge

comment:23 Changed 4 years ago by dkrenn

Last 10 new commits:

8584f57write __len__
a1678edremove TODO-list of methods (list is now in separat branch)
1c6b196write methods for maximal/minimal elements
2863321allow merge to go over all elements
9391c78derive MutablePoset from object (instead of SageObject)
70859d7cleanup: delete toset since not yet implemented
d647d95write map and mapped
e64cbd8mapping argument for .copy()
c28749cbring map and mapped back to work and use new copy-construction
ceb0b37fix bug in merge

comment:24 Changed 4 years ago by dkrenn

  • Component changed from misc to asymptotic expansions

comment:25 follow-up: Changed 4 years ago by behackl

  • Branch changed from u/dkrenn/asy/mutable-poset to u/behackl/asy/mutable-poset
  • Commit changed from ceb0b37bc7640f4300962a89eabefe5abc7263d1 to c1f8877b7dcea0e1c677d350d7f5d41be02169c8
  • Status changed from needs_review to needs_work

Hello!

I reviewed this ticket, and here are my comments:

  • MutablePoset, MutablePosetShell: derived from object vs. SageObject?
  • is_null, is_oo: is there some usecase for the reverse keyword? For predecessor and successor: this is clear, as it makes the code easier. However, I think that a reverse-keyword for is_null and is_oo is rather irritating.
  • doctests for MutablePosetShell.le: shouldn't doctests like elem1 <= elem2 be marked as indirect?
  • MutablePosetShell._copy_all_linked_: 1st sentence should be a short description. Likewise for MutablePosetShell._iter_depth_first_visit_ and MutablePosetShell._iter_topological_visit_.
  • sorted_set_by_tuple, is_MutablePoset: are these functions really necessary? Both are only used once within the whole file. The occurrence of sorted_set_by_tuple can be easily replaced by
    [...].join(repr(e) for e in sortedshells if e in shell.successors(rev))
    

and the occurrence of is_MutablePoset can be replaced by a simple isinstance-call.

  • MutablePoset.shells: I do not understand the usecase of the reverse keyword. Can it be removed?
  • MutablePoset.add: I think that a comment (in the code) that roughly explains what the passage beginning with for reverse in (False, True): does would be nice. It took me quite some time to understand and verify the functionality of this block.
  • MutablePoset.discard: why isn't this simply an alias of MutablePoset.remove? As remove has no return value, discard cannot have one either, if that was the intention.
  • Is there a particular reason for naming the parameters for all the set operations like MutablePoset.union, MutablePoset.difference etc. left and right, instead of self and other? IMHO, this disguises that the function can be called as P.union(Q).
  • Regarding all set operations: currently, it is not clear from the documentation that all set operations are performed on the set of keys. This causes something like
    sage: PR.<x> = ZZ[]
    sage: P = MutablePoset(key=lambda k: len(k.list()))
    sage: P.add(42*x)
    sage: P.add(21*x^2)
    sage: Q = MutablePoset(key=lambda k: len(k.list()))
    sage: Q.add(1111*x)
    sage: P, Q
    (poset(42*x, 21*x^2), poset(1111*x))
    sage: Q.is_subset(P)
    True
    sage: Q.union(P)
    poset(1111*x, 21*x^2)
    

and so on. In principle, I don't see this as a problem---however, I'd state this explicitly in each of these set operation functions.

  • MutablePoset.mapped: why is this function needed? Purely for semantical reasons? I'd move the doctests to MutablePoset.copy.
  • MutablePosetShell._copy_all_linked_: is the memoization using the id of the object a standard procedure? I thought about it, but I'm not entirely sure that this isn't a potential error source.

Side note: the MutablePoset is the central data structure in our AsymptoticExpansions framework (cf. #17601). In this context, the functionality has been tested extensively--and some peculiarities (like the map-function etc.) are motivated by this application.

Also, I've made a few reviewer commits concerning the documentation; the branch is attached.

As soon as the points I've raised in the comments above are discussed, this would be a positive_review from my side.

Benjamin


Last 10 new commits:

e64cbd8mapping argument for .copy()
c28749cbring map and mapped back to work and use new copy-construction
ceb0b37fix bug in merge
525bf3cMerge branch 'u/dkrenn/asy/mutable-poset' of git://trac.sagemath.org/sage into 6.9.beta5
bf1928fremove unused import
98a7939print something --> print(something)
2a7ab88several improvements to documentation (language, structure)
a4c43b7fixed two examples-blocks
a867d3aindentation (PEP 8)
c1f8877improved errors and added two doctests

comment:26 Changed 4 years ago by jmantysalo

Benjamin, please put your name to reviewers-field. Otherwise Volker will reject this.

comment:27 Changed 4 years ago by behackl

  • Reviewers set to Benjamin Hackl

Thanks for the reminder, Jori!

Benjamin

comment:28 Changed 4 years ago by dkrenn

  • Branch changed from u/behackl/asy/mutable-poset to u/dkrenn/asy/mutable-poset

comment:29 in reply to: ↑ 25 Changed 4 years ago by dkrenn

  • Branch changed from u/dkrenn/asy/mutable-poset to u/behackl/asy/mutable-poset

Replying to behackl:

  • MutablePoset, MutablePosetShell: derived from object vs. SageObject?

object.

  • is_null, is_oo: is there some usecase for the reverse keyword? For predecessor and successor: this is clear, as it makes the code easier. However, I think that a reverse-keyword for is_null and is_oo is rather irritating.

Keyword deleted.

  • doctests for MutablePosetShell.le: shouldn't doctests like elem1 <= elem2 be marked as indirect?

Yes, I've marked them.

