Hello All,
I'm using numpy to calculate determinants of matrices that look like
this (13x13):
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 1. 4. 1. 9. 4. 4. 1. 1. 4. 9. 4. 9.]
[ 1. 1. 0. 1. 4. 4. 9. 9. 4. 4. 1. 4. 1. 4.]
[ 1. 4. 1. 0. 9. 1. 4. 4. 9. 1. 4. 1. 4. 1.]
[ 1. 1. 4. 9. 0. 4. 4. 4. 1. 4. 1. 9. 4. 9.]
[ 1. 9. 4. 1. 4. 0. 4. 4. 9. 4. 1. 1. 4. 1.]
[ 1. 4. 9. 4. 4. 4. 0. 1. 1. 1. 9. 1. 9. 4.]
[ 1. 4. 9. 4. 4. 4. 1. 0. 4. 1. 9. 4. 4. 1.]
[ 1. 1. 4. 9. 1. 9. 1. 4. 0. 4. 4. 4. 4. 9.]
[ 1. 1. 4. 1. 4. 4. 1. 1. 4. 0. 9. 4. 9. 4.]
[ 1. 4. 1. 4. 1. 1. 9. 9. 4. 9. 0. 4. 1. 4.]
[ 1. 9. 4. 1. 9. 1. 1. 4. 4. 4. 4. 0. 4. 1.]
[ 1. 4. 1. 4. 4. 4. 9. 4. 4. 9. 1. 4. 0. 1.]
[ 1. 9. 4. 1. 9. 1. 4. 1. 9. 4. 4. 1. 1. 0.]]
For this matrix, I'm getting this with numpy:
2774532095.9999 971
But I have a feeling I'm exceeding the capacity of floats here. Does
anyone have an idea for how to treat this? Is it absurd to think I could
get a determinant of this matrix? Is there a python package that could
help me?
Many thanks for any answers.
James
14  7127 
On 6 jun 2007, at 13.10, James Stroud wrote:
Hello All,
I'm using numpy to calculate determinants of matrices that look like
this (13x13):
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 1. 4. 1. 9. 4. 4. 1. 1. 4. 9. 4. 9.]
[ 1. 1. 0. 1. 4. 4. 9. 9. 4. 4. 1. 4. 1. 4.]
[ 1. 4. 1. 0. 9. 1. 4. 4. 9. 1. 4. 1. 4. 1.]
[ 1. 1. 4. 9. 0. 4. 4. 4. 1. 4. 1. 9. 4. 9.]
[ 1. 9. 4. 1. 4. 0. 4. 4. 9. 4. 1. 1. 4. 1.]
[ 1. 4. 9. 4. 4. 4. 0. 1. 1. 1. 9. 1. 9. 4.]
[ 1. 4. 9. 4. 4. 4. 1. 0. 4. 1. 9. 4. 4. 1.]
[ 1. 1. 4. 9. 1. 9. 1. 4. 0. 4. 4. 4. 4. 9.]
[ 1. 1. 4. 1. 4. 4. 1. 1. 4. 0. 9. 4. 9. 4.]
[ 1. 4. 1. 4. 1. 1. 9. 9. 4. 9. 0. 4. 1. 4.]
[ 1. 9. 4. 1. 9. 1. 1. 4. 4. 4. 4. 0. 4. 1.]
[ 1. 4. 1. 4. 4. 4. 9. 4. 4. 9. 1. 4. 0. 1.]
[ 1. 9. 4. 1. 9. 1. 4. 1. 9. 4. 4. 1. 1. 0.]]
For this matrix, I'm getting this with numpy:
2774532095.9999 971
But I have a feeling I'm exceeding the capacity of floats here. Does
anyone have an idea for how to treat this? Is it absurd to think I
could
get a determinant of this matrix? Is there a python package that could
help me?
Many thanks for any answers.
James
--
http://mail.python.org/mailman/listinfo/python-list
Are you sure NumPy return float results. As far as I know, it
returns doubles
(about 16 digits)
------------------------------------------------------
"Home is not where you are born, but where your heart finds peace" -
Tommy Nordgren, "The dying old crone" to************@ comhem.se
James Stroud je napisao/la:
Hello All,
I'm using numpy to calculate determinants of matrices that look like
this (13x13):
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 1. 4. 1. 9. 4. 4. 1. 1. 4. 9. 4. 9.]
[ 1. 1. 0. 1. 4. 4. 9. 9. 4. 4. 1. 4. 1. 4.]
[ 1. 4. 1. 0. 9. 1. 4. 4. 9. 1. 4. 1. 4. 1.]
[ 1. 1. 4. 9. 0. 4. 4. 4. 1. 4. 1. 9. 4. 9.]
[ 1. 9. 4. 1. 4. 0. 4. 4. 9. 4. 1. 1. 4. 1.]
[ 1. 4. 9. 4. 4. 4. 0. 1. 1. 1. 9. 1. 9. 4.]
[ 1. 4. 9. 4. 4. 4. 1. 0. 4. 1. 9. 4. 4. 1.]
[ 1. 1. 4. 9. 1. 9. 1. 4. 0. 4. 4. 4. 4. 9.]
[ 1. 1. 4. 1. 4. 4. 1. 1. 4. 0. 9. 4. 9. 4.]
[ 1. 4. 1. 4. 1. 1. 9. 9. 4. 9. 0. 4. 1. 4.]
[ 1. 9. 4. 1. 9. 1. 1. 4. 4. 4. 4. 0. 4. 1.]
[ 1. 4. 1. 4. 4. 4. 9. 4. 4. 9. 1. 4. 0. 1.]
[ 1. 9. 4. 1. 9. 1. 4. 1. 9. 4. 4. 1. 1. 0.]]
For this matrix, I'm getting this with numpy:
2774532095.9999 971
But I have a feeling I'm exceeding the capacity of floats here. Does
anyone have an idea for how to treat this? Is it absurd to think I could
get a determinant of this matrix? Is there a python package that could
help me?
Many thanks for any answers.
James
have you tried using matlab to verify the result? matlab is very fast
and can work with large matrices, so this should be no problem for
it...
On Jun 6, 6:47 am, Tommy Nordgren <tommy.nordg... @comhem.sewrote :
On 6 jun 2007, at 13.10, James Stroud wrote:
Hello All,
I'm using numpy to calculate determinants of matrices that look like
this (13x13):
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 1. 4. 1. 9. 4. 4. 1. 1. 4. 9. 4. 9.]
[ 1. 1. 0. 1. 4. 4. 9. 9. 4. 4. 1. 4. 1. 4.]
[ 1. 4. 1. 0. 9. 1. 4. 4. 9. 1. 4. 1. 4. 1.]
[ 1. 1. 4. 9. 0. 4. 4. 4. 1. 4. 1. 9. 4. 9.]
