Hi,
it seems the cpu time reported by SAGE does not include that of the spawned
processes (sorry for using an old release :-)
mermoz% sage
----------------------------------------------------------------------
| SAGE Version 2.8.10, Release Date: 2007-10-28 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: p=65257526772644948764799212887702573391887715235981530343703506731
sage: time FindGroupOrder(p,489731259)
CPU times: user 0.87 s, sys: 0.07 s, total: 0.94 s
Wall time: 70.30
2^2 * 3^2 * 7 * 13 * 5521 * 589213 * 1103171 * 1149307 * 1310261 * 10091759 *
63065897 * 120597437 * 48024231181
I doubt the given cpu times take into account the PARI/GP computations. As a
comparison, Magma takes 55s for that computation on my computer.
The wall time is not very useful (my machine has a load of 3-4). It would be
more useful to have to cpu time used by the spawned processes, or simply the
total cpu time used by SAGE and those processes.
Paul Zimmermann
def FindGroupOrder(p,s):
K = GF(p)
v = K(4*s)
u = K(s^2-5)
x = u^3
b = 4*x*v
a = (v-u)^3*(3*u+v)
A = a/b-2
x = x/v^3
b = x^3 + A*x^2 + x
E = EllipticCurve(K,[0,b*A,0,b^2,0])
return factor(E.cardinality())
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