  • MutablePosetShell._copy_all_linked_: 1st sentence should be a short description. Likewise for MutablePosetShell._iter_depth_first_visit_ and MutablePosetShell._iter_topological_visit_.

Rewritten.

  • sorted_set_by_tuple, is_MutablePoset: are these functions really necessary? Both are only used once within the whole file. The occurrence of sorted_set_by_tuple can be easily replaced by
    [...].join(repr(e) for e in sortedshells if e in shell.successors(rev))
    

and the occurrence of is_MutablePoset can be replaced by a simple isinstance-call.

sorted_set_by_tuple: Deleted and replaced. is_MutablePoset: seems to be a standard convention to use it in Sage; see a lot of other modules.

  • MutablePoset.shells: I do not understand the usecase of the reverse keyword. Can it be removed?

I agree; deleted.

  • MutablePoset.add: I think that a comment (in the code) that roughly explains what the passage beginning with for reverse in (False, True): does would be nice. It took me quite some time to understand and verify the functionality of this block.

I've added a comment.

  • MutablePoset.discard: why isn't this simply an alias of MutablePoset.remove? As remove has no return value, discard cannot have one either, if that was the intention.

See Python's set (the same behavior there).

  • Is there a particular reason for naming the parameters for all the set operations like MutablePoset.union, MutablePoset.difference etc. left and right, instead of self and other? IMHO, this disguises that the function can be called as P.union(Q).

Changed all to self/other.

  • Regarding all set operations: currently, it is not clear from the documentation that all set operations are performed on the set of keys. This causes something like
    sage: PR.<x> = ZZ[]
    sage: P = MutablePoset(key=lambda k: len(k.list()))
    sage: P.add(42*x)
    sage: P.add(21*x^2)
    sage: Q = MutablePoset(key=lambda k: len(k.list()))
    sage: Q.add(1111*x)
    sage: P, Q
    (poset(42*x, 21*x^2), poset(1111*x))
    sage: Q.is_subset(P)
    True
    sage: Q.union(P)
    poset(1111*x, 21*x^2)
    

and so on. In principle, I don't see this as a problem---however, I'd state this explicitly in each of these set operation functions.

I've added a note in all these functions.

  • MutablePoset.mapped: why is this function needed? Purely for semantical reasons? I'd move the doctests to MutablePoset.copy.

It is a shortcut for using copy with the mapping argument (since this is a non-standard argument for a copy method, including a separate method with an approriate name seems to be a good choice)

  • MutablePosetShell._copy_all_linked_: is the memoization using the id of the object a standard procedure? I thought about it, but I'm not entirely sure that this isn't a potential error source.

Yes it is standard; see (all) deepcopy routines.

Also, I've made a few reviewer commits concerning the documentation; the branch is attached.

Cross-reviewed. Thanks.

comment:30 Changed 4 years ago by dkrenn

  • Status changed from needs_work to needs_review

comment:31 Changed 4 years ago by dkrenn

  • Branch changed from u/behackl/asy/mutable-poset to u/dkrenn/asy/mutable-poset
  • Commit changed from c1f8877b7dcea0e1c677d350d7f5d41be02169c8 to 1d52f6c6351e6eb9e92c6033b12e09c4754b8110

Last 10 new commits:

39ae466correct oo, null
fd7c881Applies --> Apply in one-line of docstring
dabad1fremove reverse in is_{null|oo} since not needed
33c4102mark doctests in .le as indirect
b31fac8rewrite a couple of one-line descriptions
17e921fremove sorted_set_by_tuple
7af4b6bremove reverse keyword from shells
a49a20dadd comment in code to make it clear what happens
89b8209change left/right to self/other
1d52f6cadd a note to the set operations methods

comment:32 follow-up: Changed 4 years ago by behackl

Hello Daniel,

I cross-reviewed your changes and have one last open question:

  • Is there a particular reason for deriving this from object instead of SageObject? Because the documentation of SageObject states that "Every object that can end up being returned to the user should inherit from SageObject."

Other than that, this is positive_review from my side; AFAIK cheuberg also wanted to cross-review this ticket, so I'll not set this to positive_review yet.

Benjamin

comment:33 in reply to: ↑ 32 Changed 4 years ago by dkrenn

Replying to behackl:

  • Is there a particular reason for deriving this from object instead of SageObject? Because the documentation of SageObject states that "Every object that can end up being returned to the user should inherit from SageObject."

Ok, then SageObject it is :)

comment:34 follow-up: Changed 4 years ago by behackl

  • Branch changed from u/dkrenn/asy/mutable-poset to u/behackl/asy/mutable-poset
  • Commit changed from 1d52f6c6351e6eb9e92c6033b12e09c4754b8110 to 3b3b2fb607a6fe8b20419170bf935d494af1efca

A short remark on this change of mind:

When deriving these classes from SageObject instead of object, and merging this ticket into #19083 (the cleanup-ticket of our AsymptoticRing), doctests were failing because we call A(poset) with an AsymptoticRing A there, which causes some peculiarities in _coerce_map_from_.

In any case, we fixed these problems there, so this can be properly derived from SageObject.

This concludes my review; cheuberg is in the process of reading the code. I'll leave setting this to positive_review to him.

