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\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input REGSET.input}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
<<*>>=
-- Input generated from RegularTriangularSetXmpPage
)clear all
R := Integer
ls : List Symbol := [x,y,z,t]
V := OVAR(ls)
E := IndexedExponents V
P := NSMP(R, V)
x: P := 'x
y: P := 'y
z: P := 'z
t: P := 't
T := REGSET(R,E,V,P)
p1 := x ** 31 - x ** 6 - x - y
p2 := x ** 8 - z
p3 := x ** 10 - t
lp := [p1, p2, p3]
zeroSetSplit(lp)$T
lts := zeroSetSplit(lp,false)$T
[coHeight(ts) for ts in lts]
f1 := y**2*z+2*x*y*t-2*x-z
f2 := -x**3*z+ 4*x*y**2*z+ 4*x**2*y*t+ 2*y**3*t+ 4*x**2- 10*y**2+ 4*x*z- 10*y*t+ 2
f3 := 2*y*z*t+x*t**2-x-2*z
f4 := -x*z**3+ 4*y*z**2*t+ 4*x*z*t**2+ 2*y*t**3+ 4*x*z+ 4*z**2-10*y*t- 10*t**2+2
lf := [f1, f2, f3, f4]
zeroSetSplit(lf)$T
lts2 := zeroSetSplit(lf,false)$T
[coHeight(ts) for ts in lts2]
degrees := [degree(ts) for ts in lts2]
reduce(+,degrees)
u : R := 2
q1 := 2*(u-1)**2+ 2*(x-z*x+z**2)+ y**2*(x-1)**2- 2*u*x+ 2*y*t*(1-x)*(x-z)+ 2*u*z*t*(t-y)+ u**2*t**2*(1-2*z)+ 2*u*t**2*(z-x)+ 2*u*t*y*(z-1)+ 2*u*z*x*(y+1)+ (u**2-2*u)*z**2*t**2+ 2*u**2*z**2+ 4*u*(1-u)*z+ t**2*(z-x)**2
q2 := t*(2*z+1)*(x-z)+ y*(z+2)*(1-x)+ u*(u-2)*t+ u*(1-2*u)*z*t+ u*y*(x+u-z*x-1)+ u*(u+1)*z**2*t
q3 := -u**2*(z-1)**2+ 2*z*(z-x)-2*(x-1)
q4 := u**2+4*(z-x**2)+3*y**2*(x-1)**2- 3*t**2*(z-x)**2 +3*u**2*t**2*(z-1)**2+u**2*z*(z-2)+6*u*t*y*(z+x+z*x-1)
lq := [q1, q2, q3, q4]
zeroSetSplit(lq,true,true)$T
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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