[ 1. 9. 4. 1. 4. 0. 4. 4. 9. 4. 1. 1. 4. 1.]
[ 1. 4. 9. 4. 4. 4. 0. 1. 1. 1. 9. 1. 9. 4.]
[ 1. 4. 9. 4. 4. 4. 1. 0. 4. 1. 9. 4. 4. 1.]
[ 1. 1. 4. 9. 1. 9. 1. 4. 0. 4. 4. 4. 4. 9.]
[ 1. 1. 4. 1. 4. 4. 1. 1. 4. 0. 9. 4. 9. 4.]
[ 1. 4. 1. 4. 1. 1. 9. 9. 4. 9. 0. 4. 1. 4.]
[ 1. 9. 4. 1. 9. 1. 1. 4. 4. 4. 4. 0. 4. 1.]
[ 1. 4. 1. 4. 4. 4. 9. 4. 4. 9. 1. 4. 0. 1.]
[ 1. 9. 4. 1. 9. 1. 4. 1. 9. 4. 4. 1. 1. 0.]]
For this matrix, I'm getting this with numpy:
2774532095.9999 971
But I have a feeling I'm exceeding the capacity of floats here. Does
anyone have an idea for how to treat this? Is it absurd to think I
could
get a determinant of this matrix? Is there a python package that could
help me?
Many thanks for any answers.
James
--
http://mail.python.org/mailman/listinfo/python-list
Are you sure NumPy return float results. As far as I know, it
returns doubles
I don't know about NumPy, but in general, a python float is a double: http://docs.python.org/lib/typesnumeric.html
"Floating point numbers are implemented using double in C. All bets on
their precision are off unless you happen to know the machine you are
working with."
(about 16 digits)
------------------------------------------------------
"Home is not where you are born, but where your heart finds peace" -
Tommy Nordgren, "The dying old crone"
tommy.nordg...@ comhem.se
James Stroud wrote:
Hello All,
I'm using numpy to calculate determinants of matrices that look like
this (13x13):
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[snip]
But I have a feeling I'm exceeding the capacity of floats here. Does
anyone have an idea for how to treat this? Is it absurd to think I could
get a determinant of this matrix? Is there a python package that could
help me?
Many thanks for any answers.
James
in order to verify that this result is correct, you could get the
eigenvector and eigenvalues of this matrix (for example with
numpy.linalg.ei g) and check that they make sense; the determinant simply
is the product of all the eigenvalues.
gd luck
James Stroud wrote:
Hello All,
I'm using numpy to calculate determinants of matrices that look like
this (13x13):
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 1. 4. 1. 9. 4. 4. 1. 1. 4. 9. 4. 9.]
[ 1. 1. 0. 1. 4. 4. 9. 9. 4. 4. 1. 4. 1. 4.]
[ 1. 4. 1. 0. 9. 1. 4. 4. 9. 1. 4. 1. 4. 1.]
[ 1. 1. 4. 9. 0. 4. 4. 4. 1. 4. 1. 9. 4. 9.]
[ 1. 9. 4. 1. 4. 0. 4. 4. 9. 4. 1. 1. 4. 1.]
[ 1. 4. 9. 4. 4. 4. 0. 1. 1. 1. 9. 1. 9. 4.]
[ 1. 4. 9. 4. 4. 4. 1. 0. 4. 1. 9. 4. 4. 1.]
[ 1. 1. 4. 9. 1. 9. 1. 4. 0. 4. 4. 4. 4. 9.]
[ 1. 1. 4. 1. 4. 4. 1. 1. 4. 0. 9. 4. 9. 4.]
[ 1. 4. 1. 4. 1. 1. 9. 9. 4. 9. 0. 4. 1. 4.]
[ 1. 9. 4. 1. 9. 1. 1. 4. 4. 4. 4. 0. 4. 1.]
[ 1. 4. 1. 4. 4. 4. 9. 4. 4. 9. 1. 4. 0. 1.]
[ 1. 9. 4. 1. 9. 1. 4. 1. 9. 4. 4. 1. 1. 0.]]
For this matrix, I'm getting this with numpy:
2774532095.9999 971
But I have a feeling I'm exceeding the capacity of floats here.
It's not that you're exceeding the capacity of float64 numbers, it's just that
there are floating point calculations taking place. The way the determinant is
calculated is by doing an LU decomposition and then multiplying down the
diagonal. Although all of your entries started as integers, floating point error
does accumulate. The answer that you got is within finfo(float64). eps of
relative error of the actual answer.
Does
anyone have an idea for how to treat this? Is it absurd to think I could
get a determinant of this matrix? Is there a python package that could
help me?
If all of your matrices are going to be integers, doing the
determinant-by-minors calculations yourself is probably easy enough to code and
will retain complete precision. http://mathworld.wolfram.com/Determi...nbyMinors.html
--
Robert Kern
"I have come to believe that the whole world is an enigma, a harmless enigma
that is made terrible by our own mad attempt to interpret it as though it had
an underlying truth."
-- Umberto Eco
James Stroud wrote:
I'm using numpy to calculate determinants of matrices that look like
this (13x13):
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 1. 4. 1. 9. 4. 4. 1. 1. 4. 9. 4. 9.]
[ 1. 1. 0. 1. 4. 4. 9. 9. 4. 4. 1. 4. 1. 4.]
[ 1. 4. 1. 0. 9. 1. 4. 4. 9. 1. 4. 1. 4. 1.]
[ 1. 1. 4. 9. 0. 4. 4. 4. 1. 4. 1. 9. 4. 9.]
[ 1. 9. 4. 1. 4. 0. 4. 4. 9. 4. 1. 1. 4. 1.]
[ 1. 4. 9. 4. 4. 4. 0. 1. 1. 1. 9. 1. 9. 4.]
[ 1. 4. 9. 4. 4. 4. 1. 0. 4. 1. 9. 4. 4. 1.]
[ 1. 1. 4. 9. 1. 9. 1. 4. 0. 4. 4. 4. 4. 9.]
[ 1. 1. 4. 1. 4. 4. 1. 1. 4. 0. 9. 4. 9. 4.]
[ 1. 4. 1. 4. 1. 1. 9. 9. 4. 9. 0. 4. 1. 4.]
[ 1. 9. 4. 1. 9. 1. 1. 4. 4. 4. 4. 0. 4. 1.]
[ 1. 4. 1. 4. 4. 4. 9. 4. 4. 9. 1. 4. 0. 1.]
[ 1. 9. 4. 1. 9. 1. 4. 1. 9. 4. 4. 1. 1. 0.]]
For this matrix, I'm getting this with numpy:
2774532095.9999 971
But I have a feeling I'm exceeding the capacity of floats here. Does
anyone have an idea for how to treat this? Is it absurd to think I could
get a determinant of this matrix? Is there a python package that could
help me?