Benjamin


Last 10 new commits:

fd7c881Applies --> Apply in one-line of docstring
dabad1fremove reverse in is_{null|oo} since not needed
33c4102mark doctests in .le as indirect
b31fac8rewrite a couple of one-line descriptions
17e921fremove sorted_set_by_tuple
7af4b6bremove reverse keyword from shells
a49a20dadd comment in code to make it clear what happens
89b8209change left/right to self/other
1d52f6cadd a note to the set operations methods
3b3b2fbobject --> SageObject
Last edited 4 years ago by behackl (previous) (diff)

comment:35 Changed 4 years ago by cheuberg

  • Branch changed from u/behackl/asy/mutable-poset to u/cheuberg/asy/mutable-poset

comment:36 in reply to: ↑ 34 ; follow-up: Changed 4 years ago by cheuberg

  • Commit changed from 3b3b2fb607a6fe8b20419170bf935d494af1efca to f7bce7e8aff4e25a23b57d1052ff13df302120e5
  • Milestone changed from sage-6.5 to sage-6.9
  • Reviewers changed from Benjamin Hackl to Benjamin Hackl, Clemens Heuberger
  • Status changed from needs_review to needs_work

Replying to behackl:

This concludes my review; cheuberg is in the process of reading the code. I'll leave setting this to positive_review to him.

I read the documentation and the code. I pushed a few reviewer commits. I have a number of rather minor issues with the documentation which I ask you to fix in order facilitate future maintainance of the code. In three instances, I propose alternative implementations, which might be more readable or slightly more efficient.

  1. Please add .. seealso:: blocks between corresponding methods of shell and poset as well as between the accessor methods (keys, elements, shells)
  2. there is an empty "Introduction" section at the beginning of the module documentation, the next heading "Example" is on the same level.
  3. this module was written as part of the asymptotic expansion effort. In contrast to the asymptotic expansion, it does not have the "experimental" decorator. I'd feel more comfortable having it, at least until a larger portion of the asymptotic expansions have been merged.
  4. MutablePoset.__init__ accepts a list of elements. This could be used in several doctests (in particular, in the set operations) as an abbreviation.
  5. MutablePosetShell.__init__: shall we check that element is not None? Otherwise, handling of special elements would probably be affected.
  6. MutablePosetShell.key: I do not understand the sentence "The element is converted by the poset to the key".
  7. MutablePosetShell.key: I am surprised that the key is not cached. I imagine that many comparisons will be needed in the lifetime of a MutablePoset, and in every case, the property key has to be resolved, which calls the property poset, which calls get_key of the poset.
  8. MutablePosetShell.__repr__: The note box in the docstring is surprising at this point: reading the source file from the top, this is the first point where the representation of the data is explained, after guessing it from is_special, is_oo, is_null above. I think that it would be better to document these conventions closer to the top, perhaps in the __init__ method or perhaps only as a comment in the source code.
  9. MutablePosetShell.__repr__: The code replicates the behaviour of is_null and is_oo. As the __repr__ method is hardly time critical, I'd prefer using is_null and is_oo, here and thus hiding the internal convention.
  10. MutablePosetShell.le: the note box could be simplified by suppressing implementation details and speaking about the special elements.
  11. MutablePosetShell.le: right <= left: neither right nor left are defined here.
  12. MutablePosetShell.le: the part if other.element is None could be simplified to return not other.successors() as self is already known not to be special here.
  13. MutablePosetShell.le: If this is time critical, self._predecessors_ could be used instead of self.predecessors().
  14. MutablePosetShell.eq: note box, see above.
  15. MutablePosetShell.eq: emphasize that elements with equal keys are considered equal? Currently, this information is somewhat hidden in the note box which at first glance only seems to explain handling of special elements.
  16. MutablePosetShell._copy_all_linked_: Short description: "Return a copy of all shells" does not correspond to the actual return value, which is only the copy of this shell.
  17. MutablePosetShell._copy_all_linked_: the interplay between this method and MutablePoset._copy_shells_ is not well documented: in particular, poset in _copy_all_linked_ is only used for setting the containing poset, but not for actual inserting into this poset.
  18. MutablePosetShell._copy_all_linked_: I do not understand why you test oo == P.oo: I think that oo is an element of the new poset Q. So oo is Q.oo would be more interesting? The current test demonstrates that the poset is not used in comparison, so that would rather belong to .eq?
  19. MutablePosetShell._search_covers_: what is the role of self in this method? It trivially influences the return value, but what else?
  20. MutablePosetShell._search_covers_: The explanation of the return value is unclear to me. Is the sentence "Note that..." meant to be a complete description? Does it change if reverse is set?
  21. MutablePosetShell._search_covers_: I think that the notions of "upper cover" and "lower cover" need a brief definition; I did not find them in Wikipedia and sage.combinat.posets.posets.FinitePoset.upper_covers defines the notion.
  22. MutablePosetShell._search_covers_: According to Wikipedia, a cover is what is called an upper cover here. This is in contrast to the default behaviour here.
  23. MutablePosetShell._search_covers_: what is the difference between this method and .predecessors? Is the shell necessarily an element of the poset? If not, then there should be a doctest covering this case.
  24. MutablePosetShell.covers: "originate" is somewhat foreign to the description of the poset.
  25. MutablePosetShell.covers: "which are at most the given shell": should that be "which are less than the given shell"?
  26. MutablePosetShell.covers see comments on MutablePosetShell._search_covers_.
  27. MutablePosetShell.covers: I think that the following would be an equivalent implementation of this method, which does not need a helper function with side effects.
            if self == shell:
                return set()
            covers = set().union(*(e.covers(shell, reverse)
                                   for e in self.successors(reverse)
                                   if e.le(shell, reverse)))
            if covers:
                return covers
            else:
                return set([self])
    
