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\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input r21bugsbig.input}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
<<*>>=
-- takes a long time
)clear completely
)set expose add constructor CyclotomicPolynomialPackage
)set message type off
)set message time off
n : PositiveInteger := 5
UZn : List(PositiveInteger) := [i for i in 1 .. n-1 | gcd(i,n) = 1]
-- K = Q(t), corps des fractions rationnelles a Phi(n) indeterminees sur Q
vars : List(Symbol) := [concat("t", i::String)::Symbol for i in 0 ..#UZn-1] ;
Zt := DistributedMultivariatePolynomial(vars, Integer) ; K :=Fraction(Zt) ;
t : List(K) := [v::K for v in vars]
-- ATTENTION : on specialise certains des indeterminees
t(#t) := 0 ; t
Zn := IntegerMod(n) ;
rapport(i : Integer, j : Integer) : Integer == -- returns <i/j> modulo n
k : Zn := i * recip(j::Zn)::Zn
return convert(k)
Phi : UP('xi, K) := map(coerce, cyclotomic(n))
-- E est l'extension cyclotomique de K par les racines n-iemes de l'unite
E := SimpleAlgebraicExtension(K, UP('xi, K), Phi) ;
xi : E := generator()$E ;
bList : List(E) := [reduce(+, [t(i+1) * xi**(i*j) for i in 0 .. #UZn-1]) for j in UZn]
-- delta(j) = delta(j, 1) avec les nouvelles notations
delta : List(E) :=
[reduce(*, [b**((j*rapport(1,k)) quo n) for b in bList for k in UZn]) for j in UZn] ;
-- verification en introduisant la liste B des Bj
B : List(E) := [reduce(*, [b**rapport(j,i) for b in bList for i in UZn]) for j in UZn] ;
[B(1)**j - b * d**n for b in B for d in delta for j in UZn]
L := SimpleAlgebraicExtension(E, UP('C1, E), C1**n - B(1)) ; C1 : L := generator()$L ;
-- retracter de L sur Zt : Zt < K < E < L
retraction(z : L) : Zt ==
zE : E := retract(z)
zK : K := retract(zE)
zt : Zt := retract(zK)
return zt
)set message time on
C : List(L) := [C1**j / d for j in UZn for d in delta] ;
-- en principe [c**n for c in C] = B
r : List(L) := [reduce(+, [c * xi**(k*j) for j in UZn for c in C]) for k in 0 .. n-1] ;
LX := UP('X, L) ; X : LX := monomial(1, 1) ;
g : LX := reduce(*, [X - rho for rho in r]) ;
f : UP('X, Zt) := map(retraction, g)
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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