L-series attached to general Euler products

[was]

This summer I wrote a package for psage (see  http://code.google.com/p/purplesage/source/browse/psage/lseries/eulerprod.py) that allows one to compute with L-series attached to general Euler products, and implemented many cases, included everything supported in Sage, and a lot more. This also did things that worked instead of the buggier #11631. This code is similar to the L-series package in Magma, I guess ( http://magma.maths.usyd.edu.au/magma/handbook/text/1503).

It would be useful to have a stable version of this code in Sage, at least the parts that don't depend on 64-bit only stuff in psage (like smalljac). The point of this ticket is to to do that.

[was]

first patch -- this implements all functionality for first version and passes all its tests. Unfortunately, the doctest coverage score is 36%. To finish this ticket, I have to get it to 100% and deal with the bugs that getting the coverage up reveals.

[cassiew1]

Second patch - Added a small function an, the class LSeriesTripleProduct, and some new doctests. Unfortunately, adding more code outbalanced the new doctests so the coverage is still very low. Noticed some bugs as well, such as zeros not being implemented, anlist allowing negative inputs, and taylor_series failing on some cases where it shouldn't. Much work yet to be done.

[was]

The patch trac_12015-part1_updated.patch has some issues:

1. It patches a file called sage/lfunctions/eulerprod_with_tripleprod.py that is not even in my patch. I'm guessing you took some old file from Sage days I had provided and started working on it. However, that has little to do with the code in the patch I posted to this ticket.

2. Why was this change made?

           118	 	sage: K.<a> = NumberField(x^2-x-1) 
    	119	        sage: K.<a> = NumberField(x^2+1) 
   

3. The code needs to be indented here, but isn't (in your patch):

           174	        EXAMPLES:: 
    	175	 
    	176	        sage: from sage.lfunctions.eulerprod import LSeries 
    	177	        sage: from sage.lfunctions.eulerprod import LSeriesDerivative 
    	178	        sage: K.<a>=NumberField(x^2+1) 
    	179	        sage: L=LSeries(K); L 
   

4. Here in your patch the code is indented (good), but there is only one colon (instead of two) after EXAMPLES:

    	508	        EXAMPLES: 
    	509	 
    	510	            sage: from sage.lfunctions.eulerprod import LSeriesAbstract 
    	511	            sage: L1 = LSeriesAbstract(conductor=1, hodge_numbers=[0], weight=1, epsilon=1, poles=[1], residues=[-1], base_field=QQ)