\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input marcbench.input}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{License}
<<*>>=

)clear completely
)set message type off
)set message time off

output(" Ex. 1: 4-body ")$OutputPackage

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
ls : List Symbol := [p,s,phi]
V := OVAR(ls)
R := Integer
E := IndexedExponents V
P := NSMP(R, V);
LP := List(P);

-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

p: P := 'p;
s: P := 's;
phi: P := 'phi;
p1:=-2*p^3+2*p^3*phi^3-4*phi^3*s*p^2+5*phi^3*s^3*p-phi^3*s^5;
p2:=-2*s*p^3-2*phi^3*s^2+phi^3*s^4-3*phi^3*s^2*p+2*phi^3*p;
p3:=-2*s^2+s^4-4*s^2*p+phi^2+1+4*p;
lp:=[p1,p2,p3];


T := REGSET(R,E,V,P);
)set message time off
zeroSetSplit(lp)$T;
)set message time on
zeroSetSplit(lp)$T;
)set message time off

output(" Ex. 2:  Wang-16 ")$OutputPackage

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
ls : List Symbol := [x,y,z,t,u];
V := OVAR(ls);
R := Integer;
E := IndexedExponents V;
P := NSMP(R, V)
LP := List(P)

-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

x: P := 'x
y: P := 'y
z: P := 'z
t: P := 't
u: P := 'u
f0 := u-2
f1:= 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
f2:= 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
f3:= -u^2*(z-1)^2+2*z*(z-x)-2*(x-1)
f4:= 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)
lp :=[f0,f1,f2,f3,f4]


T := REGSET(R,E,V,P)
)set message time off
zeroSetSplit(lp)$T
)set message time on
zeroSetSplit(lp)$T
)set message time off

output(" Ex. 3: Rose ")$OutputPackage

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
ls : List Symbol := [z,y,x]
V := OVAR(ls)
R := Integer
E := IndexedExponents V
P := NSMP(R, V)
LP := List(P)

-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

x: P := 'x;
y: P := 'y;
z: P := 'z;
f1 := 7*y**4 - 20*x**2 
f2:=  (2160*x**2 + 1512*x +315)*z**4-4000*x**2-2800*x-490 
f3 :=  (67200000*x**5 + 94080000*x**4 + 40924800*x**3 + 2634240*x**2-2300844*x-432180)*y**3 + ((40320000*x**6 + 28800000*x**5 + 21168000*x**3 + 4939200*x**2 + 347508*x)*z)*y**2 + ((-23520000*x**4-41395200*x**3-26726560*x**2-7727104*x-852355)*z**2)*y + (-10080000*x**4-28224000*x**3-15288000*x**2-1978032*x-180075)*z**3 
lp := [f1,f2,f3]


T := REGSET(R,E,V,P)
)set message time off
zeroSetSplit(lp)$T
)set message time on
zeroSetSplit(lp)$T
)set message time off

output(" Ex. 4: L-3 ")$OutputPackage

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
ls: List Symbol := [x,y,z,t];
V := OVAR ls;
R := Integer;
E := IndexedExponents V;
P := NSMP(R, V);
LP := List(P);

-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

x: P := `x;
y: P := `y;
z: P := `z
t: P := `t;
p1 := x^3 + y + z + t- 1;
p2 := x + y^3 + z + t -1;
p3 := x + y + z^3 + t-1;
p4 := x + y + z + t^3 -1;
lp := [p1,p2,p3,p4];

T := REGSET(R,E,V,P)
)set message time off
zeroSetSplit(lp)$T
)set message time on
zeroSetSplit(lp)$T
)set message time off

output(" Ex. 5:Butcher ")$OutputPackage

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
ls : List Symbol := [b1,x,y,z,t,v,u,w];
V := OVAR(ls);
R := Integer;
E := IndexedExponents V;
P := NSMP(R, V);
LP := List(P);

-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

b1: P := 'b1;
x: P := 'x;
y: P := 'y;
z: P := 'z;
t: P := 't;
u: P := 'u;
v: P := 'v;
w: P := 'w;
f0 := b1 + y + z - t - w
f1 := 2*z*u + 2*y*v + 2*t*w - 2*w**2 - w - 1 
f2 := 3*z*u**2 + 3*y*v**2 - 3*t*w**2 + 3*w**3 + 3*w**2 - t + 4*w  
f3 := 6*x*z*v - 6*t*w**2 + 6*w**3 - 3*t*w + 6*w**2 - t + 4*w  
f4 := 4*z*u**3+ 4*y*v**3+ 4*t*w**3- 4*w**4 - 6*w**3+ 4*t*w- 10*w**2- w- 1  
f5 := 8*x*z*u*v +8*t*w**3 -8*w**4 +4*t*w**2 -12*w**3 +4*t*w -14*w**2 -3*w -1  
f6 := 12*x*z*v**2+12*t*w**3 -12*w**4 +12*t*w**2 -18*w**3 +8*t*w -14*w**2 -w -1
f7 := -24*t*w**3 + 24*w**4 - 24*t*w**2 + 36*w**3 - 8*t*w + 26*w**2 + 7*w + 1 

