[sage-support] Counting of combinations

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 notorio

Re: [sage-support] TypeError in SloaneEncyclopedia

> > 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 sca

[sage-support] TypeError in SloaneEncyclopedia

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)) ~/mambaforge/envs/sage/lib/python3.10/sit

[sage-support] Problem with simplify_hypergeometric().

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 re

[sage-support] hurwitz_zeta(0, x) = ?

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 -- You received this mess

[sage-support] Compositional inverse of multivariate power series

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 wor

[sage-support] Re: Why is f.inverse() so slow?

> > 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! -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emai

[sage-support] Why is f.inverse() so slow?

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: factorial(

Re: [sage-support] The behavior of empty sums

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! Y

Re: [sage-support] The behavior of empty sums

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 informat

Re: [sage-support] The behavior of empty sums

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

Re: [sage-support] The behavior of empty sums

> 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 course

Re: [sage-support] The behavior of empty sums

> > 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* k

[sage-support] The behavior of empty sums

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 (0..n-1))

Re: [sage-support] primes -- enhancement request

> > You need to add the option "pari_isprime": > Thank you! Since the documentation says "large", and "not too large" and "much larger" but does not say what "large" means I include a table which reflects my use case. On the other hand I have no idea whether or not these bounds depend on availa

Re: [sage-support] primes -- enhancement request

> > 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

[sage-support] primes -- enhancement request

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 sage.rings

[sage-support] Re: taylor versus series

> 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 anymore

[sage-support] Re: taylor versus series

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) -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe f

[sage-support] taylor versus series

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 Sage.

[sage-support] Matrix Multiplication

>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: unsu

Re: [sage-support] Quaternions, how to speed up computation

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 d

Re: [sage-support] Quaternions, how to speed up computation

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

Re: [sage-support] Quaternions, how to speed up computation

> 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,

Re: [sage-support] Quaternions, how to speed up computation

merci beaucoup! Peter -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-sup

[sage-support] Quaternions, how to speed up computation

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]

Re: [sage-support] Re: Possible bug in numerical integration

> > > 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. /pro

Re: [sage-support] Re: Possible bug in numerical integration

> 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 -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscri

Re: [sage-support] Re: Possible bug in numerical integration

> 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 -- You received this message because you are subscribed to the Google Groups "sage-support" g

[sage-support] Re: Coming SageMathCell upgrade - please test!

--- ImportError Traceback (most recent call last) in () > 1 load('http://') 2 load('http://') 3 /home/sc_serv/sage/src/sage/structure/sage_object.pyx in sage.structure.s

Re: [sage-support] Re: Possible bug in numerical integration

> With Maxima built from recent source (approximately Maxima 5.38), > I get results that agree with what you expected Thanks Robert, yes, I suspected the numerical integration prematurely. A plot clearly shows that the culprit are the real parts of the hyperbolic functions. plot([tanh(exp(i*t)).r

[sage-support] Re: Possible bug in numerical integration

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 -- You received thi

[sage-support] Possible bug in numerical integration

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,

Re: [sage-support] The results of some integration test.

>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 s

Re: [sage-support] Re: The results of some integration test.

> 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 -- You received this message because yo

Re: [sage-support] Re: The results of some integration test.

> 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 -- You received this message because you a

[sage-support] The results of some integration test.

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] https://groups.google.com/d/msg/sc

[sage-support] Re: coefficients(x) throws TypeError

> > 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 n

[sage-support] coefficients(x) throws TypeError

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) # thi