%% Created by Maple 8.00 (IBM INTEL NT)
%% Source Worksheet: NF4.mws
%% Generated: Thu Jan 01 18:50:24 2004
\documentclass{article}
\usepackage{maple2e}
 \def\emptyline{\vspace{12pt}}
\DefineParaStyle{Maple Output}
\DefineParaStyle{Maple Output}
\DefineParaStyle{Normal}
\DefineParaStyle{Normal}
\DefineParaStyle{Warning}
\DefineCharStyle{2D Math}
\DefineCharStyle{2D Output}
\begin{document}
\pagestyle{empty}
\begin{maplegroup}
\begin{center}
à réécrire avec \&*
\end{center}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{with(StringTools):}{%
}
\end{mapleinput}

\mapleresult
\begin{maplettyout}
Warning, the assigned name Group now has a global binding
\end{maplettyout}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{# puiss : puissance nième d'un mot w}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{puiss:=proc(w,n) local res,i : res:=w : for i to n-1 do
res:=cat(w,res) od : res end;}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{puiss := proc (w, n) local res, i; res := w; for i to n-1 do res :=
cat(w,res) end do; res end proc;}{%
\maplemultiline{
\mathit{puiss} := \textbf{proc} (w, \,n) \\
\textbf{local} \,\mathit{res}, \,i; \\
\mapleIndent{1} \mathit{res} := w\,;\,\textbf{for} \,i\,\textbf{
to} \,n - 1\,\textbf{do} \,\mathit{res} := \mathrm{cat}(w, \,
\mathit{res})\,\textbf{end do} \,;\,\mathit{res} \\
\textbf{end proc}  }
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{# elementary normal form}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{enf:=proc(S) local i,res,l;res:=S:if S=du then res:=ud+1 else for i
to length(S)-1 do if substring(S,i..i+1)=du then
res:=cat(substring(S,1..i-1),ud,substring(S,i+2..length(S)))
+cat(substring(S,1..i-1),substring(S,i+2..length(S))):i:=length(S)-1
else fi od fi: res end:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{# La même linéarisée.}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{lenf:=proc(P) local j,res;if type(P,`+`) then res:=lenf(op(1,P)): for
j from 2 to nops(P) do res:=res+lenf(op(j,P)) od elif type(P,`*`) then
res:=op(1,P)*lenf(op(2,P)) elif type(P,symbol) then res:=enf(P) else
res:=expand(P) fi:res end:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{# NF normal form}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{NF:=proc(P) local i,Q;Q:=P:for i to ceil(length(P)/2)^2 do Q:=lenf(Q)
od:Q end;}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{NF := proc (P) local i, Q; Q := P; for i to ceil(1/2*length(P))^2 do
Q := lenf(Q) end do; Q end proc;}{%
\maplemultiline{
\mathit{NF} := \textbf{proc} (P) \\
\textbf{local} \,i, \,Q; \\
\mapleIndent{1} Q := P\,;\,\textbf{for} \,i\,\textbf{to} \,
\mathrm{ceil}(1/2 \ast \mathrm{length}(P))^{2}\,\textbf{do} \,Q
 := \mathrm{lenf}(Q)\,\textbf{end do} \,;\,Q \\
\textbf{end proc}  }
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{with(combinat):}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{center}