lp := [f0,f1,f2,f3,f4,f5,f6,f7]
T := REGSET(R,E,V,P)
)set message time off
zeroSetSplit(lp)$T
)set message time on
zeroSetSplit(lp)$T
)set message time off

output(" Ex. 6 : Hairer-2 ")$OutputPackage

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
ls : List Symbol := [A43,A42,A41,A32,A31,A21,B1,B2,B3,B4,C4,C3,C2];
V := OVAR(ls);
R := Integer;
E := IndexedExponents V;
P := NSMP(R, V);
LP := List(P);

-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

A43: P := 'A43;
A42: P := 'A42;
A41: P := 'A41;
A32: P := 'A32;
A31: P := 'A31;
A21: P := 'A21;
B1: P := 'B1;
B2: P := 'B2;
B3: P := `B3;
B4: P := `B4;
C4: P := `C4;
C3: P := `C3;
C2: P := `C2;
f1 := B1+B2+B3+B4-1 ;
f2 := 2*B2*C2 + 2*B3*C3 + 2*B4*C4 - 1 ;
f3 := 3*B2*C2**2 +3*B3*C3**2 +3*B4*C4**2 -1 ;
f4 := 6*B3*A32*C2 +6*B4*A42*C2 +6*B4*A43*C3 -1 ;
f5 := 4*B2*C2**3 +4*B3*C3**3 +4*B4*C4**3 -1 ;
f6 := 8*B3*C3*A32*C2 +8*B4*C4*A42*C2 +8*B4*C4*A43*C3 -1 ;
f7 := 12*B3*A32*C2**2 +12*B4*A42*C2**2 +12*B4*A43*C3**2 -1 ;
f8 := 24*B4*A43*A32*C2 -1 ;
f9 := -A21+C2 ;
f10 := -A31-A32+C3 ;
f11 := -A41-A42-A43+C4 ;

lp := [f1,f2,f3,f4,f5,f6,f7,f8,f9,f10,f11];

T := REGSET(R,E,V,P);
)set message time off
zeroSetSplit(lp)$T
)set message time on
zeroSetSplit(lp)$T
)set message time off

output(" Ex. 7 : Lichtblau ")$OutputPackage

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
ls : List Symbol := [t,y,x];
V := OVAR(ls);
R := Integer;
E := IndexedExponents V;
P := NSMP(R, V);
LP := List(P);

-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

x: P := 'x;
y: P := 'y;
t: P := 't;
p1 := x-110*t^2+495*t^3-1320*t^4+2772*t^5-5082*t^6+7590*t^7-8085*t^8+5555*t^9-2189*t^10+374*t^11;
p2 :=  y-22*t+110*t^2-330*t^3+1848*t^5-3696*t^6+3300*t^7-1650*t^8+550*t^9-88*t^10-22*t^11;
lp := [p1, p2];

T := REGSET(R,E,V,P);
)set message time off
zeroSetSplit(lp)$T
)set message time on
zeroSetSplit(lp)$T
)set message time off

output(" Ex. 8: Liu original ")$OutputPackage

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
ls : List Symbol := [x,y,z,t,a];
V := OVAR(ls);
R := Integer;
E := IndexedExponents V;
P := NSMP(R, V);
LP := List(P);

-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

x: P := 'x;
y: P := 'y;
z: P := 'z;
t: P := 't;
a: P := 'a;
p1 := y*(z-t)-x+a ;
p2 := z*(t-x)-y+a ;
p3 := t*(x-y)-z+a ;
p4 := x*(y-z)-t+a ;
lp := [p1,p2,p3,p4] ;


T := REGSET(R,E,V,P);
)set message time off
zeroSetSplit(lp)$T
)set message time on
zeroSetSplit(lp)$T
)set message time off

output(" Ex. 9: Liu homog. ")$OutputPackage

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
ls : List Symbol := [x,y,z,t,a,h];
V := OVAR(ls);
R := Integer;
E := IndexedExponents V;
P := NSMP(R, V);
LP := List(P);

-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

x: P := 'x;
y: P := 'y;
z: P := 'z;
t: P := 't;
a: P := 'a;
h: P := 'h;
p1 := y*z-y*t-x*h+a*h;
p2 := z*t-z*x-y*h+a*h;
p3 := t*x-y*t-z*h+a*h;
p4 := x*y-z*x-t*h+a*h;
lp := [p1,p2,p3,p4] ;