    (pushed as branch u/cheuberg/asy/mutable-poset-cover)
  28. MutablePosetShell._iter_depth_first_visit_: document the role of self in this method (only shells >= this shell are visited).
  29. MutablePosetShell.iter_depth_first: document the role of self in this method (only shells >= this shell are visited).
  30. MutablePosetShell._iter_topological_visit_: document the role of self in this method (only shells <= this shell are visited, emphasize the contrast to depth first.).
  31. MutablePosetShell.iter_topological_first: document the role of self in this method (only shells <= this shell are visited, emphasize the contrast to depth first.).
  32. MutablePosetShell.iter_topological_sort, last example: function C is defined, but not used.
  33. MutablePosetShell.merge: explain what merge is, in particular, that this is defined when constructing the poset.
  34. MutablePosetShell.merge: I am surprised that check=True leads to a silent failure instead of an exception and that poset._merge_ is None does not raise an exception. Document and test this behaviour?
  35. MutablePosetShell.merge: what is the difference between poset.remove and poset.discard?
  36. MutablePosetShell.merge: document that the merge function resulting in None leads to deletion of the element.
  37. MutablePosetShell.merge: document that the merge function must not change the position of the element in the poset.
  38. MutablePoset.__init__: Clarify the role of key: in particular, key does not only influence sorting, but that no two elements are allowed to have the same key.
  39. MutablePoset.__len__: Clarify that null and oo are not counted.
  40. MutablePoset.shells_topological: The sentence "If this is None, no sorting according to the representation string occurs." is unclear to me, in particular the role of the representation string.
  41. MutablePoset.keys_topological: Due to the chosen key, some of the elements added to the poset are ignored. I do not know why this is demonstrated here.
  42. MutablePoset.repr: INPUT section is incomplete.
  43. MutablePoset.repr_full: INPUT section is incomplete.
  44. MutablePoset.add: the loop for reverse in (False, True) simplifies in the second iteration: as all pairs of elements (s, l) with new covering s and l covering new have already been broken up while reverse=False. Thus it might be more straightforward to do it only once, not using reverse at all and saving a few intersections:
            new._predecessors_ = self.null.covers(new, reverse=False)
            new._successors_ = self.oo.covers(new, reverse=True)
    
            for s in new.predecessors():
                for l in s.successors().intersection(new.successors()):
                    l.predecessors().remove(s)
                    s.successors().remove(l)
                s.successors().add(new)
            for l in new.successors():
                l.predecessors().add(new)
    
    (pushed as branch u/cheuberg/asy/mutable-poset-add)
  45. MutablePoset.remove: the loop over all (not necessarily direct) successors via the depth first search iterator seems to be rather inefficient, especially if the poset is large. I propose an alternative based on the order relation and not based on the data structure:
            for upper in shell.successors():
                upper.predecessors().remove(shell)
    
            for lower in shell.predecessors():
                lower.successors().remove(shell)
                for upper in shell.successors():
                    if not any(s <= upper 
                               for s in lower.successors()):
                        lower.successors().add(upper)
                        upper.predecessors().add(lower)
    
    (pushed as branch u/cheuberg/asy/mutable-poset-remove)
  46. MutablePoset.remove, MutablePoset.discard: add "see also blocks", but also an explanation of the difference between discard and remove. I guess that both methods are available due to some compatibility concern (in that case, please add a remark in the code or the docstring). Otherwise, I'd suggest removing discard, removing the parameter raise_key_error and let the user catch the exception.
  47. MutablePoset.pop: remove key=lambda c: -c from this example as it is not pertinent to pop.
  48. MutablePoset.pop: mention that special elements cannot be popped.
  49. MutablePoset.pop: IMHO you can remove the first four line (the try: block deleting kwargs['include_special']) because setting kwargs['include_special'] = False should result in the same result.
  50. MutablePoset.union: The doctest P.union(P, Q, Q, P) neither fits the description "a poset" or "an iterable of future elements".
  51. MutablePoset.union: the word "union" sounds symmetric, however, due to keys and merge functions, it might not be commutative. The note box is not helpful for me.
  52. MutablePoset.union: the TODO box from union_update also applies here.
  53. MutablePoset.union_update: why is the semantics of other different w.r.t union, but has the same description? It would seem more logical to me if union would simply call copy and then pass its argument to update_union and let the latter function sort out the iterators?
  54. MutablePoset.difference and MutablePoset.difference_update: see comments on union and union_update
  55. MutablePoset.intersection and MutablePoset.intersection_update: see comments on union and union_update
  56. MutablePoset.intersection_update: how can the AttributeError occur? After all, self is a MutablePoset, so the method keys will be available unless something very strange happens ...
  57. MutablePoset.merge: documentation of reverse: what is the default direction?
  58. MutablePoset.merge: add doctest for RuntimeError.
  59. MutablePoset.merge: document that can_merge is applied in the sense of the condition of depth first iteration, i.e., once can_merge fails, the successors are no longer tested. This is some kind of monotonicity condition on can_merge.
  60. MutablePoset.merge: it should be mentioned somewhere that this (at first sight strange) merge magic is motivated by asymptotic expansions.
  61. MutablePoset.map: IMHO the example does alter the keys, because the key was the identity map here.
  62. MutablePoset.mapping: does the map have to be key preserving as in the method map? Is this method actually needed, see also the recent discussion on inplace vs. non-inplace operations on sage-devel?