{\large \textbf{Bonson String aléatoire de taille \TEXTsymbol{<}=N,
BSA(N)}}
\end{center}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{HW:=proc(N) cat(d,op(subs(\{1=d,0=u\},convert(N,base,2))),u) end;}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{HW := proc (N) cat(d,op(subs(\{1 = d, 0 = u\},convert(N,base,2))),u)
end proc;}{%
\[
\mathit{HW} := \textbf{proc} (N)\,\mathrm{cat}(d, \,\mathrm{op}(
\mathrm{subs}(\{1=d, \,0=u\}, \,\mathrm{convert}(N, \,\mathit{
base}, \,2))), \,u)\,\textbf{end proc} 
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{BSA:=proc(N) HW(rand(0..2^(N))()) end;}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{BSA := proc (N) HW(rand(0 .. 2^N)()) end proc;}{%
\[
\mathit{BSA} := \textbf{proc} (N)\,\mathrm{HW}(\mathrm{rand}(0
 .. 2^{N})())\,\textbf{end proc} 
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{BSA(4);}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{ddudu;}{%
\[
\mathit{ddudu}
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\emptyline
\begin{center}
\textbf{{\large W2M(w,x) : Conversion élémentaire d'un mot en
x\symbol{94}(nombre de d)}}
\end{center}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{W2M:=proc(w,x) local i,c;c:=1:for i to length(w) do if
substring(w,i)=d then c:=c*x else fi od :c end;}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{W2M := proc (w, x) local i, c; c := 1; for i to length(w) do if
substring(w,i) = d then c := c*x else NULL end if end do; c end
proc;}{%
\maplemultiline{
\mathit{W2M} := \textbf{proc} (w, \,x) \\
\textbf{local} \,i, \,c; \\
\mapleIndent{1} c := 1\,; \\
\mapleIndent{1} \textbf{for} \,i\,\textbf{to} \,\mathrm{length}(w
)\,\textbf{do} \,\textbf{if} \,\mathrm{substring}(w, \,i)=d\,
\textbf{then} \,c := c \ast x\,\textbf{else} \,\,\textbf{end if} 
\,\textbf{end do} \,; \\
\mapleIndent{1} c \\
\textbf{end proc}  }
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{F2P:=proc(F,x) local j,res;if type(F,`+`) then res:=F2P(op(1,F),x):
for j from 2 to nops(F) do res:=res+F2P(op(j,F),x) od elif type(F,`*`)
then res:=op(1,F)*F2P(op(2,F),x) elif type(F,symbol) then
res:=W2M(F,x) else res:=expand(F) fi:sort(res) end:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{F2P(NF(puiss(ud,6)),x);}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{x^6+15*x^5+65*x^4+90*x^3+31*x^2+x;}{%
\[
x^{6} + 15\,x^{5} + 65\,x^{4} + 90\,x^{3} + 31\,x^{2} + x
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{sort(SP(6,y));}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{SP(6,y);}{%
\[
\mathrm{SP}(6, \,y)
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{CE(uddududu,z);}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{CE(uddududu,z);}{%
\[
\mathrm{CE}(\mathit{uddududu}, \,z)
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{center}
SP : Polynômes de Stirling SP(r,y)=somme(c=0..r) St2(r,c)y\symbol{94}c
