The methods have been include in [http://trac.sagemath.org/ticket/19011
trac ticket #19011].
At the end of the day, it would be nice to have some kind of mechanism for
deciding which algorithm to use as they really are rather different. I made
a simply benchmark to highlight their strengths and weaknesses:
sage: benchmark()
Test 1: A very long braid on very few strands
Braid: (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
Braid rep: 0.03 seconds, Kauffman bracket: 10.33 seconds
Test 2: A very simple braid on quite a few strands
Braid: (1, 2, 3, 4, 5, 6, 7, 8)
Braid rep: 6.56 seconds, Kauffman bracket: 0.00 seconds
Code:
import time
def benchmark():
def test(b):
L = Link(b)
print "Braid: " + str(b.Tietze())
result_string = "Braid rep: {0:.2f} seconds, Kauffman bracket:
{1:.2f} seconds"
start_time = time.time()
jones = b.jones_polynomial()
testb = time.time() - start_time
start_time = time.time()
jones = L.jones_polynomial()
testl = time.time() - start_time
print result_string.format(testb, testl)
print "\nTest 1: A very long braid on very few strands"
l = 60
B = BraidGroup(2)
test(B([1]*l))
print "\nTest 2: A very simple braid on quite a few strands"
n = 9
B = BraidGroup(n)
test(B(range(1,n)))
-Søren
Den søndag den 9. august 2015 kl. 12.47.34 UTC+2 skrev mmarco:
>
> Oh, i forgot to say: please open a ticket with your code added to the
> braid class. It is definitely a nice addition. I would be happy to review
> it. write your methods inside the class definition, and consider which ones
> should be public and which ones should be hidden to the user.
>
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