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2014-12-15 19:49:04 +0200	commented answer	Problem evaluating limit: assume doesn't work! Ok, solution works with new version, but still think that imposing $k$ to be an integer is too much...
2014-12-15 17:28:16 +0200	commented answer	Problem evaluating limit: assume doesn't work! I'm trying to update my Sage version to try this but it won't let me; do you know if there's something going on with the trac server? I try: sage -upgrade, and it gives me: Upgrading to the latest development version fatal: unable to connect to trac.sagemath.org: trac.sagemath.org[0: 128.208.178.249]: errno=Connection refused
2014-12-15 13:44:04 +0200	commented answer	Problem evaluating limit: assume doesn't work! Hi @tmonteil; thanks for your anwer. I understand that assuming that k is real is much weaker than assuming that k is an integer, but, as I implicitly showed, I'm using this for non-integers inclusive. Also, I'm using Sage Version 6.1.1 (Release Date: 2014-02-04) and this doesn't work; it gives me the same error I showed, and asks me: "Is k-1 positive, negative, or zero?" (which is strange since I already defined it to be positive).
2014-12-15 04:22:50 +0200	asked a question	Problem evaluating limit: assume doesn't work! Hi everyone, I'm trying to evaluate the following limit in sage: $$\lim_{N\to \infty}\frac{6N^k(N-1)^{1-k}}{(2N-1)(k+1)},$$ where $k\neq \pm1$. From Wolfram-Alpha I know this is equal to $3/(1+k)$, but I was trying to get to that answer with sage with no progress. What I did to do it was the following: `sage: N = var('N') sage: k = var('k') sage: assume(k!=1) sage: assume(k!=-1) sage: limit((6N^k(N-1)^(1-k))/((2N-1)(k+1)),N=oo)` But I get the following error: ValueError Traceback (most recent call last) <ipython-input-7-bb63a0377d1b> in <module>() ----> 1 limit((Integer(6)Nk(N-Integer(1))*(Integer(1)-k))/((Integer(2)N-Integer(1))(k+Integer(1))),N=oo) /usr/lib/sagemath/local/lib/python2.7/site-packages/sage/calculus/calculus.pyc in limit(ex, dir, taylor, algorithm, argv) 1198 if algorithm == 'maxima': 1199 if dir is None: -> 1200 l = maxima.sr_limit(ex, v, a) 1201 elif dir in ['plus', '+', 'right', 'above']: 1202 if dir == 'above': /usr/lib/sagemath/local/lib/python2.7/site-packages/sage/interfaces/maxima_lib.py in sr_limit(self, expr, v, a, dir) 855 j = s.find('Is ') 856 s = s[j:] --> 857 raise ValueError, "Computation failed since Maxima requested additional constraints; using the 'assume' command before limit evaluation may* help (see `assume?` for more details)\n" + s 858 else: 859 raise error ValueError: Computation failed since Maxima requested additional constraints; using the 'assume' command before limit evaluation may help (see `assume?` for more details) Is k-1.0 positive or negative? In general it doesn't matter if $k$ is positive or negative, they converge to the same value. However, for the sake of completeness, let's first try to restrict $k$ to values between 0 and 1. So, I opened other sage session and did: `sage: N = var('N') sage: k = var('k') sage: assume(k>0,k<1) sage: limit((6N^k(N-1)^(1-k))/((2N-1)(k+1)),N=oo)` But I got: ValueError Traceback (most recent call last) <ipython-input-4-bb63a0377d1b> in <module>() ----> 1 limit((Integer(6)Nk(N-Integer(1))*(Integer(1)-k))/((Integer(2)N-Integer(1))(k+Integer(1))),N=oo) /usr/lib/sagemath/local/lib/python2.7/site-packages/sage/calculus/calculus.pyc in limit(ex, dir, taylor, algorithm, argv) 1198 if algorithm == 'maxima': 1199 if dir is None: -> 1200 l = maxima.sr_limit(ex, v, a) 1201 elif dir in ['plus', '+', 'right', 'above']: 1202 if dir == 'above': /usr/lib/sagemath/local/lib/python2.7/site-packages/sage/interfaces/maxima_lib.py in sr_limit(self, expr, v, a, dir) 855 j = s.find('Is ') 856 s = s[j:] --> 857 raise ValueError, "Computation failed since Maxima requested additional constraints; using the 'assume' command before limit evaluation may* help (see `assume?` for more details)\n" + s 858 else: 859 raise error ValueError: Computation failed since Maxima requested additional constraints; using the 'assume' command before limit evaluation may help (see `assume?` for more details) Is k an integer? Trying to do `sage: assume(k ...` (more)
2014-11-04 17:57:39 +0200	received badge	● Scholar (source)
2014-11-03 20:29:44 +0200	commented answer	Sage doesn't show limit of ratio of sums I see...well, I'll have to wait then. Simulations are good enough anyways to actually see the limiting value!
2014-11-02 23:23:58 +0200	asked a question	Sage doesn't show limit of ratio of sums Hi everyone, I'm new to Sage and I'm trying to obtain the following limit: $$\lim_{N\to \infty}\frac{\sum_{i=1}^{N} x_i^{5/2}}{\sum_{i=1}^N x_i^2}$$ with $x_i=(N-i)/(N-1)$. What I tried was: `i = var('i') assume(i>0,'integer') N = var('N') assume(N>0,'integer') x_i = (N-i)/(N-1) numerator = sum(x_i^(5./2.),i,1,N) denominator = sum(x_i^(2.),i,1,N) limit(numerator/denominator,N=oo)` However, this just gives me: `6limit((N - 1)sum(((N - i)/(N - 1))^2.5, i, 1, N)/(2*N^2 - N), N, +Infinity)` From what I can see, Sage has no problems with the denominator, the general formula of which was obtained easily. However, apparently it has problems obtaining the general formula for the numerator due to the fact that the exponent in the sum is not an integer. Is there a way to cope with this? How can I obtain the limit? Thanks in advance for all the help!