Opened 7 years ago
Closed 5 years ago
#14846 closed enhancement (fixed)
CycleIndexSeries derivative, integral, exponential methods are not combinatorial
Reported by:  agd  Owned by:  agd 

Priority:  major  Milestone:  sage6.8 
Component:  combinatorics  Keywords:  LazyPowerSeries, species 
Cc:  Merged in:  
Authors:  Andrew GainerDewar  Reviewers:  Martin Rubey 
Report Upstream:  N/A  Work issues:  documentation 
Branch:  ab9c7d1 (Commits)  Commit:  ab9c7d161b8318bc5edffb3bb3dd66bc5c503318 
Dependencies:  Stopgaps: 
Description (last modified by )
The CycleIndexSeries? class inherits derivative, integral, and exponential methods from its parent class LazyPowerSeries?. However, these operations (which are perfectly reasonable at the LazyPowerSeries? level) are not combinatorially natural. In fact, there is a differentiation operator on cycle index series, but it's something entirely different, and antidifferentiation is in general impossible!
In addition to being confusing, this discrepancy has the potential to hinder work using the CycleIndexSeries? class. The combinatorial operation of cycle index differentiation is very useful in enumerative work.
All that said, the existing exponential and derivative methods are used for algebraic magic tricks in some of the existing code, so it's important not to take it away altogether.
The attached patch makes the following changes:
 Adds _lps_derivative, _lps_integral, and _lps_exponential methods to CycleIndexSeries? which call up using super.
 Refactors the internal code which previously used exponential and derivative to use _lps_exponential and _lps_derivative instead.
 Implements a new derivative method which computes the combinatorial derivative of a cycle index series.
 Implements a new pointing method which implements a related combinatorial operation.
 Implements a new integral method which raises a NotImplementedError? to prevent any user confusion (since, as explained in the docstring, there may be infinitely many very distinct cycle indices with a given derivative).
 Implements a new exponential method which returns the composition E(self) for E the cycle index series of SetSpecies?.
 Implements a new logarithm method which returns the composition Ω(self) for Ω the cycle index series implemented in CombinatorialLogarithmSeries?.
Docstrings and doctests are included for everything but the _lps_* methods, which just call up to super
. I'm not sure what a doctest for these would even look like, but I'm open to suggestions.
Attachments (1)
Change History (39)
comment:1 Changed 7 years ago by
comment:2 Changed 7 years ago by
 Status changed from new to needs_review
comment:3 Changed 7 years ago by
I have uploaded a new version of the patch which makes a small change: rather than building the terms of the derivative of a CycleIndexSeries? using an opaque list concatenation, I have used the CycleIndexSeriesRing?.term method.
comment:4 Changed 7 years ago by
 Branch set to u/agd/cis_deriv_int_exp_methods
comment:5 Changed 7 years ago by
Please make it clear whether the patch or the git branch should be merged. In the latter case, change the milestone to sage6.0.
comment:6 Changed 7 years ago by
 Branch u/agd/cis_deriv_int_exp_methods deleted
comment:7 Changed 7 years ago by
 Description modified (diff)
Changed 7 years ago by
comment:9 Changed 7 years ago by
 Status changed from needs_review to needs_work
 Work issues set to documentation
Could you please add doctests to the three _lps functions ?
comment:10 Changed 7 years ago by
 Branch set to u/agd/cis/deriv
 Commit set to 5ce33898e941771132cdf94837a4baf16a2cfddb
 Milestone changed from sage5.13 to sage6.0
 Status changed from needs_work to needs_review
Skeletal doctests added for the three _lps_* functions. I have no idea whether this is the *right* way to test this sort of method, but at least it's *a* test.
Additionally, I've switched back over to using Git to manage this—the old Mercurial workflow is just too confusing. How do I tell the build bot to ignore the attachments and only use the branch?
comment:11 Changed 6 years ago by
 Milestone changed from sage6.0 to sage6.1
comment:12 Changed 6 years ago by
 Commit changed from 5ce33898e941771132cdf94837a4baf16a2cfddb to 5547d749d9136f0eddf4400237183b78245e3f51
Branch pushed to git repo; I updated commit sha1. New commits:
5547d74  Merge branch 'develop' into cis/deriv