\end{center}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{SP:=proc(r,y) sum(stirling2(r,c)*y^c,c=0..r) end;}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{SP := proc (r, y) sum(stirling2(r,c)*y^c,c = 0 .. r) end proc;}{%
\[
\mathit{SP} := \textbf{proc} (r, \,y)\,\mathrm{sum}(\mathrm{
stirling2}(r, \,c) \ast y^{c}, \,c=0 .. r)\,\textbf{end proc} 
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{SP(4,y);}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{y+7*y^2+6*y^3+y^4;}{%
\[
y + 7\,y^{2} + 6\,y^{3} + y^{4}
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{center}
Polynômes de Stirling Généralisés SP(r,y)=somme(c=0..r)
St2(r,c)y\symbol{94}c\textbf{ par la formule (32)}
\end{center}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{FG:=(x,y,r)->exp(y*((1/(1-(r-1)*x))^(1/(r-1))-1));}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{FG := proc (x, y, r) options operator, arrow;
exp(y*((1/(1-(r-1)*x))^(1/(r-1))-1)) end proc;}{%
\[
\mathit{FG} := (x, \,y, \,r)\rightarrow e^{ \left(  \! y\,
 \left(  \! (\frac {1}{1 - (r - 1)\,x})^{(\frac {1}{r - 1})} - 1
 \!  \right)  \!  \right) }
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{center}
\textbf{{\large Matrix Stringology }}
\end{center}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{seq([k,F2P(NF(puiss(uudud,k)),y)],k=0..7);}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{[0, F2P(uuudd+uud,y)], [1, F2P(uuudd+uud,y)], [2,
F2P(uuuuuudddd+8*uuuuuddd+14*uuuudd+4*uuud,y)], [3,
F2P(uuuuuuuuudddddd+21*uuuuuuuuddddd+138*uuuuuuudddd+330*uuuuuuddd+252
*uuuuudd+36*uuuud,y)], [4,
F2P(3744*uuuuuuuuuddddd+11304*uuuuuuuudddd+uuuuuuuuuuuudddddddd+40*uuu
uuuuuuuuddddddd+576*uuuuuuuuuudddddd+576*uuuuud+6624*uuuuuudd+14688*uu
uuuuuddd,y)], [5,
F2P(65*uuuuuuuuuuuuuuddddddddd+1640*uuuuuuuuuuuuudddddddd+950400*uuuuu
uuuudddd+14400*uuuuuud+20680*uuuuuuuuuuuuddddddd+uuuuuuuuuuuuuuudddddd
dddd+510120*uuuuuuuuuuddddd+140040*uuuuuuuuuuudddddd+244800*uuuuuuudd+
806400*uuuuuuuuddd,y)], [6,
F2P(90936000*uuuuuuuuuudddd+55296000*uuuuuuuuuddd+6708960*uuuuuuuuuuuu
uddddddd+69876000*uuuuuuuuuuuddddd+96*uuuuuuuuuuuuuuuuuddddddddddd+375
0*uuuuuuuuuuuuuuuudddddddddd+77700*uuuuuuuuuuuuuuuddddddddd+934200*uuu
uuuuuuuuuuudddddddd+518400*uuuuuuud+28607760*uuuuuuuuuuuudddddd+uuuuuu
uuuuuuuuuuuudddddddddddd+12182400*uuuuuuuudd,y)], [7,
F2P(4686595200*uuuuuuuuuuddd+5817601440*uuuuuuuuuuuuudddddd+7434*uuuuu
uuuuuuuuuuuuuudddddddddddd+25401600*uuuuuuuud+1918884240*uuuuuuuuuuuuu
uddddddd+51283260*uuuuuuuuuuuuuuuuddddddddd+787449600*uuuuuuuuudd+1041
9948000*uuuuuuuuuuuuddddd+4302900*uuuuuuuuuuuuuuuuudddddddddd+10156406
400*uuuuuuuuuuudddd+229194*uuuuuuuuuuuuuuuuuuddddddddddd+133*uuuuuuuuu
uuuuuuuuuuuddddddddddddd+392852880*uuuuuuuuuuuuuuudddddddd+uuuuuuuuuuu
uuuuuuuuuudddddddddddddd,y)];}{%
\maplemultiline{
[0, \,\mathrm{F2P}(\mathit{uuudd} + \mathit{uud}, \,y)], \,[1, \,
\mathrm{F2P}(\mathit{uuudd} + \mathit{uud}, \,y)],  \\
[2, \,\mathrm{F2P}(\mathit{uuuuuudddd} + 8\,\mathit{uuuuuddd} + 
