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\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input CLIF.input}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
<<*>>=
-- Input generated from CliffordAlgebraXmpPage
)clear all
-- Input generated from ugxCliffordComplexPage
)clear all
K := Fraction Polynomial Integer
m := matrix [[-1]]
C := CliffordAlgebra(1, K, quadraticForm m)
i: C := e(1)
x := a + b * i
y := c + d * i
x * y
-- Input generated from ugxCliffordQuaternPage
)clear all
K := Fraction Polynomial Integer
m := matrix [[-1,0],[0,-1]]
H := CliffordAlgebra(2, K, quadraticForm m)
i: H := e(1)
j: H := e(2)
k: H := i * j
x := a + b * i + c * j + d * k
y := e + f * i + g * j + h * k
x + y
x * y
y * x
-- Input generated from ugxCliffordExteriorPage
)clear all
K := Fraction Polynomial Integer
Ext := CliffordAlgebra(3, K, quadraticForm 0)
i: Ext := e(1)
j: Ext := e(2)
k: Ext := e(3)
x := x1*i + x2*j + x3*k
y := y1*i + y2*j + y3*k
x + y
x * y + y * x
dual2 a == coefficient(a,[2,3]) * i + coefficient(a,[3,1]) * j + coefficient(a,[1,2]) * k
dual2(x*y)
-- Input generated from ugxCliffordDiracPage
)clear all
K := Fraction Integer
g := matrix [[1,0,0,0], [0,-1,0,0], [0,0,-1,0], [0,0,0,-1]]
D := CliffordAlgebra(4,K, quadraticForm g)
gam := [e(i)$D for i in 1..4]
m := 1; n:= 2; r := 3; s := 4;
lhs := reduce(+, [reduce(+, [ g(l,t)*gam(l)*gam(m)*gam(n)*gam(r)*gam(s)*gam(t) for l in 1..4]) for t in 1..4])
rhs := 2*(gam s * gam m*gam n*gam r + gam r*gam n*gam m*gam s)
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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