Hi all,
please consider this counting of special combinations:
def C(n, k):
return Compositions(n, max_part=k, inner=[k]).cardinality()
for n in (0..4): print([C(n, k) for k in (0..n)])
[0]
[0, 1]
[0, 1, 1]
[0, 1, 1, 1]
[0, 1, 2, 1, 1]
Edge cases are
>
> Broken, indeed. Hardly any tests in sage/databases/sloane.py, no
> wonder this happens.
> See https://trac.sagemath.org/ticket/34655
> Does > oeis([1,2,3,4,5], 1) not do what you want?
Thank you Dima!
The Internet variant works. But my use case is not a single search,
but a repeated
Hello!
> SloaneEncyclopedia.find([1,2,3,4,5], 1)
TypeError Traceback (most recent call last)
/tmp/ipykernel_447/420583060.py in ()
> 1
SloaneEncyclopedia.find([Integer(1),Integer(2),Integer(3),Integer(4),Integer(5)],
Integer(1))
Please consider
def H(n,k): return hypergeometric([-k, -n + k], [-k], -1)
def T(n,k): return int(H(n,k).n())
def S(n,k): return H(n,k).simplify_hypergeometric()
for n in range(8):
print([T(n, k) for k in range(n+1)])
print([S(n, k) for k in range(n+1)])
The
Mathematica: HurwitzZeta[0, x] = 1/2 - x
Maple: Zeta(0, 0, x) = -x + 1/2
Sage 9.2:hurwitz_zeta(0, x) = hurwitz_zeta(0, x)
--- this is OK:
Mathematica: HurwitzZeta[0, 1] = -1/2
Maple: Zeta(0, 0, 1) = -1/2
Sage 9.2:hurwitz_zeta(0, 1) = -1/2
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The compositional inverse (with respect to x) of
y(t, x) = x - t*(exp(x) - 1)
is
1/(1-t)*y + t/(1-t)^3*y^2/2! + (t+2*t^2)/(1-t)^5*y^3/3! +
(t+8*t^2+6*t^3)/(1-t)^7*y^4/4! + ...
Apparently multivariate power series rings do not know how
to reverse a series.
Perhaps there is a
>
> Maybe try to alter that via:
> f = prod((1 - x^n + O(x^size))^a(n) for n in (1..size))
>
Yes, that is the solution. Thank you so much!
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Hi all,
I wanted to implement the Euler Transformation.
https://oeis.org/wiki/Euler_transform
My first attempt was:
def EulerTransform(size, a):
R. = ZZ[[]]
f = prod((1 - x^n)^a(n) for n in (1..size)) + O(x^size)
return f.inverse().list()
print(EulerTransform(6, lambda n:
Am Di., 25. Juni 2019 um 11:29 Uhr schrieb slelievre <
samuel.lelie...@gmail.com>:
> So, replace
>
> sum(binomial(m*n-1, m*k)*OmegaPolynomial(m,k) for k in (0..n-1))
>
> by
>
> sum((binomial(m*n-1, m*k)*OmegaPolynomial(m, k) for k in (0 .. n-1)),
> RR['x'].zero())
>
Now, this is clever!
Am Di., 25. Juni 2019 um 10:49 Uhr 'luisfe' :
| When n =0, k ranges from 0 to -1 so there is no k and the list
constructed in ib(n,m)
| is just the empty list. Not an empty list of polynomials, just an empty
list.
Well, then the way 'sum' is implemented is possibly improvable?
The type
Am Montag, 17. Juni 2019 14:27:40 UTC+2 schrieb luisfe:
>
> On Mon, Jun 17, 2019 at 5:18 AM Peter Luschny wrote:
>>
>>> def ib(m, n): return sum(binomial(m*n-1, m*k)*OmegaPolynomial(m,k) for k
>>> in (0..n-1))
>>>
>>> The terms "b
> Are you saying, the error message it spits out,
>>
> AttributeError: 'int' object has no attribute 'list',
> is misleading?
>
As I see it the problem is that the sum runs over (0..n-1).
Thus for n = 0 it returns by convention the integer 0 for the
empty sum (is this correct?) which of
>
> I don't know what OmegaPolynomial is. However, if you replace it by
> cyclotomic_polynomial,
> it seems to work as expected, doesn't it?
>
No, it does not. You missed the question.
>
> sage: *def* *ib*(m, n): *return* sum(binomial(m*n-*1*,
> m*k)*cyclotomic_polynomial(m*(k+*1*)) *for*
Hi,
I think we should be confident that the sum of integers is
again an integer, the sum of rational numbers a rational number
and that the sum of polynomials is a polynomial.
With Sage this is not the case.
def ib(m, n): return sum(binomial(m*n-1, m*k)*OmegaPolynomial(m,k) for k in
>
> You did not say what command you were using.
>
Oh, I thought that was clear from the error message: prime_range.
The function (implementing the factorial) is on GitHub
ValueError: Cannot compute primes beyond 436273290
I think SageMath should do better.
Cheers, Peter
/opt/sagemath-8.4/local/lib/python2.7/site-packages/sage/rings/fast_arith.pyx
in sage.rings.fast_arith.prime_range
(build/cythonized/sage/rings/fast_arith.c:3390)() 46 from
> In the mean time, you can accomplish your computations without using SR:
> sage: R.=QQ[[]]
> sage: (1 - x - sqrt(1 - 6*x + x^2))/(2*x)
> 1 + 2*x + 6*x^2 + 22*x^3 + 90*x^4 + 394*x^5 + ...
Does this only work in interactive mode? As soon as I try to
capture it in a function it doesn't work
Thank you Simon for your detailed explanations.