14\,\mathit{uuuudd} + 4\,\mathit{uuud}, \,y)], [3, \mathrm{F2P}(
 \\
\mathit{uuuuuuuuudddddd} + 21\,\mathit{uuuuuuuuddddd} + 138\,
\mathit{uuuuuuudddd} + 330\,\mathit{uuuuuuddd} \\
\mbox{} + 252\,\mathit{uuuuudd} + 36\,\mathit{uuuud}, \,y)], [4, 
\mathrm{F2P}(3744\,\mathit{uuuuuuuuuddddd} \\
\mbox{} + 11304\,\mathit{uuuuuuuudddd} + \mathit{
uuuuuuuuuuuudddddddd} + 40\,\mathit{uuuuuuuuuuuddddddd} \\
\mbox{} + 576\,\mathit{uuuuuuuuuudddddd} + 576\,\mathit{uuuuud}
 + 6624\,\mathit{uuuuuudd} + 14688\,\mathit{uuuuuuuddd},  \\
y)], [5, \mathrm{F2P}(65\,\mathit{uuuuuuuuuuuuuuddddddddd} + 1640
\,\mathit{uuuuuuuuuuuuudddddddd} \\
\mbox{} + 950400\,\mathit{uuuuuuuuudddd} + 14400\,\mathit{uuuuuud
} + 20680\,\mathit{uuuuuuuuuuuuddddddd} \\
\mbox{} + \mathit{uuuuuuuuuuuuuuudddddddddd} + 510120\,\mathit{
uuuuuuuuuuddddd} \\
\mbox{} + 140040\,\mathit{uuuuuuuuuuudddddd} + 244800\,\mathit{
uuuuuuudd} + 806400\,\mathit{uuuuuuuuddd}, \,y) \\
], [6, \mathrm{F2P}(90936000\,\mathit{uuuuuuuuuudddd} + 55296000
\,\mathit{uuuuuuuuuddd} \\
\mbox{} + 6708960\,\mathit{uuuuuuuuuuuuuddddddd} + 69876000\,
\mathit{uuuuuuuuuuuddddd} \\
\mbox{} + 96\,\mathit{uuuuuuuuuuuuuuuuuddddddddddd} + 3750\,
\mathit{uuuuuuuuuuuuuuuudddddddddd} \\
\mbox{} + 77700\,\mathit{uuuuuuuuuuuuuuuddddddddd} + 934200\,
\mathit{uuuuuuuuuuuuuudddddddd} \\
\mbox{} + 518400\,\mathit{uuuuuuud} + 28607760\,\mathit{
uuuuuuuuuuuudddddd} \\
\mbox{} + \mathit{uuuuuuuuuuuuuuuuuudddddddddddd} + 12182400\,
\mathit{uuuuuuuudd}, \,y)], [7, \mathrm{F2P}( \\
4686595200\,\mathit{uuuuuuuuuuddd} + 5817601440\,\mathit{
uuuuuuuuuuuuudddddd} \\
\mbox{} + 7434\,\mathit{uuuuuuuuuuuuuuuuuuudddddddddddd} + 
25401600\,\mathit{uuuuuuuud} \\
\mbox{} + 1918884240\,\mathit{uuuuuuuuuuuuuuddddddd} \\
\mbox{} + 51283260\,\mathit{uuuuuuuuuuuuuuuuddddddddd} + 
787449600\,\mathit{uuuuuuuuudd} \\
\mbox{} + 10419948000\,\mathit{uuuuuuuuuuuuddddd} \\
\mbox{} + 4302900\,\mathit{uuuuuuuuuuuuuuuuudddddddddd} + 
10156406400\,\mathit{uuuuuuuuuuudddd} \\
\mbox{} + 229194\,\mathit{uuuuuuuuuuuuuuuuuuddddddddddd} \\
\mbox{} + 133\,\mathit{uuuuuuuuuuuuuuuuuuuuddddddddddddd} \\
\mbox{} + 392852880\,\mathit{uuuuuuuuuuuuuuudddddddd} \\
\mbox{} + \mathit{uuuuuuuuuuuuuuuuuuuuudddddddddddddd}, \,y)] }
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{Sw:=proc(w,n,k) coeff(F2P(NF(puiss(w,k)),y),y,n) end;}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Sw := proc (w, n, k) coeff(F2P(NF(puiss(w,k)),y),y,n) end proc;}{%
\[
\mathit{Sw} := \textbf{proc} (w, \,n, \,k)\,\mathrm{coeff}(
\mathrm{F2P}(\mathrm{NF}(\mathrm{puiss}(w, \,k)), \,y), \,y, \,n)
\,\textbf{end proc} 
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{with(LinearAlgebra):}{%
}
\end{mapleinput}

\mapleresult
\begin{maplettyout}
Warning, the name Map has been rebound
