All the introductory reading on formal power series and computation from the
classical methods meetup.
on formal power series.
Review how painful it was to extract coefficients of a composition of power
series even in O(n3) time
using classical techniques.
M. Douglas McIlroy’s
Power series, power serious
functional pearl from JFP. This is a wonderful introduction to practical
computing with power series, which themselves have direct connections to
Analytic Combinatorics through generating functions. It shows how lazy (but
automatically memoized) stream types (such as Haskell’s lists) make these
computations signifcantly simpler than doing things the “direct” way.
Spend some time thinking about your novel knot/novel knot integration for show
and tell.
Agenda:
Novel Knots show and tell. Try to show up with some unique not that you
developed or else some unique way of putting knots together in a working,
practical system (or aesthetic display). It’s fine if you later discover that
your knot or system was already developed elsewhere; the idea is to get the
creative juices flowing and explore how knots work.
Check out the novel knots or knot systems/integrations everybody has
developed over the past few weeks.
Critique and enhance each others’ discoveries.
Work through the Power Series, Power Serious paper. The goal is to get
through all basic series operations (including series composition; the same
stuff we did with classical techniques).
I don’t expect to get through “advanced” use cases involving reversion,
differentiation/integration, or differential equations. We can do a
follow-up session on that if there’s interest.
Compare the lazy technique to the classical technique from last time.
Ease or difficulty of implementation
Understandability (especially for somebody without the requisite background)