Here's some anecdotal evidence that your result may be correct:
import operator
m = eval("""[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 1. 4. 1. 9. 4. 4. 1. 1. 4. 9. 4. 9.]
[ 1. 1. 0. 1. 4. 4. 9. 9. 4. 4. 1. 4. 1. 4.]
[ 1. 4. 1. 0. 9. 1. 4. 4. 9. 1. 4. 1. 4. 1.]
[ 1. 1. 4. 9. 0. 4. 4. 4. 1. 4. 1. 9. 4. 9.]
[ 1. 9. 4. 1. 4. 0. 4. 4. 9. 4. 1. 1. 4. 1.]
[ 1. 4. 9. 4. 4. 4. 0. 1. 1. 1. 9. 1. 9. 4.]
[ 1. 4. 9. 4. 4. 4. 1. 0. 4. 1. 9. 4. 4. 1.]
[ 1. 1. 4. 9. 1. 9. 1. 4. 0. 4. 4. 4. 4. 9.]
[ 1. 1. 4. 1. 4. 4. 1. 1. 4. 0. 9. 4. 9. 4.]
[ 1. 4. 1. 4. 1. 1. 9. 9. 4. 9. 0. 4. 1. 4.]
[ 1. 9. 4. 1. 9. 1. 1. 4. 4. 4. 4. 0. 4. 1.]
[ 1. 4. 1. 4. 4. 4. 9. 4. 4. 9. 1. 4. 0. 1.]
[ 1. 9. 4. 1. 9. 1. 4. 1. 9. 4. 4. 1. 1. 0.]]""".replace("." ,
".,").repla ce("]", "],"))[0]
M = [[int(x) for x in row] for row in m]
def subdet(m, rowindex):
return [row[1:] for index, row in enumerate(m) if index != rowindex]
def det(m):
if len(m) == 1:
return m[0][0]
sign = 1
sigma = 0
for index, row in enumerate(m):
x = row[0]
if x:
sigma += sign * x * det(subdet(m, index))
sign = -sign
return sigma
def common_multiple (items):
items = set(items)
items.discard(0 )
if items:
return reduce(operator .mul, items)
else:
return 0
def det3(m, switch_algo=8):
p = 1
q = 1
while 1:
if len(m) == switch_algo:
a, b = divmod(p*det(m) , q)
assert b == 0
return a
cm = common_multiple (row[0] for row in m)
if cm == 0: return 0
sign = 1
e = enumerate(m)
for first_index, first_row in e:
if first_row[0]:
f = cm // first_row[0]
assert (cm % first_row[0]) == 0
p *= sign * cm
q *= f
first_row[:] = [f*x for x in first_row[1:]]
break
first_row[:] = first_row[1:]
sign = -sign
for index, row in e:
if row[0]:
f = cm // row[0]
assert (cm % row[0]) == 0
q *= f
row[:] = [f*x - fx for x, fx in zip(row[1:], first_row)]
else:
row[:] = row[1:]
del m[first_index]
if __name__ == "__main__":
import pprint
pprint.pprint(M )
result = det3(M)
assert result == 2774532096
print "det(M) =", result
As I use only integers, any errors should be algorithmic rather than caused
by rounding.
Peter
James Stroud wrote:
For this matrix, I'm getting this with numpy:
2774532095.9999 971
But I have a feeling I'm exceeding the capacity of floats here.
Does anyone have an idea for how to treat this?
Not if you don't state your requirements more precisely. E. g. what
precision do you need?
Is it absurd to think I could get a determinant of this matrix?
Absolutely not.
Is there a python package that could help me?
Help doing what?
BTW, scilab says this:
-->det(A)
ans =
2.7745320960000 E+09
-->ans-2774532095.9999 971
ans =
2.8610229492188 E-06
-->
The error is 15 magnitudes below your result -- what do you want
more? :)
Regards,
Björn
P.S.:
>>print 2774532095.9999 971
2774532096.0
>>>
--
BOFH excuse #118:
the router thinks its a printer.
On Wed, 06 Jun 2007 04:10:43 -0700, James Stroud wrote:
Hello All,
I'm using numpy to calculate determinants of matrices that look like
this (13x13):
[snip matrix]
For this matrix, I'm getting this with numpy:
2774532095.9999 971
But I have a feeling I'm exceeding the capacity of floats here. Does
anyone have an idea for how to treat this? Is it absurd to think I could
get a determinant of this matrix? Is there a python package that could
help me?
Is there a particular reason you think there is a problem? The determinant
given is pretty close to the integer 2774532096. Assuming that is the
correct value, the difference between:
2.7745320960000 000e9 and
2.7745320959999 971e9
gives a relative error of 1.0311731312618 234e-13 percent. How much
precision were you after? :-)
I suspect that if there is a problem with the matrix, it is less likely
to be because of the size of floats and more likely that the matrix is
ill-conditioned.
I don't know if numpy will calculate the condition number of the matrix,
or estimate it. If it does, do so -- a large condition number == trouble. http://en.wikipedia.org/wiki/Condition_number
Another way to see if the matrix is ill-conditioned is to make a small
perturbation to it (say, change two or three of the entries by 0.0001 or
so), then calculate the determinate. If the result is radically different,
then the matrix is probably ill-conditioned and there is likely no help
for you except numerical black magic and/or using a different matrix.
--
Steven.
Hello,
Thank you to those who responded for your answers. They were very
helpful and I'm confident now that numpy is calculating accurate
determinants for these matrices.
But I think I need to restate my problem a little as suggested by some
becuase I'm still bewildered.
First, here is the relevant part of my code:
# start of code
def main(word, repeats, trials):
encodings = encode(word, CODE)
random.shuffle( encodings)
values = []
pb = PB(tk.Tk())
for i in xrange(trials):
if i % 100 == 0:
pb.update(float (i)/trials)
random.seed()
encodings = random.sample(e ncodings, repeats)
distmat = build_distmat(e ncodings)
print
print distmat
values.append(d et(distmat))
values.sort()
# print values
print set(values)
# end of code
Here are some notes about the code:
1. PB is a progress bar because this takes a while for a lot of trials.
2. encodings is a complete list equivalent encodings of word.
3. distmat is a representation of the distances between the sample as
integers for purposes of calculating the "content" of the hyperspace
defined by this pairwise distance matrix (Cayley-Menger determinant).
