Differences between revisions 1 and 9 (spanning 8 versions)
 ⇤ ← Revision 1 as of 2008-11-05 23:01:57 → Size: 706 Editor: was Comment: ← Revision 9 as of 2008-11-10 03:51:03 → ⇥ Size: 1734 Editor: SouravSenGupta Comment: Deletions are marked like this. Additions are marked like this. Line 2: Line 2: TODO:    1. 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)    2. 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    3. Doctest everything, making sure it all works 100% and fix issues with coercion, complex inputs, etc., as they are systematically uncovered.    4. Possibly maybe change from digits to bits prec.    5. Optimize.----------------------------------------------------- Line 19: Line 41: Dokchiter's Paper: attachment:dokchitser.pdf

# Dokchitser Project for Sage Days 11

TODO:

1. Modularize the code (break into the following classes and sort dependencies)
2. 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
3. Doctest everything, making sure it all works 100% and fix issues with coercion, complex inputs, etc., as they are systematically uncovered.
4. Possibly maybe change from digits to bits prec.
5. Optimize.

From Jen:

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: attachment:dokchitser.pdf

days11/projects/dokchitser (last edited 2008-11-14 13:42:12 by anonymous)