Dokchitser Project for Sage Days 11
- Modularize the code (break into the following classes and sort dependencies)
- LSeries (Is already in there. Have to free it from the other 3 modules)
GammaFactor (Done and documented)
IncompleteGeneralizedGammaFactor (To be done)
InverseMellinGammaFactor (To be done)
- Stuff still computed using gp:
- Delta polynomials in _recursions_at_infinity (search for comment below)
- _without_gp (gamma_series) has this line
- sinser = sage_eval(rs(gp_eval('Vec(sin(Pi*(%s)))'%(z0+x))))
- init_Ginf: still uses pari (see below)
- Ginf: still uses pari to evaluate continued fraction
- Doctest everything, making sure it all works 100% and fix issues with coercion, complex inputs, etc., as they are systematically uncovered.
- Possibly maybe change from digits to bits prec.
Here's the version (closest to Dokchitser's original pari code) that still uses continued fraction approximation:
(needs gamma_series.py to run:
The version with Pade approximation (l5.py) has a negligible speedup but only really works for low precision. I'm not sure if Pade gives us a means of computing bounds (I think Mike Rubinstein said that continued fractions won't). Also, l4.py doesn't work for imaginary inputs yet - some coercion with SymbolicRing that I didn't try.
Dokchiter's Paper: dokchitser.pdf