T := REGSET(R,E,V,P);
)set message time off
zeroSetSplit(lp)$T
)set message time on
zeroSetSplit(lp)$T
)set message time off

output(" Ex. 10: Vermeer ")$OutputPackage

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
ls : List Symbol := [w,v,u,y,x];
V := OVAR(ls);
R := Integer;
E := IndexedExponents V;
P := NSMP(R, V);
LP := List(P);

-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

x: P := 'x;
y: P := 'y;
u: P := 'u;
v: P := 'v;
w: P := 'w;
p1 := (x - u) ** 2 + (y - v) ** 2 - 1 ;
p2 := v ** 2 - u ** 3 ;
p3 := 2 * v * (x - u) + 3 * u ** 2 * (y - v) ;
f1 := (3 * w * u ** 2 - 1) ;
f2 := (2 * w * v - 1) ;
p4 := f1 * f2 ;
lp := [p1,p2,p3,p4] ;


T := REGSET(R,E,V,P);
)set message time off
zeroSetSplit(lp)$T;
)set message time on
zeroSetSplit(lp)$T;
)set message time off

output(" Ex. 11: Wu-Wang-2" )

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
ls : List Symbol := reverse [x10,x11,x12,x13,x21,x22,x23,x30,x101,x102,x103,x104,x105]
V := OVAR(ls);
R := Integer;
E := IndexedExponents V;
P := NSMP(R, V);
LP := List(P);

-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

x10: P := 'x10;
x11:P := 'x11;
x12:P := 'x12;
x13:P := 'x13;
x21:P := 'x21;
x22:P := 'x22;
x23:P := 'x23;
x30:P := 'x30;
x101:P := 'x101;
x102:P := 'x102;
x103:P := 'x103;
x104:P := 'x104;
x105:P := 'x105;f1:=x21-x12-x13;
f2:=x22-x11-x13;
f3:=x23-x11-x12;
f4:=x30-x11^3-x12^3-x13^3;
f5:=x21*x22*x23-x10*x30;
f6:=x10+x101*f1+x102*f2+x103*f3+x104*f4+x105*f5;
f7 := differentiate(f6,'x11);
f8 := differentiate(f6,'x12);
f9 := differentiate(f6,'x13);
f10 := differentiate(f6,'x21);
f11 := differentiate(f6,'x21);
f12 := differentiate(f6,'x22);
f13 := differentiate(f6,'x23);
f14 := differentiate(f6,'x23);
f15 := differentiate(f6,'x30);
f16 := differentiate(f6,'x10);
lp:=[f1,f2,f3,f4,f5,f6,f7,f8,f9,f10,f11,f12,f13,f14,f15,f16];



T := REGSET(R,E,V,P);
)set message time off
zeroSetSplit(lp)$T
)set message time on
zeroSetSplit(lp)$T
)set message time off

output(" Ex. 12: f-633 ")$OutputPackage

-----------------------------------------------------------------------------
--% Domains Definitions
-----------------------------------------------------------------------------

)clear all
ls : List Symbol := [U6,U5,U4,U3,U2,u6,u5,u4,u3,u2];
V := OVAR(ls);
R := Integer;
E := IndexedExponents V;
P := NSMP(R, V);
LP := List(P);

-----------------------------------------------------------------------------
--% Initialisations
-----------------------------------------------------------------------------

U6: P := 'U6;
U5: P := 'U5;
U4: P := 'U4;
U3: P := 'U3;
U2: P := 'U2;
u6: P := 'u6;
u5: P := 'u5;
u4: P := 'u4;
u3: P := 'u3;
u2: P := 'u2;
p1 := 2*u6 + 2*u5 + 2*u4 + 2*u3 + 2*u2 + 1;
p2 := 8*U5*u6 + 8*U5*u5 + 8*U4*u6 +8*U4*u5 + 8*U4*u4 + 8*U3*u6 + 8*U3*u5 + 8*U3*u4 + 8*U3*u3 + 8*U2*u6 +8*U2*u5 + 8*U2*u4 + 8*U2*u3 + 8*U2*u2 -13;
p3 := 2*U6 + 2*U5 + 2*U4 + 2*U3 +2*U2 + 1;
p4 := 8*U6*u5 + 8*U6*u4 + 8*U6*u3 + 8*U6*u2 + 8*U5*u5 + 8*U5*u4 +8*U5*u3 + 8*U5*u2 + 8*U4*u4 + 8*U4*u3 + 8*U4*u2 + 8*U3*u3 + 8*U3*u2 +8*U2*u2 -13;
p6 := U2*u2 -1;
p7 := U3*u3 -1;
p8 := U4*u4 -1;
p9 := U5*u5 -1;
p10 := U6*u6 -1;
lp := [p1,p2,p3,p4,p6,p7,p8,p9,p10];



T := REGSET(R,E,V,P);
)set message time off
zeroSetSplit(lp)$T
)set message time on
zeroSetSplit(lp)$T
)set message time off

@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}