New commits:

8de4188Trac #17693: minor language adjustments
740852eTrac #17693: command instead of description for short descriptions
347656cTrac #17693: language adjustment: whether instead of if
4774baaTrac #17693: corrections in documentation
fe5d2f1Trac #17693: additional doctest
e4f1feaTrac #17693: fix indentations and whitespace
254951dTrac #17693: add keyword in doctest for clarity
f7bce7eTrac #17693: remove superfluous doctest

comment:37 Changed 4 years ago by dkrenn

  • Branch changed from u/cheuberg/asy/mutable-poset to u/dkrenn/asy/mutable-poset

comment:38 Changed 4 years ago by git

  • Commit changed from f7bce7e8aff4e25a23b57d1052ff13df302120e5 to 3c69f6be24c5776593d3e067d8c723cd5c192e8e

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

34e34dcTrac #17693, comment 36, 19--23: improve docstring of covers (former _search_covers_)
490c223Trac #17693, comment 36, 28--31: document role of self
3de0a1dTrac #17693, comment 36, 33: explicitly mention merge and can_merge at top of docstring
485b46fTrac #17693, comment 36, 34: raise exceptions when merge is not possible
d5d6beccheck=False in MutablePoset.merge since checked already before
6da3db1Trac #17693, comment 36, 37: extend doc to mention more explicitly that merge is not allowed to change keys
f1e9f9eTrac #17693, comment 36, 38: clarify parameter key
ae0cad9Trac #17693, comment 36, 60: mention motivation asymptoic expansions in merge method
ec15597Trac #17693: alternative implementation add
3c69f6bMerge remote-tracking branch 'origin/u/cheuberg/asy/mutable-poset-add' into t/17693/asy/mutable-poset

comment:39 in reply to: ↑ 36 ; follow-up: Changed 4 years ago by dkrenn

Replying to cheuberg:

I read the documentation and the code. I pushed a few reviewer commits.

Cross-reviewed. One commit added.

I have a number of rather minor issues with the documentation which I ask you to fix in order facilitate future maintainance of the code. In three instances, I propose alternative implementations, which might be more readable or slightly more efficient.

Thanks; see my comments below.

  1. Please add .. seealso:: blocks between corresponding methods of shell and poset as well as between the accessor methods (keys, elements, shells)

Done.

  1. there is an empty "Introduction" section at the beginning of the module documentation, the next heading "Example" is on the same level.

Deleted.

  1. this module was written as part of the asymptotic expansion effort. In contrast to the asymptotic expansion, it does not have the "experimental" decorator. I'd feel more comfortable having it, at least until a larger portion of the asymptotic expansions have been merged.

Activated it; it seems (for some (to me) unknown reason) the warning appears now in every doctest and not only once in the file. Thus, deactivated it again; and I am for keeping it this way.

  1. MutablePoset.__init__ accepts a list of elements. This could be used in several doctests (in particular, in the set operations) as an abbreviation.

Good idea. Done.

  1. MutablePosetShell.__init__: shall we check that element is not None? Otherwise, handling of special elements would probably be affected.

MutablePosetShell? is typically used by the MutablePoset?; and there, adding a None-element is forbidden (see :meth:add).

  1. MutablePosetShell.key: I do not understand the sentence "The element is converted by the poset to the key".

Rewritten.

  1. MutablePosetShell.key: I am surprised that the key is not cached. I imagine that many comparisons will be needed in the lifetime of a MutablePoset, and in every case, the property key has to be resolved, which calls the property poset, which calls get_key of the poset.

Now it is cached (see also follow up ticket #19281).

  1. MutablePosetShell.__repr__: The note box in the docstring is surprising at this point: reading the source file from the top, this is the first point where the representation of the data is explained, after guessing it from is_special, is_oo, is_null above. I think that it would be better to document these conventions closer to the top, perhaps in the __init__ method or perhaps only as a comment in the source code.

Added a note in the class description.

  1. MutablePosetShell.__repr__: The code replicates the behaviour of is_null and is_oo. As the __repr__ method is hardly time critical, I'd prefer using is_null and is_oo, here and thus hiding the internal convention.

Rewritten.

  1. MutablePosetShell.le: the note box could be simplified by suppressing implementation details and speaking about the special elements.

Done.

  1. MutablePosetShell.le: right <= left: neither right nor left are defined here.

Rewritten.

  1. MutablePosetShell.le: the part if other.element is None could be simplified to return not other.successors() as self is already known not to be special here.

True; rewritten.

  1. MutablePosetShell.le: If this is time critical, self._predecessors_ could be used instead of self.predecessors().

Changed.

  1. MutablePosetShell.eq: note box, see above.

Simplified.

  1. MutablePosetShell.eq: emphasize that elements with equal keys are considered equal? Currently, this information is somewhat hidden in the note box which at first glance only seems to explain handling of special elements.

Rewritten note box.

  1. MutablePosetShell._copy_all_linked_: Short description: "Return a copy of all shells" does not correspond to the actual return value, which is only the copy of this shell.

Rewritten.

  1. MutablePosetShell._copy_all_linked_: the interplay between this method and MutablePoset._copy_shells_ is not well documented: in particular, poset in _copy_all_linked_ is only used for setting the containing poset, but not for actual inserting into this poset.

Extended description of parameter poset.

  1. MutablePosetShell._copy_all_linked_: I do not understand why you test oo == P.oo: I think that oo is an element of the new poset Q.

oo == P.oo tests that Q.oo is mapped to P.oo.

So oo is Q.oo would be more interesting?

oo is Q.oo is False since oo is not in Q, but just a copy of the oo in P with parent-poset Q. Inserting this into Q is done in _copy_shells_.

The current test demonstrates that the poset is not used in comparison, so that would rather belong to .eq?

I do not understand what you mean (but it is already late...).

  1. MutablePosetShell._search_covers_: what is the role of self in this method? It trivially influences the return value, but what else?

_search_covers_ does not exist anymore (see 27).

  1. MutablePosetShell._search_covers_: The explanation of the return value is unclear to me. Is the sentence "Note that..." meant to be a complete description? Does it change if reverse is set?

_search_covers_ does not exist anymore (see 27).

