These are the tests from the Lewis/Wester test suite for polynomial
systems. Some details of Singular's performance:

A:	divide factorials		ok
B:	sum 1/i				ok
C:	gcd (big integers)		ok
D:	sum rational functions		ok
E:	sum rational functions		ok
F:	gcd(2 var polys)		ok
G:	gcd(3 var polys)		ok
G_p:	G mod 181			ok
H:	det (Hilbert(80))		with bareiss ok
I:	invert(Hilbert(40))		with inverse ok
J:	check I				ok
K:	invert(Hilbert(70))		with inverse ok
L:	check K				ok
M1:	det(sparse, rank 26, 5 var)	ok	
M2:	det(sparse, rank 101, 5 var)	ok
N:	subst algebraic numbers		no chance
O1:	3 dets (sparse, rank 15, 22 var)	ok
O2:	gcd of dets			no chance -- memory/time
P:	det(sparse, rank 101, rationals)	ok
P':	det(less sparse, rank 101, rationals)	ok
Q:	det(sparse, rank 101, 1-var)		ok
Q':	det(less sparse, rank 101, 1-var)	ok
Pp:     P mod 181			ok
P'p:	P' mod 181			ok
Qp:	Q mod 181			ok
Q'p:	Q' mod 181			ok
S:	Hermite form			N/A
T:	Hermite form			N/A
U:	Smith form			N/A
V:	Smith form			N/A
W1:	Smith form			N/A
W2:	Smith form			N/A
X:	gcd(Galousfield, minpoly)	very long
Y:	det(Galousfield, minpoly)	ok

For the original stuff they used to benchmark singular, see 'singall'.
For mupad and maple sources, see 'mupadall', 'mapleall'.
For more details, see also www.fordham.edu/lewis/cacomp.html