Implement method to expand cycle index series as symmetric function in variables

[agd]

The cycle index series of a species is a symmetric function in the power-sum basis. Expanding this symmetric function in a set of underlying variables can reveal interesting enumerative information about the species; the coefficients of this underlying power series count "partially-labeled" structures in a Pólya-theoretic sense.

The attached patch adds an expand_as_sf method to the CycleIndexSeries? class which performs this expansion. It essentially just calls the expand method of the underlying symmetric functions, then uses the result as the terms of a LazyPowerSeries?.

This code is doctested and ready for review.

[agd]

For the patchbot:

apply trac_14906-cycle_index_expand_as_sf.patch

[mguaypaq]

The patchbot is complaining about a problem with the commit message (it shouldn't contain the [mq] that it currently starts with, and it should include the ticket number 14906 somewhere). I'll let you fix this yourself.

Meanwhile, the code is straightforward and documented, and the html and pdf documentation both build without errors and look fine. I'll play around with the code some more, but it's looking good so far!

[agd]

Thanks for the feedback! I have uploaded a new patch which corrects the commit message.

[mguaypaq]

I checked that the output of this function on a few examples agrees with the data from Table 4.1 (Cycle index series of particular species) from Bergeron, Labelle and Leroux's book "Combinatorial Species and Tree-Like Structures", so I believe that it's mathematically correct.

Also, the commit message issue is now fixed.

The only potential problem is the patchbot's startup_time plugin which failed in the latest round of testing. However, the patch only adds a small method to an existing class, so I can't believe that it would really cause a speed regression.

Positive review!

[agd]

Thanks for the review! The startup_time failure is a mystery to me as well; as you say, this is just one small method!

[jdemeyer]

Please make it clear whether the patch or the git branch should be merged. In the latter case, change the milestone to sage-6.0.