  1. MutablePosetShell._search_covers_: I think that the notions of "upper cover" and "lower cover" need a brief definition; I did not find them in Wikipedia and sage.combinat.posets.posets.FinitePoset.upper_covers defines the notion.

_search_covers_ does not exist anymore (see 27). Incooperated in covers.

  1. MutablePosetShell._search_covers_: According to Wikipedia, a cover is what is called an upper cover here. This is in contrast to the default behaviour here.

_search_covers_ does not exist anymore (see 27).

  1. MutablePosetShell._search_covers_: what is the difference between this method and .predecessors? Is the shell necessarily an element of the poset? If not, then there should be a doctest covering this case.

_search_covers_ does not exist anymore (see 27). Incooperated in covers.

  1. MutablePosetShell.covers: "originate" is somewhat foreign to the description of the poset.

Rewritten.

  1. MutablePosetShell.covers: "which are at most the given shell": should that be "which are less than the given shell"?

Rewritten.

  1. MutablePosetShell.covers see comments on MutablePosetShell._search_covers_.

Rewritten.

  1. MutablePosetShell.covers: I think that the following would be an equivalent implementation of this method, which does not need a helper function with side effects.
            if self == shell:
                return set()
            covers = set().union(*(e.covers(shell, reverse)
                                   for e in self.successors(reverse)
                                   if e.le(shell, reverse)))
            if covers:
                return covers
            else:
                return set([self])
    
    (pushed as branch u/cheuberg/asy/mutable-poset-cover)

Merged and minor simplification.

  1. MutablePosetShell._iter_depth_first_visit_: document the role of self in this method (only shells >= this shell are visited).

Documented.

  1. MutablePosetShell.iter_depth_first: document the role of self in this method (only shells >= this shell are visited).

Documented.

  1. MutablePosetShell._iter_topological_visit_: document the role of self in this method (only shells <= this shell are visited, emphasize the contrast to depth first.).

Documented.

  1. MutablePosetShell.iter_topological_first: document the role of self in this method (only shells <= this shell are visited, emphasize the contrast to depth first.).

Documented.

  1. MutablePosetShell.iter_topological_sort, last example: function C is defined, but not used.

Deleted.

  1. MutablePosetShell.merge: explain what merge is, in particular, that this is defined when constructing the poset.

Documented.

  1. MutablePosetShell.merge: I am surprised that check=True leads to a silent failure instead of an exception and that poset._merge_ is None does not raise an exception. Document and test this behaviour?

Behavior changed.

  1. MutablePosetShell.merge: what is the difference between poset.remove and poset.discard?

See Python's set.

  1. MutablePosetShell.merge: document that the merge function resulting in None leads to deletion of the element.

Done.

  1. MutablePosetShell.merge: document that the merge function must not change the position of the element in the poset.

Mentioned this more explicitly in docs

  1. MutablePoset.__init__: Clarify the role of key: in particular, key does not only influence sorting, but that no two elements are allowed to have the same key.

Done.

  1. MutablePoset.__len__: Clarify that null and oo are not counted.

Done.

  1. MutablePoset.shells_topological: The sentence "If this is None, no sorting according to the representation string occurs." is unclear to me, in particular the role of the representation string.

Rewritten.

  1. MutablePoset.keys_topological: Due to the chosen key, some of the elements added to the poset are ignored. I do not know why this is demonstrated here.

Removed.

  1. MutablePoset.repr: INPUT section is incomplete.

Completed.

  1. MutablePoset.repr_full: INPUT section is incomplete.

Completed.

  1. MutablePoset.add: the loop for reverse in (False, True) simplifies in the second iteration: as all pairs of elements (s, l) with new covering s and l covering new have already been broken up while reverse=False. Thus it might be more straightforward to do it only once, not using reverse at all and saving a few intersections:
            new._predecessors_ = self.null.covers(new, reverse=False)
            new._successors_ = self.oo.covers(new, reverse=True)
    
            for s in new.predecessors():
                for l in s.successors().intersection(new.successors()):
                    l.predecessors().remove(s)
                    s.successors().remove(l)
                s.successors().add(new)
            for l in new.successors():
                l.predecessors().add(new)
    
    (pushed as branch u/cheuberg/asy/mutable-poset-add)

Merged and cross-reviewed....ok.

  1. MutablePoset.remove: the loop over all (not necessarily direct) successors via the depth first search iterator seems to be rather inefficient, especially if the poset is large. I propose an alternative based on the order relation and not based on the data structure:
            for upper in shell.successors():
                upper.predecessors().remove(shell)
    
            for lower in shell.predecessors():
                lower.successors().remove(shell)
                for upper in shell.successors():
                    if not any(s <= upper 
                               for s in lower.successors()):
                        lower.successors().add(upper)
                        upper.predecessors().add(lower)
    
    (pushed as branch u/cheuberg/asy/mutable-poset-remove)

This needs comparisons of the elements, but one of the main ideas of this data structure is that comparisions are only needed for inserting an element into the poset and none needed once it is inside. Thus I am for keeping the current solution. However, I am fine with introducing (now or at any point later) an algorithm option which makes it possible to select different removing algorithms depending on the situation.

  1. MutablePoset.remove, MutablePoset.discard: add "see also blocks", but also an explanation of the difference between discard and remove. I guess that both methods are available due to some compatibility concern (in that case, please add a remark in the code or the docstring). Otherwise, I'd suggest removing discard, removing the parameter raise_key_error and let the user catch the exception.

Python's set has both, remove and discard. Thus this mutable poset should have it as well. Note-block added. Seealso added.

  1. MutablePoset.pop: remove key=lambda c: -c from this example as it is not pertinent to pop.

Done.

  1. MutablePoset.pop: mention that special elements cannot be popped.

Done.

