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\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input DERHAM.input}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
<<*>>=
-- Input generated from DeRhamComplexXmpPage
)clear all
coefRing := Integer
lv : List Symbol := [x,y,z]
der := DERHAM(coefRing,lv)
R := Expression coefRing
f : R := x**2*y*z-5*x**3*y**2*z**5
g : R := z**2*y*cos(z)-7*sin(x**3*y**2)*z**2
h : R :=x*y*z-2*x**3*y*z**2
dx : der := generator(1)
dy : der := generator(2)
dz : der := generator(3)
[dx,dy,dz] := [generator(i)$der for i in 1..3]
alpha : der := f*dx + g*dy + h*dz
beta : der := cos(tan(x*y*z)+x*y*z)*dx + x*dy
exteriorDifferential alpha;
exteriorDifferential %
gamma := alpha * beta
exteriorDifferential(gamma) - (exteriorDifferential(alpha)*beta - alpha * exteriorDifferential(beta))
a : BOP := operator('a)
b : BOP := operator('b)
c : BOP := operator('c)
sigma := a(x,y,z) * dx + b(x,y,z) * dy + c(x,y,z) * dz
theta := a(x,y,z) * dx * dy + b(x,y,z) * dx * dz + c(x,y,z) * dy * dz
totalDifferential(a(x,y,z))$der
exteriorDifferential sigma
exteriorDifferential theta
one : der := 1
g1 : der := a([x,t,y,u,v,z,e]) * one
h1 : der := a([x,y,x,t,x,z,y,r,u,x]) * one
exteriorDifferential g1
exteriorDifferential h1
coefficient(gamma, dx*dy)
coefficient(gamma, one)
coefficient(g1,one)
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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