I'm pretty sure it's a bug. Sage doesn't like little Schroeder either.
LittleSchroeder = (1 + x - sqrt(1 - 6*x + x^2))/(4*x)
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Hi,
I get with Maple:
LargeSchroeder := (1 - x - sqrt(1 - 6*x + x^2))/(2*x);
series(LargeSchroeder, x, 6);
taylor(LargeSchroeder, x=0, 6);
1+2*x+6*x^2+22*x^3+90*x^4+394*x^5+O(x^6)
1+2*x+6*x^2+22*x^3+90*x^4+394*x^5+O(x^6)
Both functions give the same result. Not so with
>From Sage Quick Reference: Linear Algebra, Robert A. Beezer:
Matrix Multiplication
u = vector(QQ, [1,2,3]), v = vector(QQ, [1,2])
A = matrix(QQ, [[1,2,3],[4,5,6]])
B = matrix(QQ, [[1,2],[3,4]])
u*A, A*v, B*A, B^6, B^(-3) all possible
However u*A or A*v give:
TypeError:
You say: "hijack vs shut up, which one is more serious? Accusing
someone hijacking something is a very serious accusation."
I certainly didn't mean it as a 'very serious accusation' like
hijacking people or planes. I used the term "hijacked" as a
technical term like it is defined in the urban
Kolen Cheung:
>
> And if anyone is dictating this, that one is surely not you, even if
> you're the OP. Shut up.
>
You reconfirm the obvious, namely that you cannot behave.
> On Monday, November 19, 2018 at 4:43:44 AM UTC-8, Peter Luschny wrote:
>>
>> > Hi, I’m
> Hi, I’m trying to translate this Sage syntax to Python syntax (i.e. using
sage as a Python library.) But I got stuck even on the first command.
Why do you hijack this thread with a completely different topic?
I'm sure that your question and the answers of the experts are of
interest to many,
merci beaucoup!
Peter
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How can I speed up this computation?
H. = QuaternionAlgebra(SR, -1, -1)
def Q(a, b, c, d): return H(a + b*i + c*j + d*k)
def P(n): return Q(x+1,1,1,1)*P(n-1) if n > 0 else Q(1,0,0,0)
def p(n): return P(n)[0].list()
for n in (0..20): print [n], p(n)
[0] [1]
[1] [1, 1]
>
> > on SMC terminal
> > $ sage-develop
> >
> > gives you 7.3.beta2
>
> Now how can I use this kernel in my yupyter notebook?
> Ahh, it's there also! Is this new? Anyway thanks for this hint!
>
This was perhaps not a good idea. It's been long since I got so many ugly
error messages.
> on SMC terminal
> $ sage-develop
>
> gives you 7.3.beta2
Now how can I use this kernel in my yupyter notebook?
Ahh, it's there also! Is this new? Anyway thanks for this hint!
Peter
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> Your Sage is too old, this Pynac bug (existing for years) was fixed
> months ago and should be in 7.2.
Thanks Ralf!
As I said I work on SMC. So I have to wait until William updates the cloud.
Peter
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Further investigation shows that things work with the
integrand defined as:
def f(t): return exp(x*exp(i*t)-v*i*t)*(exp(exp(i*t))/cosh(exp(i*t))-1)
So the source of the trouble seems to be related to the identity
(exp(exp(I*t))/cosh(exp(I*t))-1) = tanh(exp(I*t))
Peter
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Hi,
I tested on SMC, SageMath 6.10.
Consider the numerical integral:
def T(v):
def f(t): return (tanh(exp(i*t))/exp(i*t*v)).real()
c = integral_numerical(f(t), 0, 2*pi)[0]
return (c*gamma(v+1)/(2*pi)).n()
print [round(T(n)) for n in range(10)]
Sage returned: [0, 1, 0, -1, 0, 8, 0,
I have put the test suite in a Sage worksheet and added some comments.
I have moved the worksheet. It is now the public project 'CharlwoodFifty'
at https://cloud.sagemath.com/
Unfortunately I do not know how to give a link to this project.
Peter
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Your methodology for diffs back assumes
correctly computing the derivative and correctly
comparing symbolic expressions and for the latter
counterexamples are known
Yes. This is just an indicator of possible problems, nothing more.
diffs back checks f == 0 which is incorrect a priori, it should
It would be great to have them in a file similar to wester.py. Can you
open a ticket?
I have put the test suite in a Sage worksheet and added some comments.
Perhaps this is useful?
http://www.luschny.de/math/quad/CharlwoodIntegrationTest.sws
Peter
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Recently two integration test suites were discussed at sci.math.symbolic
[1], [2].
I executed the tests with Sage and put the results on my webpage [3].
Not all results are favorable for Sage. Maybe this is worth to be
noted by some Sage developers.
Peter
[1]
Hi, with Sage Notebook Version 4.7.2:
Z0 = 1118557440*x^5 + 180204024*x^4 + 15195180*x^3 +
523250*x^2 + 4095*x + 1
Z1 = 4115105280L*x^6 + 1118557440*x^5 + 180204024*x^4 + 15195180*x^3 +
523250*x^2 + 4095*x + 1
print Z0.coefficients(x) # this works;
print Z1.coefficients(x) #
Hi, with Sage Notebook Version 4.7.2:
Z0 = 1118557440*x^5 + 180204024*x^4 + 15195180*x^3 +
523250*x^2 + 4095*x + 1
Z1 = 4115105280L*x^6 + 1118557440*x^5 + 180204024*x^4 + 15195180*x^3 +
^
Was this L intentional?
No, it was not. Your
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