Hi Francois,
> I play with random in order to approximate Pi by Monte-Carlo method.
>
> sage: n=10^5 ; len(filter(lambda t:t, [random()^2+random^2() < 1 for k in
> [1..n]])) / len([1..n])
>
> The test looks at the point (random(), random()) and tests if it's in the
> quarter circle.
> The result may be about pi/4.
>
> I get 0. Indeed the result of len is an int, not a Integer.
>
> Must I retain that len(L) is a Python int ?
> What is the advantage to get a Python int from len(L) ? What are the others
> cases ?
Unfortunately yes ! This is written in python specifications:
object.__len__(self)
Called to implement the built-in function len(). Should return the length
of the object, an integer >= 0. Also, an object that doesn’t define a
__nonzero__() method and whose __len__() method returns zero is considered
to be false in a Boolean context.
> Is it a way to get an Integer without change of the syntax ?
Unfortunately not ! Here is what happens if you try
sage: class bla(object):
....: def __len__(self): return Integer(10)^100
....:
sage: toto = bla()
sage: len(toto)
---------------------------------------------------------------------------
OverflowError Traceback (most recent call last)
[...]
OverflowError: long int too large to convert to int
As a consequence in Sage, the number of element of a set S is computed by
S.cardinality() which can be any large Integer or even Infinity.
> I dislike the Integer(len(....)), and in tex I code lenORI = len ; len =
> Integer(lenORI))
> Is there a method for Sage.
Why not making a loop::
success = 1
for k in [1..n]:
if random()^2 + random()^2 < 1:
success + =1
approx = success / n
Cheers,
Florent
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