4. det is numpy.linalg.de t
I get fairly unintuitive results, because if I run it once for 10 (or
1000 or 100,000) the set of values are all essentially the same:
set([-733163520.00005 591, -733163520.00004 566, -733163519.99998 546,
-733163520.00002 789, -733163519.99999 189, -733163519.99997 83,
-733163519.99997 58, -733163520.00002 348, -733163519.99996 936,
-733163520.00004 542])
If I run it again on 10 (or 1000) the set is basically homogenous but
now of different values (terribly confusing):
set([12048175104.000 01, 12048175104.000 015, 12048175104.000 046,
12048175103.999 994, 12048175104.000 023, 12048175103.999 981,
12048175103.999 998, 12048175103.999 99])
How could this be? This holds for 10 trials or 100000 trials. Below is
the output from the above runs.
Is this a problem with the rng? All of these matrices look different.
I'm certain this can't happen by chance.
Thank you again.
James
euler 70% ./simplex.py
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 4. 9. 9. 4. 4. 9. 9. 1. 9. 16. 9. 9.]
[ 1. 4. 0. 9. 9. 4. 4. 16. 16. 4. 9. 9. 1. 4.]
[ 1. 9. 9. 0. 9. 9. 16. 4. 4. 16. 9. 1. 4. 4.]
[ 1. 9. 9. 9. 0. 16. 4. 4. 9. 9. 9. 9. 4. 9.]
[ 1. 4. 4. 9. 16. 0. 9. 4. 4. 4. 4. 9. 9. 4.]
[ 1. 4. 4. 16. 4. 9. 0. 16. 9. 1. 9. 9. 9. 9.]
[ 1. 9. 16. 4. 4. 4. 16. 0. 1. 9. 4. 4. 9. 4.]
[ 1. 9. 16. 4. 9. 4. 9. 1. 0. 4. 9. 1. 9. 9.]
[ 1. 1. 4. 16. 9. 4. 1. 9. 4. 0. 9. 9. 9. 9.]
[ 1. 9. 9. 9. 9. 4. 9. 4. 9. 9. 0. 9. 16. 1.]
[ 1. 16. 9. 1. 9. 9. 9. 4. 1. 9. 9. 0. 4. 4.]
[ 1. 9. 1. 4. 4. 9. 9. 9. 9. 9. 16. 4. 0. 9.]
[ 1. 9. 4. 4. 9. 4. 9. 4. 9. 9. 1. 4. 9. 0.]]
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 4. 16. 4. 9. 16. 4. 4. 9. 9. 1. 9. 9.]
[ 1. 4. 0. 9. 9. 1. 9. 9. 9. 16. 9. 4. 4. 9.]
[ 1. 16. 9. 0. 4. 4. 1. 9. 9. 9. 4. 9. 9. 1.]
[ 1. 4. 9. 4. 0. 16. 9. 9. 1. 9. 4. 1. 9. 9.]
[ 1. 9. 1. 4. 16. 0. 4. 4. 16. 9. 4. 9. 9. 4.]
[ 1. 16. 9. 1. 9. 4. 0. 9. 16. 9. 9. 9. 4. 4.]
[ 1. 4. 9. 9. 9. 4. 9. 0. 4. 1. 4. 4. 9. 9.]
[ 1. 4. 9. 9. 1. 16. 16. 4. 0. 4. 4. 4. 4. 9.]
[ 1. 9. 16. 9. 9. 9. 9. 1. 4. 0. 4. 9. 9. 9.]
[ 1. 9. 9. 4. 4. 4. 9. 4. 4. 4. 0. 9. 16. 4.]
[ 1. 1. 4. 9. 1. 9. 9. 4. 4. 9. 9. 0. 9. 16.]
[ 1. 9. 4. 9. 9. 9. 4. 9. 4. 9. 16. 9. 0. 9.]
[ 1. 9. 9. 1. 9. 4. 4. 9. 9. 9. 4. 16. 9. 0.]]
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 9. 9. 4. 9. 4. 9. 9. 9. 9. 9. 16. 4.]
[ 1. 9. 0. 1. 9. 4. 9. 4. 16. 9. 9. 9. 4. 1.]
[ 1. 9. 1. 0. 9. 4. 9. 9. 9. 9. 16. 9. 4. 4.]
[ 1. 4. 9. 9. 0. 1. 9. 9. 4. 9. 4. 16. 9. 9.]
[ 1. 9. 4. 4. 1. 0. 16. 16. 9. 4. 9. 9. 4. 4.]
[ 1. 4. 9. 9. 9. 16. 0. 1. 4. 4. 4. 4. 4. 16.]
[ 1. 9. 4. 9. 9. 16. 1. 0. 4. 9. 1. 9. 4. 9.]
[ 1. 9. 16. 9. 4. 9. 4. 4. 0. 4. 1. 9. 9. 16.]
[ 1. 9. 9. 9. 9. 4. 4. 9. 4. 0. 4. 1. 4. 9.]
[ 1. 9. 9. 16. 4. 9. 4. 1. 1. 4. 0. 9. 9. 9.]
[ 1. 9. 9. 9. 16. 9. 4. 9. 9. 1. 9. 0. 4. 9.]
[ 1. 16. 4. 4. 9. 4. 4. 4. 9. 4. 9. 4. 0. 9.]
[ 1. 4. 1. 4. 9. 4. 16. 9. 16. 9. 9. 9. 9. 0.]]
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 9. 9. 1. 9. 4. 1. 16. 9. 9. 4. 9. 4.]
[ 1. 9. 0. 4. 9. 1. 9. 9. 4. 4. 9. 4. 9. 4.]
[ 1. 9. 4. 0. 16. 4. 1. 9. 4. 4. 9. 4. 4. 16.]
[ 1. 1. 9. 16. 0. 9. 9. 4. 16. 9. 9. 9. 4. 4.]
[ 1. 9. 1. 4. 9. 0. 9. 9. 9. 9. 16. 4. 9. 9.]
[ 1. 4. 9. 1. 9. 9. 0. 9. 4. 1. 9. 4. 9. 16.]
[ 1. 1. 9. 9. 4. 9. 9. 0. 9. 16. 9. 4. 9. 4.]
[ 1. 16. 4. 4. 16. 9. 4. 9. 0. 1. 4. 9. 9. 9.]
[ 1. 9. 4. 4. 9. 9. 1. 16. 1. 0. 4. 9. 9. 9.]
[ 1. 9. 9. 9. 9. 16. 9. 9. 4. 4. 0. 9. 4. 1.]
[ 1. 4. 4. 4. 9. 4. 4. 4. 9. 9. 9. 0. 16. 4.]
[ 1. 9. 9. 4. 4. 9. 9. 9. 9. 9. 4. 16. 0. 9.]
[ 1. 4. 4. 16. 4. 9. 16. 4. 9. 9. 1. 4. 9. 0.]]
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 16. 4. 9. 4. 9. 4. 16. 4. 1. 4. 9. 9.]
[ 1. 16. 0. 4. 4. 16. 4. 9. 1. 9. 9. 4. 4. 4.]
