Differences between revisions 5 and 6
 ⇤ ← Revision 5 as of 2008-11-05 23:04:23 → Size: 754 Editor: was Comment: ← Revision 6 as of 2008-11-09 11:05:16 → ⇥ Size: 1208 Editor: was Comment: Deletions are marked like this. Additions are marked like this. Line 2: Line 2: TODO:    1. 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    2. Doctest.-----------------------------------------------------

# Dokchitser Project for Sage Days 11

TODO:

1. 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
2. Doctest.

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)