# Revision history [back]

Not an answer, but it doesn't fit in a comment box and relevant, I think. With:

def test1():
count = 0
for a in k:
for b in k:
if not f.subs(x=a, y=b):
count += 1
return count

def test2():
count = 0
for a in k:
for b in k:
if not f(a, b):
count += 1
return count

def test3():
count = 0
for a in k:
for b in k:
if not (b^3+b+4*a):
count += 1
return count


we get

sage: timeit('test1()')
25 loops, best of 3: 24.6 ms per loop
sage: timeit('test2()')
5 loops, best of 3: 64.1 ms per loop
sage: timeit('test3()')
125 loops, best of 3: 2.73 ms per loop


so, surprisingly, subs is quite a bit faster than "polynomial evaluation", and unsurprisingly writing out the expression explicitly is of course even faster than either.

The subs method gives back a result in a ring that's a little too large for the purposes, though (this is as documented):

sage: parent(f.subs(x=k(1),y=k(1)))
Multivariate Polynomial Ring in x, y over Finite Field in a of size 5^2
sage: parent(f(k(1),k(1)))
Finite Field in a of size 5^2