[ 1. 4. 4. 0. 1. 9. 4. 9. 9. 9. 9. 4. 9. 4.]
[ 1. 9. 4. 1. 0. 9. 9. 9. 9. 9. 16. 4. 9. 9.]
[ 1. 4. 16. 9. 9. 0. 9. 1. 9. 4. 9. 9. 4. 16.]
[ 1. 9. 4. 4. 9. 9. 0. 9. 1. 16. 4. 9. 9. 1.]
[ 1. 4. 9. 9. 9. 1. 9. 0. 4. 1. 9. 4. 9. 16.]
[ 1. 16. 1. 9. 9. 9. 1. 4. 0. 9. 9. 4. 9. 4.]
[ 1. 4. 9. 9. 9. 4. 16. 1. 9. 0. 9. 4. 9. 9.]
[ 1. 1. 9. 9. 16. 9. 4. 9. 9. 9. 0. 9. 4. 4.]
[ 1. 4. 4. 4. 4. 9. 9. 4. 4. 4. 9. 0. 16. 9.]
[ 1. 9. 4. 9. 9. 4. 9. 9. 9. 9. 4. 16. 0. 9.]
[ 1. 9. 4. 4. 9. 16. 1. 16. 4. 9. 4. 9. 9. 0.]]
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 4. 1. 9. 4. 9. 16. 9. 9. 9. 4. 9. 9.]
[ 1. 4. 0. 9. 4. 9. 16. 9. 4. 16. 9. 1. 4. 9.]
[ 1. 1. 9. 0. 16. 9. 4. 9. 4. 4. 4. 9. 16. 4.]
[ 1. 9. 4. 16. 0. 4. 16. 4. 4. 9. 9. 4. 1. 4.]
[ 1. 4. 9. 9. 4. 0. 4. 9. 9. 9. 9. 9. 9. 16.]
[ 1. 9. 16. 4. 16. 4. 0. 9. 9. 1. 4. 9. 9. 9.]
[ 1. 16. 9. 9. 4. 9. 9. 0. 1. 9. 9. 9. 9. 4.]
[ 1. 9. 4. 4. 4. 9. 9. 1. 0. 9. 9. 4. 9. 4.]
[ 1. 9. 16. 4. 9. 9. 1. 9. 9. 0. 1. 9. 4. 4.]
[ 1. 9. 9. 4. 9. 9. 4. 9. 9. 1. 0. 16. 9. 4.]
[ 1. 4. 1. 9. 4. 9. 9. 9. 4. 9. 16. 0. 1. 9.]
[ 1. 9. 4. 16. 1. 9. 9. 9. 9. 4. 9. 1. 0. 4.]
[ 1. 9. 9. 4. 4. 16. 9. 4. 4. 4. 4. 9. 4. 0.]]
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 9. 9. 4. 9. 9. 9. 9. 1. 16. 9. 4. 9.]
[ 1. 9. 0. 4. 9. 9. 9. 16. 4. 9. 9. 1. 4. 9.]
[ 1. 9. 4. 0. 16. 16. 9. 9. 4. 4. 1. 4. 4. 9.]
[ 1. 4. 9. 16. 0. 1. 4. 4. 16. 4. 9. 9. 4. 4.]
[ 1. 9. 9. 16. 1. 0. 9. 1. 9. 9. 9. 4. 4. 4.]
[ 1. 9. 9. 9. 4. 9. 0. 9. 4. 9. 4. 9. 16. 9.]
[ 1. 9. 16. 9. 4. 1. 9. 0. 9. 4. 4. 9. 9. 1.]
[ 1. 9. 4. 4. 16. 9. 4. 9. 0. 9. 9. 1. 9. 16.]
[ 1. 1. 9. 4. 4. 9. 9. 4. 9. 0. 9. 9. 4. 4.]
[ 1. 16. 9. 1. 9. 9. 4. 4. 9. 9. 0. 9. 9. 4.]
[ 1. 9. 1. 4. 9. 4. 9. 9. 1. 9. 9. 0. 4. 16.]
[ 1. 4. 4. 4. 4. 4. 16. 9. 9. 4. 9. 4. 0. 9.]
[ 1. 9. 9. 9. 4. 4. 9. 1. 16. 4. 4. 16. 9. 0.]]
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 4. 9. 9. 4. 9. 4. 9. 4. 4. 16. 4. 4.]
[ 1. 4. 0. 9. 9. 9. 4. 9. 16. 9. 1. 9. 4. 9.]
[ 1. 9. 9. 0. 4. 16. 9. 9. 4. 9. 9. 4. 1. 9.]
[ 1. 9. 9. 4. 0. 9. 16. 4. 1. 4. 16. 9. 9. 4.]
[ 1. 4. 9. 16. 9. 0. 9. 1. 9. 4. 9. 9. 9. 9.]
[ 1. 9. 4. 9. 16. 9. 0. 9. 9. 16. 1. 4. 4. 9.]
[ 1. 4. 9. 9. 4. 1. 9. 0. 4. 4. 9. 9. 4. 9.]
[ 1. 9. 16. 4. 1. 9. 9. 4. 0. 4. 9. 9. 9. 1.]
[ 1. 4. 9. 9. 4. 4. 16. 4. 4. 0. 9. 4. 16. 1.]
[ 1. 4. 1. 9. 16. 9. 1. 9. 9. 9. 0. 9. 4. 4.]
[ 1. 16. 9. 4. 9. 9. 4. 9. 9. 4. 9. 0. 9. 9.]
[ 1. 4. 4. 1. 9. 9. 4. 4. 9. 16. 4. 9. 0. 16.]
[ 1. 4. 9. 9. 4. 9. 9. 9. 1. 1. 4. 9. 16. 0.]]
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 4. 4. 9. 4. 4. 4. 9. 4. 9. 1. 16. 16.]
[ 1. 4. 0. 9. 9. 9. 1. 4. 4. 9. 16. 4. 9. 16.]
[ 1. 4. 9. 0. 9. 16. 9. 9. 4. 9. 9. 9. 9. 4.]
[ 1. 9. 9. 9. 0. 4. 16. 9. 9. 9. 1. 9. 4. 4.]
[ 1. 4. 9. 16. 4. 0. 9. 4. 9. 4. 4. 4. 4. 9.]
[ 1. 4. 1. 9. 16. 9. 0. 4. 4. 9. 9. 1. 9. 9.]
[ 1. 4. 4. 9. 9. 4. 4. 0. 9. 1. 9. 9. 4. 9.]
[ 1. 9. 4. 4. 9. 9. 4. 9. 0. 16. 9. 9. 1. 9.]
[ 1. 4. 9. 9. 9. 4. 9. 1. 16. 0. 9. 9. 9. 9.]
