ToDo ⊲ 35 ⊳

This file implements formal power series. It could certainly be extended to encode
Laurant series and Puiseux series. However, we currently very much rely on the fact
that a formal power series is a function from ℕ to R and not from ℤ or ℚ. The code
is tested in the file test/series.as.nw.
rhx ⊲ 24 ⊳ 02-Feb-2007: We should implement the multiplication
algorithm of formal power series as given in [vdH02]. Currently we use the standard
convolution algorithm in FormalPowerSeries to compute the n-th coefficient of a
product.

Basically, a formal power series (implemented through the domain FormalPowerSeries is given through a DataStream. However, we add a few more fields to the data structure since we want to allow recursive definitions of formal power series. Full laziness, also says that neither the arithmetic operations on power series nor their creation using new is allowed to do any real computation. They are O(1) operations.

More details can be found at the documentation of FormalPowerSeries.

196⟨* 13⟩+≡ ⊲55 307 ⊳

-------------------------------------------------------------------

----

---- Combinat

---- Copyright (C) Ralf Hemmecke <ralf@hemmecke.de>

---- svn co svn://svn.risc.uni-linz.ac.at/hemmecke/combinat/

----

-------------------------------------------------------------------

#include "combinat"

macro {

ArithmeticType == with {

0: %;

1: %;

zero?: % -> Boolean;

+: (%, %) -> %;

*: (%, %) -> %;

}

}

⟨cat: FormalPowerSeriesCategory 199⟩

⟨dom: SeriesOrder 289⟩

⟨dom: FormalPowerSeries 242⟩

-------------------------------------------------------------------

----

---- Combinat

---- Copyright (C) Ralf Hemmecke <ralf@hemmecke.de>

---- svn co svn://svn.risc.uni-linz.ac.at/hemmecke/combinat/

----

-------------------------------------------------------------------

#include "combinat"

macro {

ArithmeticType == with {

0: %;

1: %;

zero?: % -> Boolean;

+: (%, %) -> %;

*: (%, %) -> %;

}

}

⟨cat: FormalPowerSeriesCategory 199⟩

⟨dom: SeriesOrder 289⟩

⟨dom: FormalPowerSeries 242⟩