Initial population.

1 files changed, 50 insertions, 0 deletions

diff --git a/src/input/galois.input.pamphlet b/src/input/galois.input.pamphlet
new file mode 100644
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--- /dev/null
+++ b/src/input/galois.input.pamphlet
@@ -0,0 +1,50 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input galois.input}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+<<*>>=
+
+-- Input for page GaloisGroupPage
+)clear all
+
+p := x**5 - 5*x + 12
+q := resultant(eval(p,x,y),-eval(p,x,y-x),y)
+q1 := exquo(q, x**5)
+factoredQ := factor q1
+r := nthFactor(factoredQ,1)
+beta := rootOf(eval(r,x,b))
+p := p::UP(x,INT)::UP(x,AN)
+algFactors := factor(p,[beta])
+factor(p)
+factor1 := nthFactor(algFactors,1)
+root1 := -coefficient(factor1,0)
+roots := [-coefficient(nthFactor(algFactors,i),0) for i in 1..5]
+(a1,a2,a3,a4,a5) := (roots.1,roots.2,roots.3,roots.4,roots.5)
+eval(r,x,a1 - a2)
+eval(r,x,a1 - a3)
+eval(r,x,a1 - a4)
+eval(r,x,a1 - a5)
+bb := a1 - a4
+aa1 := subst(a1,beta = bb)
+aa2 := subst(a2,beta = bb)
+aa3 := subst(a3,beta = bb)
+aa4 := subst(a4,beta = bb)
+aa5 := subst(a5,beta = bb)
+(aa1 = a1) :: Boolean
+(aa1 = a2) :: Boolean
+(aa1 = a3) :: Boolean
+(aa1 = a4) :: Boolean
+(aa1 = a5) :: Boolean
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}