\end{maplettyout}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{matrix(7,7,(j,i)->Sw(ud,i-1,j-1));}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{matrix([[0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0,
0, 0], [0, 1, 3, 1, 0, 0, 0], [0, 1, 7, 6, 1, 0, 0], [0, 1, 15, 25,
10, 1, 0], [0, 1, 31, 90, 65, 15, 1]]);}{%
\[
 \left[ 
{\begin{array}{rrrrrrr}
0 & 1 & 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 1 & 0 & 0 & 0 & 0 \\
0 & 1 & 3 & 1 & 0 & 0 & 0 \\
0 & 1 & 7 & 6 & 1 & 0 & 0 \\
0 & 1 & 15 & 25 & 10 & 1 & 0 \\
0 & 1 & 31 & 90 & 65 & 15 & 1
\end{array}}
 \right] 
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{matrix(7,7,(j,i)->Sw(udu,i-1,j-1));}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{matrix([[1, 1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0], [2, 4, 1, 0, 0,
0, 0], [6, 18, 9, 1, 0, 0, 0], [24, 96, 72, 16, 1, 0, 0], [120, 600,
600, 200, 25, 1, 0], [720, 4320, 5400, 2400, 450, 36, 1]]);}{%
\[
 \left[ 
{\begin{array}{rrrrrrr}
1 & 1 & 0 & 0 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 & 0 & 0 & 0 \\
2 & 4 & 1 & 0 & 0 & 0 & 0 \\
6 & 18 & 9 & 1 & 0 & 0 & 0 \\
24 & 96 & 72 & 16 & 1 & 0 & 0 \\
120 & 600 & 600 & 200 & 25 & 1 & 0 \\
720 & 4320 & 5400 & 2400 & 450 & 36 & 1
\end{array}}
 \right] 
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{NF(duu);NF(duuduu);}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{uud+2*u;}{%
\[
\mathit{uud} + 2\,u
\]
%
}
\end{maplelatex}

\begin{maplelatex}
\mapleinline{inert}{2d}{uuuudd+6*uuud+6*uu;}{%
\[
\mathit{uuuudd} + 6\,\mathit{uuud} + 6\,\mathit{uu}
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{ matrix(7,7,(j,i)->Sw(duu,i-1,j-1));}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{matrix([[2, 1, 0, 0, 0, 0, 0], [2, 1, 0, 0, 0, 0, 0], [6, 6, 1, 0, 0,
0, 0], [24, 36, 12, 1, 0, 0, 0], [120, 240, 120, 20, 1, 0, 0], [720,
1800, 1200, 300, 30, 1, 0], [5040, 15120, 12600, 4200, 630, 42,
1]]);}{%
\[
 \left[ 
{\begin{array}{rrrrrrr}
2 & 1 & 0 & 0 & 0 & 0 & 0 \\
2 & 1 & 0 & 0 & 0 & 0 & 0 \\
6 & 6 & 1 & 0 & 0 & 0 & 0 \\
24 & 36 & 12 & 1 & 0 & 0 & 0 \\
120 & 240 & 120 & 20 & 1 & 0 & 0 \\
720 & 1800 & 1200 & 300 & 30 & 1 & 0 \\
5040 & 15120 & 12600 & 4200 & 630 & 42 & 1
\end{array}}
 \right] 
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{NF(puiss(udduu,2));}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{uuuuuudddd+14*uuuuuddd+54*uuuudd+60*uuud+12*uu;}{%
\[
\mathit{uuuuuudddd} + 14\,\mathit{uuuuuddd} + 54\,\mathit{uuuudd}
 + 60\,\mathit{uuud} + 12\,\mathit{uu}
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{matrix(7,7,(j,i)->Sw(uduu,i-1,j-1));}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{matrix([[2, 1, 0, 0, 0, 0, 0], [2, 1, 0, 0, 0, 0, 0], [8, 7, 1, 0, 0,
0, 0], [48, 57, 15, 1, 0, 0, 0], [384, 561, 207, 26, 1, 0, 0], [3840,
6555, 3045, 545, 40, 1, 0], [46080, 89055, 49185, 11220, 1185, 57,
1]]);}{%
\[
 \left[ 
{\begin{array}{rrrrrrr}
2 & 1 & 0 & 0 & 0 & 0 & 0 \\
2 & 1 & 0 & 0 & 0 & 0 & 0 \\
8 & 7 & 1 & 0 & 0 & 0 & 0 \\
48 & 57 & 15 & 1 & 0 & 0 & 0 \\
