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Re: [Axiom-developer] docstrings created by aldor
From: |
Martin Rubey |
Subject: |
Re: [Axiom-developer] docstrings created by aldor |
Date: |
12 Apr 2007 20:27:33 +0200 |
User-agent: |
Gnus/5.09 (Gnus v5.9.0) Emacs/21.4 |
Martin Rubey <address@hidden> writes:
> Do you know which part (i.e., boot or lisp function) is responsible for
> creating libdb.text?
>
> I guess it is created from the asy file, but even that I do not know.
OK, that one is pretty sure now. Furthermore, it seems that minus signs start
always after exactly 500 characters, however, the number of minus signs
appearing at this position varies. After 500 more characters, I get minus signs
again, but there may be some other characters inbetween, as here:
(unfortunately, copy pasting modifies some characters, so the positions are not
exact anymore below)
Martin
dCycleIndexSeries`0`x`()->Join(FormalPowerSeriesCategory(SparseDistributedPolynomial(ACFraction(ACInteger),CycleIndexVariable,SparseIndexedPowerProduct(CycleIndexVariable,ACMachineInteger))),etc)``CYCLEIN`\begin{addescription}{Cycle
index series.} \adthistype{} is the domain that represents \useterm{cycle
index series}, \ie, \useterm{formal power series} in infinitely many
variables $x_1,x_2,x_3,\ldots$ of the form \begin{gather}
f(x_1,x_2,\ldots)=\sum_{j_1+2j_2+\dots<\i----------------nfty}
f_{(j_1,j_2,j_3,\ldots)} x_1^{j_1} x_2^{j_2} x_3^{j_3}\cdots \end{gather}
We group certain terms together and obtain \begin{gather}
f(x_1,x_2,\ldots)=\sum_{n\geq0}
\sum_{\substack{j=(j_1,\ldots,j_n)\in\setN^n\\j_1+2j_2+\dots+nj_n=n}}
f_j x_1^{j_1} x_2^{j_2} \cdots x_n^{j_n} \end{gather} where the
polynomial under the outer sum is the \emph{sum} (over all
\useterm[isomorphism types]{isomorphism type}) of certain \useterm[cycle
index-- p--ol--yn--om--ia--ls--]{--cycle index polynomial} of degree $n$.
In fact, if $f=Z_F$ for some \useterm{combinatorial species} $F$ then $f_j =
\frac{\fix F[j]}{\aut j}$ where $\aut(j)$ is defined by~\eqref{eq:def:aut}.
If we denote by $\setN^{(\setN)}$ the set of finite sequences of natural
numbers then a \useterm{cycle index series} $f$ is a function from
$\setN^{(\setN)}$ to $\setQ$ in anology to the fact that a \useterm{formal
power series} (over $\setQ$) is a f--unct--ion -- f--rom --$\se--tN$ --to
$--\setQ$. \end{addescription}