comment:13 Changed 6 years ago by
 Reviewers set to mantepse
comment:14 followup: ↓ 16 Changed 6 years ago by
Hi Andrew,
I'd suggest to really remove access to the three inherited methods, and rewrite the methods that use _lps_exponential accordingly:
 in set_species, we really want to return the "true" exponential cycle index series
 in partition_species, the "true" exponential of the "true" exponential  1
 in subset_species, the square of the "true" exponential
Finally, the implementation of the "true" exponential can be taken from what's in set_species in sage 6.0.
As far as I can see, the other two methods _lps_derivative and _lps_integral are not used anywhere.
This might have a speed penalty, but I'd worry about that only if it's serious. I think it's not a good idea to make the cycle index series depend on the species code, as in the proposed patch.
I would perhaps also put the definition for the combinatorial logarithm into the same file. I think at some point we should reorganise the files in the species directory..
Martin
comment:15 Changed 6 years ago by
 Commit changed from 5547d749d9136f0eddf4400237183b78245e3f51 to dd77e4ae6388bd8ad52d7f6a13848fe6490b25d2
comment:16 in reply to: ↑ 14 Changed 6 years ago by
Thanks for the suggestions!
Replying to mantepse:
I'd suggest to really remove access to the three inherited methods, and rewrite the methods that use _lps_exponential accordingly:
Sounds good to me. Done, in the latest push.
 in set_species, we really want to return the "true" exponential cycle index series
 in partition_species, the "true" exponential of the "true" exponential  1
 in subset_species, the square of the "true" exponential
I have rewritten all of these to use algebraic operations on the exponential CIS.
As far as I can see, the other two methods _lps_derivative and _lps_integral are not used anywhere.
Seems to be true. I just included them for completeness. They're gone now.
This might have a speed penalty, but I'd worry about that only if it's serious. I think it's not a good idea to make the cycle index series depend on the species code, as in the proposed patch.
Actually, I think the new way should actually be *faster*, there's just one instance of the exponential series which gets cached and handed around.
I would perhaps also put the definition for the combinatorial logarithm into the same file.
Once I wrote the other stuff, this seemed very reasonable, so I've done that as well.
comment:17 Changed 6 years ago by
 Status changed from needs_review to positive_review
comment:18 Changed 6 years ago by
Reviewer name must be full name. Also please fill in your name on the trac.sagemath.org homepage.
comment:19 Changed 6 years ago by
 Reviewers changed from mantepse to Martin Rubey
comment:20 Changed 6 years ago by
 Keywords LazyPowerSeries species added
comment:21 followup: ↓ 25 Changed 6 years ago by
 Status changed from positive_review to needs_info
One (minor) issue is the removal of combinatorial_logarithm.py which might need to be deprecated. I've also done a "rebase" of this on top of #15673 which makes the code a little bit cleaner. This is in branch "u/mhansen/ticket/14846" . Ideally, I'd prefer to have #15673 go in first since the rebase/merge of this ticket is easier than the other way around.
See http://git.sagemath.org/sage.git/log/?h=u/mhansen/ticket/14846
comment:22 Changed 6 years ago by
 Milestone changed from sage6.1 to sage6.2
comment:23 Changed 6 years ago by
 Commit changed from dd77e4ae6388bd8ad52d7f6a13848fe6490b25d2 to c7d73451550ce689a96668a210ab04b86d3a66ad
Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:
30fcfde  Initial work on new streams

96e4ea3  Make streams know about their order / aorder

a076622  Move generating_series over to new streams format

9e56173  Fix issue in LazyPowerSeries.__repr__ with (eventually) constant streams

fa83ccc  More work on moving generating_series over to new format

3b56620  Fix repr in recursive species

ea1902a  Fix cycle species cis

458bdaf  Fix bug in generating_series

9b038bb  Clean up order_operation and make the default to return 0

fefaacf  Start making the basic species use Streams directly

comment:24 Changed 6 years ago by
 Commit changed from c7d73451550ce689a96668a210ab04b86d3a66ad to 334c0956250038eae2d6efc915231e650b13be79
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
a630924  Implement combinatorial derivative, etc. for CycleIndexSeries

5ce3389  Add doctests for _lps_* methods

5547d74  Merge branch 'develop' into cis/deriv

c1998f2  Merge remotetracking branch 'origin/develop' into cis/deriv

ca21d87  Redesign patch to eliminate _lps_* methods and bad dependencies

dd77e4a  Move log and exp series code to generating_series.py

6989f3f  Merge remotetracking branch 'origin/develop' into cisderiv

2d3b466  Merge remotetracking branch 'origin/u/mhansen/ticket/14846' into cisderiv

4efe9b0  Rename CycleIndexSeriesRing.omega() to logarithm_series

334c095  Rename CycleIndexSeriesRing().exponential() to exponential_series()