384 & 561 & 207 & 26 & 1 & 0 & 0 \\
3840 & 6555 & 3045 & 545 & 40 & 1 & 0 \\
46080 & 89055 & 49185 & 11220 & 1185 & 57 & 1
\end{array}}
 \right] 
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{M1:=Matrix(4,9,(j,i)->Sw(udduu,i-1,j));}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{M1 := Matrix(\%id = 12705224);}{%
\[
\mathit{M1} :=  \left[ 
{\begin{array}{rrrrrrrrr}
2 & 4 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\
12 & 60 & 54 & 14 & 1 & 0 & 0 & 0 & 0 \\
144 & 1296 & 2232 & 1296 & 306 & 30 & 1 & 0 & 0 \\
2880 & 40320 & 109440 & 105120 & 45000 & 9504 & 1016 & 52 & 1
\end{array}}
 \right] 
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{M1 := Matrix(\%id = 11622284);}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{M1 := Matrix(\%id = 11622284);}{%
\[
\mathit{M1} :=  \left[ 
{\begin{array}{c}
4\,, \,1\,, \,0\,, \,0\,, \,0\,, \,0\,, \,0\,, \,0\,, \,0\,, \,0
 \\
60\,, \,54\,, \,14\,, \,1\,, \,0\,, \,0\,, \,0\,, \,0\,, \,0\,, 
\,0 \\
1296\,, \,2232\,, \,1296\,, \,306\,, \,30\,, \,1\,, \,0\,, \,0\,
, \,0\,, \,0 \\
40320\,, \,109440\,, \,105120\,, \,45000\,, \,9504\,, \,1016\,, 
\,52\,, \,1\,, \,0\,, \,0 \\
1728000\,, \,6696000\,, \,9360000\,, \,6051600\,, \,2050560\,, \,
388200\,, \,42000\,, \,2550\,, \,80\,, \,1
\end{array}}
 \right] 
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{V1:=Vector(1..10,1);}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{V1 := Vector(\%id = 11193424);}{%
\[
\mathit{V1} :=  \left[ 
{\begin{array}{r}
1 \\
1 \\
1 \\
1 \\
1 \\
1 \\
1 \\
1 \\
1 \\
1
\end{array}}
 \right] 
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{?Multiply}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{MatrixVectorMultiply(M1,V1);}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{_rtable[13177636];}{%
\[
 \left[ 
{\begin{array}{r}
4 \\
157 \\
14712 \\
2485381 \\
657310956
\end{array}}
 \right] 
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{M1:=Matrix(5,10,(j,i)->Sw(uduuuud,i,j)):MatrixVectorMultiply(M1,V1);}
{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{_rtable[13177716];}{%
\[
 \left[ 
{\begin{array}{r}
5 \\
219 \\
22073 \\
3937737 \\
1087688521
\end{array}}
 \right] 
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{M1:=Matrix(5,10,(j,i)->Sw(duuuuud,i,j)):MatrixVectorMultiply(M1,V1);}
{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{_rtable[13177796];}{%
\[
 \left[ 
{\begin{array}{r}
6 \\
291 \\
31486 \\
5930561 \\
1711777006
\end{array}}
 \right] 
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{M1:=Matrix(5,10,(j,i)->Sw(uuuuudd,i,j)):MatrixVectorMultiply(M1,V1);}
{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{_rtable[13177876];}{%
\[
 \left[ 
{\begin{array}{r}
1 \\
31 \\
2481 \\
371881 \\
89281461
\end{array}}
 \right] 
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\end{mapleinput}

\end{maplegroup}
\end{document}
%% End of Maple 8.00 Output