  1. MutablePoset.pop: IMHO you can remove the first four line (the try: block deleting kwargs['include_special']) because setting kwargs['include_special'] = False should result in the same result.

Deleted.

  1. MutablePoset.union: The doctest P.union(P, Q, Q, P) neither fits the description "a poset" or "an iterable of future elements".

Rewritten INPUT-block

  1. MutablePoset.union: the word "union" sounds symmetric, however, due to keys and merge functions, it might not be commutative. The note box is not helpful for me.

Note added/changed.

  1. MutablePoset.union: the TODO box from union_update also applies here.

Copied.

  1. MutablePoset.union_update: why is the semantics of other different w.r.t union, but has the same description? It would seem more logical to me if union would simply call copy and then pass its argument to update_union and let the latter function sort out the iterators?

Indeed. Code rewritten.

  1. MutablePoset.difference and MutablePoset.difference_update: see comments on union and union_update

Done.

  1. MutablePoset.intersection and MutablePoset.intersection_update: see comments on union and union_update

Done.

  1. MutablePoset.intersection_update: how can the AttributeError occur? After all, self is a MutablePoset, so the method keys will be available unless something very strange happens ...

True. Code simplified.

  1. MutablePoset.merge: documentation of reverse: what is the default direction?

Documented.

  1. MutablePoset.merge: add doctest for RuntimeError.

Added.

  1. MutablePoset.merge: document that can_merge is applied in the sense of the condition of depth first iteration, i.e., once can_merge fails, the successors are no longer tested. This is some kind of monotonicity condition on can_merge.

Added note.

  1. MutablePoset.merge: it should be mentioned somewhere that this (at first sight strange) merge magic is motivated by asymptotic expansions.

Mentioned.

  1. MutablePoset.map: IMHO the example does alter the keys, because the key was the identity map here.

Example changed.

  1. MutablePoset.mapping: does the map have to be key preserving as in the method map? Is this method actually needed, see also the recent discussion on inplace vs. non-inplace operations on sage-devel?

Added a note on key-order preservation.

I think having MutablePoset.mapping is useful (from a ui point of view) since one would not naturally thinks that the copy method has a parameter for applying a mapping function.

comment:40 Changed 4 years ago by dkrenn

  • Status changed from needs_work to needs_review

comment:41 Changed 4 years ago by cheuberg

  • Branch changed from u/dkrenn/asy/mutable-poset to u/cheuberg/asy/mutable-poset

comment:42 Changed 4 years ago by git

  • Commit changed from 3c69f6be24c5776593d3e067d8c723cd5c192e8e to 4deddbd1a09e0e60273797cb89becdc651325b9c

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

db042e0Trac #17693: fix ReSt and hyperlink issues
bbe02efTrac #17693: minor language issues and typos
4deddbdTrac #17693: remove comment on non-commutativity for difference and update_difference

comment:43 in reply to: ↑ 39 ; follow-up: Changed 4 years ago by cheuberg

  • Status changed from needs_review to needs_work

Thank you for your changes. I added three commits. See my remaining comments below.

Replying to dkrenn:

Replying to cheuberg:

  1. this module was written as part of the asymptotic expansion effort. In contrast to the asymptotic expansion, it does not have the "experimental" decorator. I'd feel more comfortable having it, at least until a larger portion of the asymptotic expansions have been merged.

Activated it; it seems (for some (to me) unknown reason) the warning appears now in every doctest and not only once in the file. Thus, deactivated it again; and I am for keeping it this way.

ok.

  1. MutablePosetShell.key: I am surprised that the key is not cached. I imagine that many comparisons will be needed in the lifetime of a MutablePoset, and in every case, the property key has to be resolved, which calls the property poset, which calls get_key of the poset.

Now it is cached (see also follow up ticket #19281).

I rather thought about calling key in __init__ as I guess that the key will be needed at least once in the lifetime of every MutablePosetShell.

  1. MutablePosetShell._copy_all_linked_: I do not understand why you test oo == P.oo: I think that oo is an element of the new poset Q.

oo == P.oo tests that Q.oo is mapped to P.oo.

wouldn't oo.is_oo do it without comparing shells of different posets, which might be confusing?

So oo is Q.oo would be more interesting?

oo is Q.oo is False since oo is not in Q, but just a copy of the oo in P with parent-poset Q.

that would be good to test (and comment on).

Inserting this into Q is done in _copy_shells_.

The current test demonstrates that the poset is not used in comparison, so that would rather belong to .eq?

I do not understand what you mean (but it is already late...).

I mean that shells e and f might be equal even if they do belong to different posets; this might be an interesting doctest or example for equality.

  1. MutablePosetShell._search_covers_: According to Wikipedia, a cover is what is called an upper cover here. This is in contrast to the default behaviour here.

_search_covers_ does not exist anymore (see 27).

This does not solve the problem.

What about renaming the method covers to lower_covers (and adapting the docstring slightly, removing "upper " from the one-sentence-description as well as from the definition?) For symmetry, a method upper_covers would be nice.

  1. MutablePoset.remove: the loop over all (not necessarily direct) successors via the depth first search iterator seems to be rather inefficient, especially if the poset is large. I propose an alternative based on the order relation and not based on the data structure:
            for upper in shell.successors():
                upper.predecessors().remove(shell)
    
            for lower in shell.predecessors():
                lower.successors().remove(shell)
                for upper in shell.successors():
                    if not any(s <= upper 
                               for s in lower.successors()):
                        lower.successors().add(upper)
                        upper.predecessors().add(lower)
    
    (pushed as branch u/cheuberg/asy/mutable-poset-remove)

This needs comparisons of the elements, but one of the main ideas of this data structure is that comparisions are only needed for inserting an element into the poset and none needed once it is inside. Thus I am for keeping the current solution. However, I am fine with introducing (now or at any point later) an algorithm option which makes it possible to select different removing algorithms depending on the situation.

