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A (slightly) faster multiplication algorithm of univariate polynomnials over R. Currently, this is known as _mul_fateman() in rings/polynomial_element.py but needs to be faster, probably through PARI or PyrexDELTA: I've finally started working on this. See my ext/polynomial_pyx.pyx for a preview. As predicted, the speedup is nice. Only integers are handled for now.  A (slightly) faster multiplication algorithm of univariate polynomnials over R. Currently, this is known as _mul_fateman() in rings/polynomial_element.py but needs to be faster, probably through PARI or Pyrex 
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DELTA: Thanks to Dr Lambov, this now compiles on 386 and AMD64 and PPC. I've built a new version and posted patches.  
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=== Automatic build+testing === * sage br is nice, but how about an option to also run tests on any file that is being rebuilt? 

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Didier
Email: MailTo(dfdeshom AT SPAMFREE gmail DOT com)
SAGErelated projects
Quaddouble integration
Implement a wrapper for the quad double library (C++) available at http://www.cs.berkeley.edu/~yozo/ : http://sage.math.washington.edu/home/dfdeshom/custom/patches/qdrfcinterface.txt
Modifying Mercurial
There is a turorial here: http://sage.math.washington.edu:9001/ModifyingMercurial There is also a mercurial spkg with better error messages here: http://sage.math.washington.edu/home/dfdeshom/custom/hgsage/mercurial20070209.spkg
Multiplication algorithm
A (slightly) faster multiplication algorithm of univariate polynomnials over R. Currently, this is known as _mul_fateman() in rings/polynomial_element.py but needs to be faster, probably through PARI or Pyrex
RealLib inclusion
RealLib3 as an alternate source for computing real numbers.
RealLib vs MPFR:
RealLib should not be a replacementto MPFR. MPFR has its uses and is
faster than RealLib3
Tweaking Hermes
Logging of sessions using mathml through hermes:
 Improve, add fonts to hermes
 The final goal is to be able to reproduce the entire documentation
 in mathmml format. This is currently possible if you hack up some missing
fonts and avoid to generate the table of contents. Quite a pain I'll post a link to the generated doc
 in mathmml format. This is currently possible if you hack up some missing
Logging of pictures in dvi and mathml logger.
 Possible, but slightly tricky (how do you include a jpeg file in a DVI file
 without converting it to an EPS file?).
Doctest Status
Does each method have an example? Instead of checking by hand a handy script could be used. I have a script that does that: [http://sage.math.washington.edu/home/dfdeshom/sage/devel/sage/docteststatus.py http://sage.math.washington.edu/home/dfdeshom/sage/devel/sage/docteststatus.py ] For example, here is the output for integer.pyx:
Results for sage/ext/integer.pyx  Total number of tests : 87 Number of tests with examples: 42 Tests with no examples : __int__, __div_, _interface_init_, _xgcd, __cmp__, factor, factorial, __mul_, integer, __add_, __richcmp__, __floordiv, __nonzero__, crt, _and, _lcm, __long__, __str_malloc, rational_reconstruction, _mpfr_, parent, __sub_, pmem_malloc, __and__, _reduce_set, __float__, _pari_, _rshift, __invert__, _latex_, _mathml_, copy, valuation, _or, _im_gens_, __hash__, GCD_list, __reduce__, LCM_list, __new__, is_unit, __dealloc__, __repr__, __or__, _lshift ********************************************************************************