Nice, I didn't know about .derivative(). For calculus presented in the tutorial (http://modular.math.washington.edu/sage/doc/html/tut/ node22.html) you do everything in Maxima calls/functions. An explanation in the tutorial (and as a google group posting as I have an assignment due tomorrow!) of the options and trade-offs for performing calculus computations would be helpful.
I'm doing density estimation right now for a statistics/probability class which involves maximizing log-likelihood formulas. I would be happy to provide material for a short tutorial on how to do this as I learn it myself. Perhaps first we could show how to estimate the single parameter of an exponential density, then showing how to estimate the 2 parameters of a normal density using partial derivatives, and finally show how to estimate the 2 parameters of a logistic density using gradient ascent (we were told that maximizing the system of equations resulting from taking the partial derivatives of the logistic log-likelihood formula is a problem that cannot be solved analytically, so we're doing this iterative estimation method). What do you think, and by the way, do you have a solve() method for finding function maxima? Brian On May 7, 10:09 am, William Stein <[EMAIL PROTECTED]> wrote: > On Monday 07 May 2007 10:11 am, Brian Harris wrote: > > > Thanks for the scatter plot pointers. For question 2, imagine > > something like: > > f(x) = 5 * SUM(1<i<10, x^i) > > Probably not standard sum notation, but I hope it's clear. Now I want > > to use SAGE to compute f'(x). > > This doesn't help you today, but in SAGE-2.5 (which will be much > more aimed at Calculus use), which will be released this week, > you'll be able to do this: > > sage: f = 5*sum(x^i for i in range(1,10)); f > 5*(x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x) > sage: f.derivative() > 5*(9*x^8 + 8*x^7 + 7*x^6 + 6*x^5 + 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1) > > Actually, the above would also work in sage-2.4, but would > have slightly different output. > > Maybe you could send some more complicated examples along these > lines that you're interested in. They are useful to us, since > we can add them as examples in the reference manual and/or > tutorial. > > william > > > > > On May 6, 9:04 pm, Marshall Hampton <[EMAIL PROTECTED]> wrote: > > > I'm not completely sure what you mean for your question 2 - can you > > > give an example? > > > > For your first question, if you have a tuple of 2D data called 'data', > > > then in the notebook you can do > > > > show(point(data)) > > > > and you get a scatterplot. In the reference manual under 2D-plotting > > > there is more information on graphics primitives, such as adding > > > colors (http://modular.math.washington.edu/sage/doc/html/ref/module- > > > sage.plot.plot.html). > > > > There is also a list_plot command, so you can do > > > > show(list_plot(data)) > > > > to a list of data points; this has a 'plotjoined' option. > > > > Hopefully that helps. I am not a SAGE guru, so there may be other > > > nice options as well. > > > > -M.Hampton > > > > On May 6, 2:49 pm, Brian <[EMAIL PROTECTED]> wrote: > > > > 1. How do you do scatter plots in SAGE, without using an interface to > > > > underlying commercial software like MATLAB? > > > > > 2. Can maxima or another tool compute [partial] derivatives or > > > > integrals containing arithmetic sums or products? > > -- > William Stein > Associate Professor of Mathematics > University of Washington --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
