SSL Notes 4/27

Notes today: Sam

Notes Thursday: Emilie
Snacks Thursday: Carl

Notes Tuesday: Brendan
Snacks Tuesday: Sam

We go over the works-in-progress of the various groups.

Newton's Method paper:

Various edits:

Change R to C as the field we are working over.

Modify equations 2a) and 2b) (to reflect eq. (15)).

We discuss the presentation of the numerator of eq. (15).
Jim makes the point that our result is not useful to numerical analysts,
so we should change of the wording of "Newton's method is uninteresting 
as a numerical method" since it *is* interesting to them.

We should have a transitional version of P_n and Q_n in two variables, 
be fore stating the noncommutative version.


We discuss the issue of the placement of the recursive definitions of 
P_n and Q_n.  We should note that C-star refers to the Riemann sphere.
Put the commuting diagram of maps back in.

Move x^(2^n) terms to the front for clarity's sake.

Obtain references for noncommuting q-binomial theorem, Moebius 
transformations, Newton's method (either from an elementary calculus 
or a dynamics perspective).

Perhaps Knuth? Semi-numerical methods (transposition to non-numerical
methods).  We also discuss some features of Paul's write-up on the 
"cube-snake" recurrence, which is intended to be a more informal 
write-up. There are minor notational and grammatical corrections 
which Paul plans on incorporating into subsequent drafts.