This should be discussed when more benchmarking results are available. I opened #19300 for that.

  1. MutablePoset.difference and MutablePoset.difference_update: see comments on union and union_update

Done.

removed comment on non-commutativity because difference is non-commutative by definition.

  1. MutablePoset.intersection and MutablePoset.intersection_update: see comments on union and union_update

Done.

Remove comment on non-commutativity? merge does not play a role here, and keys might be covered in the previous sentence?

  1. MutablePoset.update_union: "Due to keys and a merge function... this operation might not be commutative": This method is non-commutative by definition, as self is changed and other is not. So perhaps: "left.update_union(right)" and "right.update_union(left) might result in different posets"? The same for other update_... methods where non-commutativity might be surprising.

comment:44 Changed 4 years ago by dkrenn

  • Branch changed from u/cheuberg/asy/mutable-poset to u/dkrenn/asy/mutable-poset

comment:45 in reply to: ↑ 43 Changed 4 years ago by dkrenn

  • Commit changed from 4deddbd1a09e0e60273797cb89becdc651325b9c to 4e73b4576e1e949b7257d858fbeb958152df9f66

Replying to cheuberg:

Thank you for your changes. I added three commits. See my remaining comments below.

Cross-review...ok.

  1. MutablePosetShell.key: I am surprised that the key is not cached. I imagine that many comparisons will be needed in the lifetime of a MutablePoset, and in every case, the property key has to be resolved, which calls the property poset, which calls get_key of the poset.

Now it is cached (see also follow up ticket #19281).

I rather thought about calling key in __init__ as I guess that the key will be needed at least once in the lifetime of every MutablePosetShell.

Oh...yes, I agree; changed.

  1. MutablePosetShell._copy_all_linked_: I do not understand why you test oo == P.oo: I think that oo is an element of the new poset Q.

oo == P.oo tests that Q.oo is mapped to P.oo.

wouldn't oo.is_oo do it without comparing shells of different posets, which might be confusing?

True. Changed.

So oo is Q.oo would be more interesting?

oo is Q.oo is False since oo is not in Q, but just a copy of the oo in P with parent-poset Q.

that would be good to test (and comment on).

Inserted.

Inserting this into Q is done in _copy_shells_.

The current test demonstrates that the poset is not used in comparison, so that would rather belong to .eq?

I do not understand what you mean (but it is already late...).

I mean that shells e and f might be equal even if they do belong to different posets; this might be an interesting doctest or example for equality.

Now I understand what you mean. Inserted a doctest there.

  1. MutablePosetShell._search_covers_: According to Wikipedia, a cover is what is called an upper cover here. This is in contrast to the default behaviour here.

_search_covers_ does not exist anymore (see 27).

This does not solve the problem.

What about renaming the method covers to lower_covers (and adapting the docstring slightly, removing "upper " from the one-sentence-description as well as from the definition?) For symmetry, a method upper_covers would be nice.

Good idea; changed and inserted upper_covers.

  1. MutablePoset.intersection and MutablePoset.intersection_update: see comments on union and union_update

Done.

Remove comment on non-commutativity? merge does not play a role here, and keys might be covered in the previous sentence?

Removed.

  1. MutablePoset.update_union: "Due to keys and a merge function... this operation might not be commutative": This method is non-commutative by definition, as self is changed and other is not. So perhaps: "left.update_union(right)" and "right.update_union(left) might result in different posets"? The same for other update_... methods where non-commutativity might be surprising.

Changed.


New commits:

f7bd83aTrac #17693, comment 43, 7: do caching of key in __init__
a554d69rac #17693, comment 43, 18: use .is_oo to test for oo in doctest
3ac7ed1rac #17693, comment 43, 18: add a doctest "oo is Q.oo"
2f675b3Trac #17693, comment 43, 18: add a doctest in eq (comparing elements in different posets)
f064a3bTrac #17693, comment 43, 22: covers --> lower_covers, upper_covers
bea925cTrac #17693, comment 43, 55: remove comment on non-commutativity
4e73b45Trac #17693, comment 43, 63: extend/rewrite non-commutativity note

comment:46 Changed 4 years ago by dkrenn

  • Status changed from needs_work to needs_review

comment:47 Changed 4 years ago by cheuberg

  • Branch changed from u/dkrenn/asy/mutable-poset to u/cheuberg/asy/mutable-poset

comment:48 Changed 4 years ago by git

  • Commit changed from 4e73b4576e1e949b7257d858fbeb958152df9f66 to a0b3d7bce3325e271e53b0a83047a6f80ac28a22

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

e8d8d2cTrac #17693: typos
4b7f929Trac #17693: fix two copy&paste errors
a0b3d7bTrac #17693: ReSt improvement

comment:49 follow-up: Changed 4 years ago by cheuberg

  • Status changed from needs_review to positive_review

Added three final reviewer commits.

Doctests pass, documentation builds, documentation seems to be fine, code seems to be fine.

comment:50 in reply to: ↑ 49 Changed 4 years ago by dkrenn

Replying to cheuberg:

Added three final reviewer commits.

Thanks; checked.

Doctests pass, documentation builds, documentation seems to be fine, code seems to be fine.

:)

comment:51 Changed 4 years ago by vbraun

  • Branch changed from u/cheuberg/asy/mutable-poset to a0b3d7bce3325e271e53b0a83047a6f80ac28a22
  • Resolution set to fixed
  • Status changed from positive_review to closed
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