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\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input CARTEN.input}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
<<*>>=
-- Input generated from CartesianTensorXmpPage
)clear all
CT := CARTEN(i0 := 1, 2, Integer)
t0: CT := 8
rank t0
v: DirectProduct(2, Integer) := directProduct [3,4]
Tv: CT := v
m: SquareMatrix(2, Integer) := matrix [[1,2],[4,5]]
Tm: CT := m
n: SquareMatrix(2, Integer) := matrix [[2,3],[0,1]]
Tn: CT := n
t1: CT := [2, 3]
rank t1
t2: CT := [t1, t1]
t3: CT := [t2, t2]
tt: CT := [t3, t3]; tt := [tt, tt]
rank tt
Tmn := product(Tm, Tn)
Tmv := contract(Tm,2,Tv,1)
Tm*Tv
Tmv = m * v
t0()
t1(1+1)
t2(2,1)
t3(2,1,2)
Tmn(2,1,2,1)
t0[]
t1[2]
t2[2,1]
t3[2,1,2]
Tmn[2,1,2,1]
cTmn := contract(Tmn,1,2)
trace(m) * n
contract(Tmn,1,2) = trace(m) * n
contract(Tmn,1,3) = transpose(m) * n
contract(Tmn,1,4) = transpose(m) * transpose(n)
contract(Tmn,2,3) = m * n
contract(Tmn,2,4) = m * transpose(n)
contract(Tmn,3,4) = trace(n) * m
tTmn := transpose(Tmn,1,3)
transpose Tmn
transpose Tm = transpose m
rTmn := reindex(Tmn, [1,4,2,3])
tt := transpose(Tm)*Tn - Tn*transpose(Tm)
Tv*(tt+Tn)
reindex(product(Tn,Tn),[4,3,2,1])+3*Tn*product(Tm,Tm)
delta: CT := kroneckerDelta()
contract(Tmn, 2, delta, 1) = reindex(Tmn, [1,3,4,2])
epsilon:CT := leviCivitaSymbol()
contract(epsilon*Tm*epsilon, 1,2) = 2 * determinant m
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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