Hello,
I needed to get all elements of a vector-space over a finite field. Here are
three approaches, each ~ 10x faster than the previous:
A = random_matrix(GF(5), 5, 10)
#------
timeit('all2 = A.row_space().list()')
5 loops, best of 3: 1.07 s per loop
#------
timeit('all = [i*A for i in VectorSpace(GF(5),5)]')
5 loops, best of 3: 166 ms per loop
#------
def free_mod_iter(module):
R = module.base_ring()
L = module.gens()
if len(L) == 1:
for i in R:
yield i * L[0]
else:
el = L[0]
for rest in gen(L[1:], R):
for i in R:
yield rest + i * el
timeit('list(free_mod_iter(A.row_space()))')
25 loops, best of 3: 14.7 ms per loop
sage: list(free_mod_iter(A.row_space())).sort() ==
A.row_space().list().sort()
True
Is the 3rd solution, already in Sage? It's basically the same as a generator
for rational points on elliptic curves that Robert Bradshaw showed me at
Sage Days 22. If not, it probably should be, but I am not sure where it fits
(free_module.py is a 5k loc).
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