[ 1. 9. 16. 9. 1. 4. 9. 9. 9. 9. 0. 4. 4. 1.]
[ 1. 1. 4. 9. 9. 4. 1. 9. 9. 9. 4. 0. 16. 9.]
[ 1. 16. 9. 9. 4. 4. 9. 4. 1. 9. 4. 16. 0. 4.]
[ 1. 16. 16. 4. 4. 9. 9. 9. 9. 9. 1. 9. 4. 0.]]
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 4. 4. 16. 4. 16. 9. 9. 1. 4. 4. 9. 4.]
[ 1. 4. 0. 9. 9. 9. 9. 9. 16. 9. 4. 1. 9. 9.]
[ 1. 4. 9. 0. 9. 9. 9. 16. 4. 1. 9. 4. 9. 1.]
[ 1. 16. 9. 9. 0. 9. 4. 4. 1. 16. 4. 4. 4. 9.]
[ 1. 4. 9. 9. 9. 0. 4. 9. 4. 9. 16. 9. 9. 9.]
[ 1. 16. 9. 9. 4. 4. 0. 4. 9. 9. 9. 9. 1. 16.]
[ 1. 9. 9. 16. 4. 9. 4. 0. 9. 9. 4. 9. 1. 9.]
[ 1. 9. 16. 4. 1. 4. 9. 9. 0. 9. 9. 9. 9. 4.]
[ 1. 1. 9. 1. 16. 9. 9. 9. 9. 0. 4. 9. 4. 4.]
[ 1. 4. 4. 9. 4. 16. 9. 4. 9. 4. 0. 4. 4. 9.]
[ 1. 4. 1. 4. 4. 9. 9. 9. 9. 9. 4. 0. 9. 4.]
[ 1. 9. 9. 9. 4. 9. 1. 1. 9. 4. 4. 9. 0. 16.]
[ 1. 4. 9. 1. 9. 9. 16. 9. 4. 4. 9. 4. 16. 0.]]
set([31247376384.000 099, 31247376384.000 187, 31247376384.000 217,
31247376383.999 92, 31247376384.000 214, 31247376383.999 863,
31247376384.000 294, 31247376383.999 889, 31247376384.000 324,
31247376383.999 947])
euler 71% ./simplex.py
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 9. 9. 4. 9. 9. 9. 1. 4. 4. 1. 4. 1.]
[ 1. 9. 0. 16. 4. 9. 4. 16. 9. 16. 9. 16. 4. 9.]
[ 1. 9. 16. 0. 4. 1. 9. 4. 9. 4. 1. 4. 9. 4.]
[ 1. 4. 4. 4. 0. 1. 16. 9. 4. 9. 1. 9. 9. 1.]
[ 1. 9. 9. 1. 1. 0. 9. 4. 9. 4. 4. 4. 16. 4.]
[ 1. 9. 4. 9. 16. 9. 0. 9. 16. 9. 16. 4. 9. 9.]
[ 1. 9. 16. 4. 9. 4. 9. 0. 4. 1. 9. 4. 16. 9.]
[ 1. 1. 9. 9. 4. 9. 16. 4. 0. 1. 4. 4. 4. 4.]
[ 1. 4. 16. 4. 9. 4. 9. 1. 1. 0. 9. 1. 9. 9.]
[ 1. 4. 9. 1. 1. 4. 16. 9. 4. 9. 0. 9. 4. 1.]
[ 1. 1. 16. 4. 9. 4. 4. 4. 4. 1. 9. 0. 9. 4.]
[ 1. 4. 4. 9. 9. 16. 9. 16. 4. 9. 4. 9. 0. 9.]
[ 1. 1. 9. 4. 1. 4. 9. 9. 4. 9. 1. 4. 9. 0.]]
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 9. 1. 9. 4. 1. 4. 4. 9. 9. 9. 1. 4.]
[ 1. 9. 0. 4. 4. 9. 9. 4. 16. 9. 9. 16. 4. 9.]
[ 1. 1. 4. 0. 9. 9. 1. 4. 4. 16. 9. 9. 4. 1.]
[ 1. 9. 4. 9. 0. 16. 4. 9. 9. 4. 16. 16. 9. 16.]
[ 1. 4. 9. 9. 16. 0. 9. 4. 4. 4. 1. 4. 1. 4.]
[ 1. 1. 9. 1. 4. 9. 0. 4. 1. 16. 9. 9. 4. 4.]
[ 1. 4. 4. 4. 9. 4. 4. 0. 9. 16. 1. 4. 1. 9.]
[ 1. 4. 16. 4. 9. 4. 1. 9. 0. 9. 4. 4. 9. 1.]
[ 1. 9. 9. 16. 4. 4. 16. 16. 9. 0. 9. 9. 9. 9.]
[ 1. 9. 9. 9. 16. 1. 9. 1. 4. 9. 0. 1. 4. 4.]
[ 1. 9. 16. 9. 16. 4. 9. 4. 4. 9. 1. 0. 9. 4.]
[ 1. 1. 4. 4. 9. 1. 4. 1. 9. 9. 4. 9. 0. 9.]
[ 1. 4. 9. 1. 16. 4. 4. 9. 1. 9. 4. 4. 9. 0.]]
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 9. 9. 9. 16. 9. 16. 4. 9. 4. 9. 9. 16.]
[ 1. 9. 0. 4. 16. 9. 4. 1. 9. 1. 4. 4. 9. 4.]
[ 1. 9. 4. 0. 9. 4. 9. 1. 9. 4. 4. 9. 1. 1.]
[ 1. 9. 16. 9. 0. 4. 16. 9. 4. 9. 9. 9. 4. 4.]
[ 1. 16. 9. 4. 4. 0. 4. 4. 9. 9. 4. 1. 1. 4.]
[ 1. 9. 4. 9. 16. 4. 0. 9. 16. 4. 4. 1. 9. 9.]
[ 1. 16. 1. 1. 9. 4. 9. 0. 4. 4. 9. 9. 4. 1.]
[ 1. 4. 9. 9. 4. 9. 16. 4. 0. 16. 16. 16. 9. 9.]
[ 1. 9. 1. 4. 9. 9. 4. 4. 16. 0. 4. 4. 9. 1.]
[ 1. 4. 4. 4. 9. 4. 4. 9. 16. 4. 0. 1. 1. 9.]
[ 1. 9. 4. 9. 9. 1. 1. 9. 16. 4. 1. 0. 4. 9.]
[ 1. 9. 9. 1. 4. 1. 9. 4. 9. 9. 1. 4. 0. 4.]
[ 1. 16. 4. 1. 4. 4. 9. 1. 9. 1. 9. 9. 4. 0.]]
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 4. 4. 16. 4. 4. 1. 9. 9. 1. 9. 4. 4.]