comment:25 in reply to: ↑ 21 Changed 6 years ago by
 Dependencies set to 15673
Replying to mhansen:
One (minor) issue is the removal of combinatorial_logarithm.py which might need to be deprecated.
Ah, yes, this is an important point. I sometimes forget that other people might have used my code… =D
I've also done a "rebase" of this on top of #15673 which makes the code a little bit cleaner. This is in branch "u/mhansen/ticket/14846" . Ideally, I'd prefer to have #15673 go in first since the rebase/merge of this ticket is easier than the other way around.
I don't yet understand everything that's happening with #15673, but I'm starting to take a look at it. I'm definitely open to the idea, though—better series code will make all our work easier! I've taken a look at your rebased version of this, and have a few thoughts upfront:
 In the docstring for the deprecated
CombinatorialLogarithmSeries()
, you point the reader toCycleIndexSeriesRing(R).exponential()
, but in fact this should be toCycleIndexSeriesRing(R).omega()
.
 Relatedly, I'd argue that the
CycleIndexSeriesRing(R).omega()
andCycleIndexSeriesRing(R).exponential()
methods should instead be namedlogarithm_series()
andexponential_series()
. In the first place, the Ω notation is not totally standard (it's used by Labelle, but other authors have called this virtual species "Con" or other things); in the second, I think it's conceptually important to emphasize that these objects are series and not operations, since the operations are implemented asCycleIndexSeries().exponential()
andCycleIndexSeries().logarithm()
respectively. (Of course, the documentation should mention the relationship between the two!)
CycleIndexSeriesRing.LogarithmStream
appears to be internal, so the docstring ofCycleIndexSeries.logarithm()
should refer instead toCycleIndexSeriesRing.logarithm_series
.
I've updated the ticket branch to use your code with these changes. I've also set a dependency on #15673. (Evidently, I bungled the ticket modifications a bit, but I think it's all sorted now.)
New commits:
6989f3f Merge remotetracking branch 'origin/develop' into cisderiv
2d3b466 Merge remotetracking branch 'origin/u/mhansen/ticket/14846' into cisderiv
4efe9b0 Rename CycleIndexSeriesRing.omega() to logarithm_series
334c095 Rename CycleIndexSeriesRing().exponential() to exponential_series()
comment:26 Changed 6 years ago by
 Dependencies changed from 15673 to #15673
comment:27 Changed 6 years ago by
 Commit changed from 334c0956250038eae2d6efc915231e650b13be79 to 538dde76d0e116f67e1115337193fe12c48ce62b
Branch pushed to git repo; I updated commit sha1. New commits:
538dde7  Fix broken docstring in combinatorial_logarithm.py

comment:28 Changed 6 years ago by
Cool, your changes look good to me!
comment:29 Changed 6 years ago by
 Milestone changed from sage6.2 to sage6.3
comment:30 followup: ↓ 32 Changed 6 years ago by
 Dependencies #15673 deleted
While #15673 looks like it will bring some muchneeded improvements to the algebraic machinery of species in Sage, it also looks like it's going to take a while to implement. I've been fielding questions from other researchers who would like to use the code in #14347, which definitely depends on this one, so I'd be very grateful if we could move forward on this one now. I will, of course, be happy to revisit the issue in the context of #15673 once that situation stabilizes!
comment:31 Changed 6 years ago by
 Milestone changed from sage6.3 to sage6.4
comment:32 in reply to: ↑ 30 Changed 6 years ago by
I agree. I wonder what happened to #16137.
comment:33 Changed 5 years ago by
 Milestone changed from sage6.4 to sage6.6
comment:34 Changed 5 years ago by
 Commit changed from 538dde76d0e116f67e1115337193fe12c48ce62b to ab9c7d161b8318bc5edffb3bb3dd66bc5c503318
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
ab9c7d1  Rebase #14846 on current mainline Sage

comment:35 Changed 5 years ago by
Since #15673 seems to have died on the vine, I have rebuilt the code for this commit on top of current mainline Sage 6.7. All doctests in combinat/species
pass.
comment:36 Changed 5 years ago by
 Milestone changed from sage6.6 to sage6.8
 Status changed from needs_info to needs_review
comment:37 Changed 5 years ago by
 Status changed from needs_review to positive_review
I played with the code and the examples, and found myself happy. For example,
sage: T = CombinatorialSpecies() sage: X = species.SingletonSpecies() sage: E = species.SetSpecies() sage: T.define(X*E(T)) sage: s = T.cycle_index_series() sage: oeis(s.logarithm().generating_series().counts(12)) 0: A133297: a(n) = n!*Sum_{k=1..n} (1)^(k+1)*n^(nk1)/(nk)!. sage: oeis(s.pointing().generating_series().counts(12)[1:]) 0: A000312: Number of labeled mappings from n points to themselves (endofunctions): n^n. 1: A177885: (1n)^(n1). 2: A086783: Discriminant of the polynomial x^n  1. sage: oeis(s.pointing().isotype_generating_series().counts(12)[1:]) 0: A000107: Number of rooted trees with n nodes and a single labeled node; pointed rooted trees; vertebrates.
Thanks for the code and thanks for the patience!
comment:38 Changed 5 years ago by
 Branch changed from u/agd/cis/deriv to ab9c7d161b8318bc5edffb3bb3dd66bc5c503318
 Resolution set to fixed
 Status changed from positive_review to closed
For the patchbot:
apply trac_14846_cis_deriv_int_exp_methods.patch