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20210127 18:33:09 +0100  marked best answer  Factoring expression involving exponentials I've got a complicated expression, which looks like: e(4ik+3iω+ip)−e(4ik+2iω+2ip)−e(4ik+2iω)+e(4ik+iω+ip)+2e(2ik+4iω+ip)−e(2ik+3iω+2ip)−e(2ik+3iω) + ... How would you do to factor the exponentials with the same power of k, i.e. e(4ik)(...) + e(2ik)(...) and so on? 
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20181203 17:46:47 +0100  marked best answer  Substitution of several variables Let $f=f(x_1(t),x_2(t))$ be defined as follows: $f = x_1(t)  \mu x_1(t)^2 x_2(t)$. Now, I need to to substitute the term containing $x_1^2(t) x_2(t)$ in $f$ by some new auxiliary variable $x_3(t)$, that is, to obtain $f = x_1(t)  \mu x_3(t) $. However, this code doesn't work: Some ideas? Thanks. This code is motivated by symbolic manipulation with ODEs (think of $f$ as being the righthand side term in the autonomous ODE system $\dot{x}(t) = f(x(t))$ ). 
20181107 19:40:18 +0100  commented answer  finding general term of a sequence For the OP: Sage ships with the command 
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20180930 00:49:46 +0100  commented question  solving an iterated optimization problem

20180920 13:17:38 +0100  commented answer  div, grad and curl once again I couldn't resist to comment that the vector calculus example notebooks are delightful! 
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20180917 21:23:22 +0100  marked best answer  Computing polyhedron from MIP I want to run the following code (I'm using SAGE v6.10 release version 20151218): However, it outputs the error message:
I noticed that if instead of using real variables I use only integer variables, then it works fine. For instance: outputs:
What do you suggest to overcome this problem? Thanks 
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20180327 20:48:55 +0100  commented answer  Bug in general power of a matrix Thanks for finding and fixing the bug. Feel free to CC me when you create the ticket. 
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20171123 16:28:19 +0100  answered a question  Numerical approximation of multiple integral For numerical integrals in Sage, use numerical_integral. The function integrate is more appropriate for symbolic integration. With your example: The first component is the value of the integral, and the second component is an error estimate. As far as i'm aware, Sage does not expose a multidimensional numerical integration function. This can be worked around by a nested call to 
20171120 00:44:52 +0100  answered a question  Scatter search optimisation
Check those provided by SciPy's optimization and root finding library. All of them are available through the Sage interpreter by calling the appropriate In some (but not all) cases, Sage provides an interface to these algorithms, so that you can directly use Sage symbolic functions as arguments. It is worth mentioning that "out there" you'll find dozens of Python libraries for mathematical optimization (*). Notice that standard Python packages can be installed with the terminal command
and if the installation goes well, it is available the next time you start Sage via (*) See eg.: 
20171118 11:06:19 +0100  commented question  command to get eigenvalues this is of course not great  to post the same question in several places at the very same time! , but i grant the OP that there is no way to know in advance that roughly the same people are reading both lists: just checked the FAQ and the HELP of this site, and i see no references to the googlegroups lists. 
20171116 22:31:40 +0100  commented question  how to create a matrix valued function? actually i also expect that evaluating the symbolic matrix should be available (which currently isn't, as you've shown), in the same way that it works for scalar functions, 
20171115 11:26:15 +0100  commented answer  Problem evaluating a very tiny integral ok, i see. since Arb is already in C there could be some Cython wrapper for this library that can be used from Sage. 