[ 1. 4. 0. 4. 9. 1. 9. 9. 4. 16. 4. 1. 4. 9.]
[ 1. 4. 4. 0. 9. 4. 4. 1. 1. 9. 9. 1. 9. 9.]
[ 1. 16. 9. 9. 0. 16. 9. 9. 9. 4. 16. 4. 16. 4.]
[ 1. 4. 1. 4. 16. 0. 9. 9. 1. 9. 4. 4. 4. 9.]
[ 1. 4. 9. 4. 9. 9. 0. 1. 4. 4. 1. 4. 4. 16.]
[ 1. 1. 9. 1. 9. 9. 1. 0. 4. 4. 4. 4. 9. 9.]
[ 1. 9. 4. 1. 9. 1. 4. 4. 0. 4. 9. 1. 9. 16.]
[ 1. 9. 16. 9. 4. 9. 4. 4. 4. 0. 9. 9. 16. 9.]
[ 1. 1. 4. 9. 16. 4. 1. 4. 9. 9. 0. 9. 1. 9.]
[ 1. 9. 1. 1. 4. 4. 4. 4. 1. 9. 9. 0. 9. 16.]
[ 1. 4. 4. 9. 16. 4. 4. 9. 9. 16. 1. 9. 0. 9.]
[ 1. 4. 9. 9. 4. 9. 16. 9. 16. 9. 9. 16. 9. 0.]]
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 9. 4. 4. 9. 1. 9. 4. 4. 9. 1. 1. 9.]
[ 1. 9. 0. 16. 1. 9. 9. 4. 9. 9. 16. 4. 4. 4.]
[ 1. 4. 16. 0. 9. 9. 9. 9. 4. 9. 4. 4. 9. 16.]
[ 1. 4. 1. 9. 0. 9. 9. 4. 9. 9. 16. 1. 1. 4.]
[ 1. 9. 9. 9. 9. 0. 9. 9. 16. 16. 4. 16. 4. 9.]
[ 1. 1. 9. 9. 9. 9. 0. 4. 1. 1. 9. 4. 4. 4.]
[ 1. 9. 4. 9. 4. 9. 4. 0. 1. 4. 16. 9. 4. 1.]
[ 1. 4. 9. 4. 9. 16. 1. 1. 0. 1. 9. 4. 9. 4.]
[ 1. 4. 9. 9. 9. 16. 1. 4. 1. 0. 4. 4. 9. 1.]
[ 1. 9. 16. 4. 16. 4. 9. 16. 9. 4. 0. 9. 16. 9.]
[ 1. 1. 4. 4. 1. 16. 4. 9. 4. 4. 9. 0. 4. 9.]
[ 1. 1. 4. 9. 1. 4. 4. 4. 9. 9. 16. 4. 0. 4.]
[ 1. 9. 4. 16. 4. 9. 4. 1. 4. 1. 9. 9. 4. 0.]]
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 4. 4. 1. 9. 9. 4. 16. 1. 9. 1. 9. 4.]
[ 1. 4. 0. 9. 1. 9. 4. 9. 9. 1. 4. 4. 4. 16.]
[ 1. 4. 9. 0. 9. 4. 4. 1. 16. 4. 1. 4. 4. 9.]
[ 1. 1. 1. 9. 0. 16. 4. 9. 9. 4. 4. 4. 4. 9.]
[ 1. 9. 9. 4. 16. 0. 9. 4. 9. 4. 9. 9. 16. 4.]
[ 1. 9. 4. 4. 4. 9. 0. 1. 4. 9. 1. 4. 4. 16.]
[ 1. 4. 9. 1. 9. 4. 1. 0. 9. 4. 4. 1. 9. 9.]
[ 1. 16. 9. 16. 9. 9. 4. 9. 0. 16. 9. 9. 9. 4.]
[ 1. 1. 1. 4. 4. 4. 9. 4. 16. 0. 9. 1. 9. 9.]
[ 1. 9. 4. 1. 4. 9. 1. 4. 9. 9. 0. 9. 1. 16.]
[ 1. 1. 4. 4. 4. 9. 4. 1. 9. 1. 9. 0. 9. 9.]
[ 1. 9. 4. 4. 4. 16. 4. 9. 9. 9. 1. 9. 0. 16.]
[ 1. 4. 16. 9. 9. 4. 16. 9. 4. 9. 16. 9. 16. 0.]]
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 16. 4. 4. 9. 1. 4. 1. 9. 9. 1. 9. 9.]
[ 1. 16. 0. 9. 9. 4. 9. 16. 16. 4. 9. 16. 4. 9.]
[ 1. 4. 9. 0. 9. 4. 1. 9. 9. 9. 4. 1. 4. 1.]
[ 1. 4. 9. 9. 0. 1. 9. 1. 4. 9. 4. 4. 16. 4.]
[ 1. 9. 4. 4. 1. 0. 4. 4. 9. 16. 1. 9. 9. 1.]
[ 1. 1. 9. 1. 9. 4. 0. 9. 4. 16. 4. 4. 4. 4.]
[ 1. 4. 16. 9. 1. 4. 9. 0. 4. 9. 1. 4. 9. 4.]
[ 1. 1. 16. 9. 4. 9. 4. 4. 0. 9. 9. 4. 16. 9.]
[ 1. 9. 4. 9. 9. 16. 16. 9. 9. 0. 16. 4. 9. 9.]
[ 1. 9. 9. 4. 4. 1. 4. 1. 9. 16. 0. 9. 4. 1.]
[ 1. 1. 16. 1. 4. 9. 4. 4. 4. 4. 9. 0. 9. 4.]
[ 1. 9. 4. 4. 16. 9. 4. 9. 16. 9. 4. 9. 0. 9.]
[ 1. 9. 9. 1. 4. 1. 4. 4. 9. 9. 1. 4. 9. 0.]]
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 1. 9. 9. 1. 9. 4. 1. 4. 9. 9. 4. 4.]
[ 1. 1. 0. 9. 9. 4. 4. 4. 4. 4. 9. 16. 4. 1.]
[ 1. 9. 9. 0. 1. 4. 4. 4. 4. 16. 9. 9. 1. 4.]
[ 1. 9. 9. 1. 0. 4. 4. 1. 4. 9. 16. 9. 4. 4.]
[ 1. 1. 4. 4. 4. 0. 9. 1. 4. 9. 9. 9. 1. 9.]
[ 1. 9. 4. 4. 4. 9. 0. 9. 4. 16. 16. 9. 9. 1.]
[ 1. 4. 4. 4. 1. 1. 9. 0. 9. 4. 9. 16. 1. 9.]
[ 1. 1. 4. 4. 4. 4. 4. 9. 0. 9. 16. 4. 9. 1.]
[ 1. 4. 4. 16. 9. 9. 16. 4. 9. 0. 4. 9. 9. 9.]
[ 1. 9. 9. 9. 16. 9. 16. 9. 16. 4. 0. 4. 4. 16.]
[ 1. 9. 16. 9. 9. 9. 9. 16. 4. 9. 4. 0. 16. 9.]
[ 1. 4. 4. 1. 4. 1. 9. 1. 9. 9. 4. 16. 0. 9.]
[ 1. 4. 1. 4. 4. 9. 1. 9. 1. 9. 16. 9. 9. 0.]]
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 16. 1. 4. 4. 9. 4. 9. 4. 9. 4. 1. 4.]
[ 1. 16. 0. 16. 9. 4. 9. 16. 4. 9. 4. 16. 9. 9.]
[ 1. 1. 16. 0. 1. 9. 9. 1. 9. 9. 9. 4. 4. 4.]
[ 1. 4. 9. 1. 0. 16. 4. 4. 4. 4. 4. 9. 1. 9.]
[ 1. 4. 4. 9. 16. 0. 16. 9. 9. 9. 16. 9. 9. 9.]
[ 1. 9. 9. 9. 4. 16. 0. 9. 4. 1. 1. 1. 4. 4.]
[ 1. 4. 16. 1. 4. 9. 9. 0. 16. 9. 9. 4. 9. 4.]
[ 1. 9. 4. 9. 4. 9. 4. 16. 0. 9. 9. 9. 4. 16.]
[ 1. 4. 9. 9. 4. 9. 1. 9. 9. 0. 1. 4. 1. 4.]
[ 1. 9. 4. 9. 4. 16. 1. 9. 9. 1. 0. 4. 4. 1.]
[ 1. 4. 16. 4. 9. 9. 1. 4. 9. 4. 4. 0. 9. 1.]
[ 1. 1. 9. 4. 1. 9. 4. 9. 4. 1. 4. 9. 0. 9.]
[ 1. 4. 9. 4. 9. 9. 4. 4. 16. 4. 1. 1. 9. 0.]]
[[ 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[ 1. 0. 16. 4. 9. 9. 1. 4. 4. 9. 4. 4. 1. 9.]
[ 1. 16. 0. 16. 9. 4. 9. 16. 9. 4. 4. 16. 9. 9.]
[ 1. 4. 16. 0. 4. 16. 4. 4. 9. 9. 9. 1. 9. 9.]
[ 1. 9. 9. 4. 0. 4. 9. 4. 4. 16. 4. 1. 4. 1.]
[ 1. 9. 4. 16. 4. 0. 16. 9. 9. 9. 9. 9. 4. 4.]
[ 1. 1. 9. 4. 9. 16. 0. 4. 4. 9. 1. 4. 4. 9.]
[ 1. 4. 16. 4. 4. 9. 4. 0. 4. 4. 9. 1. 9. 1.]
[ 1. 4. 9. 9. 4. 9. 4. 4. 0. 9. 1. 9. 1. 1.]
[ 1. 9. 4. 9. 16. 9. 9. 4. 9. 0. 16. 9. 16. 9.]
[ 1. 4. 4. 9. 4. 9. 1. 9. 1. 16. 0. 9. 1. 4.]
[ 1. 4. 16. 1. 1. 9. 4. 1. 9. 9. 9. 0. 9. 4.]
[ 1. 1. 9. 9. 4. 4. 4. 9. 1. 16. 1. 9. 0. 4.]
[ 1. 9. 9. 9. 1. 4. 9. 1. 1. 9. 4. 4. 4. 0.]]
set([-167037108224.00 009, -167037108224.00 006, -167037108223.99 988,
-167037108223.99 979, -167037108223.99 997, -167037108224.00 003])
This thread has been closed and replies have been disabled. Please start a new discussion. Similar topics | |
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by: marktang |
last post by:
ONU (Optical Network Unit) is one of the key components for providing high-speed Internet services. Its primary function is to act as an endpoint device located at the user's premises. However, people are often confused as to whether an ONU can Work As a Router. In this blog post, we’ll explore What is ONU, What Is Router, ONU & Router’s main usage, and What is the difference between ONU and Router. Let’s take a closer look !
Part I. Meaning of...
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by: Hystou |
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Most computers default to English, but sometimes we require a different language, especially when relocating. Forgot to request a specific language before your computer shipped? No problem! You can effortlessly switch the default language on Windows 10 without reinstalling. I'll walk you through it.
First, let's disable language synchronization. With a Microsoft account, language settings sync across devices. To prevent any complications,...
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by: Oralloy |
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Hello folks,
I am unable to find appropriate documentation on the type promotion of bit-fields when using the generalised comparison operator "<=>".
The problem is that using the GNU compilers, it seems that the internal comparison operator "<=>" tries to promote arguments from unsigned to signed.
This is as boiled down as I can make it.
Here is my compilation command:
g++-12 -std=c++20 -Wnarrowing bit_field.cpp
Here is the code in...
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by: jinu1996 |
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In today's digital age, having a compelling online presence is paramount for businesses aiming to thrive in a competitive landscape. At the heart of this digital strategy lies an intricately woven tapestry of website design and digital marketing. It's not merely about having a website; it's about crafting an immersive digital experience that captivates audiences and drives business growth.
The Art of Business Website Design
Your website is...
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by: Hystou |
last post by:
Overview:
Windows 11 and 10 have less user interface control over operating system update behaviour than previous versions of Windows. In Windows 11 and 10, there is no way to turn off the Windows Update option using the Control Panel or Settings app; it automatically checks for updates and installs any it finds, whether you like it or not. For most users, this new feature is actually very convenient. If you want to control the update process,...
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by: isladogs |
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The next Access Europe User Group meeting will be on Wednesday 1 May 2024 starting at 18:00 UK time (6PM UTC+1) and finishing by 19:30 (7.30PM).
In this session, we are pleased to welcome a new presenter, Adolph Dupré who will be discussing some powerful techniques for using class modules.
He will explain when you may want to use classes instead of User Defined Types (UDT). For example, to manage the data in unbound forms.
Adolph will...
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by: 6302768590 |
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Hai team
i want code for transfer the data from one system to another through IP address by using C# our system has to for every 5mins then we have to update the data what the data is updated we have to send another system
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by: muto222 |
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How can i add a mobile payment intergratation into php mysql website.
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by: bsmnconsultancy |
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In today's digital era, a well-designed website is crucial for businesses looking to succeed. Whether you're a small business owner or a large corporation in Toronto, having a strong online presence can significantly impact your brand's success. BSMN Consultancy, a leader in Website Development in Toronto offers valuable insights into creating effective websites that not only look great but also perform exceptionally well. In this comprehensive...
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